FANDOM


(E100#^^#^###100 - E100#^^(#^#^7)100)
(E100#^^#^###100 - E100#^^(#^#^7)100)
(One intermediate revision by one user not shown)
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|E100#^^#^####10
 
|E100#^^#^####10
 
|\(f_{\varphi({\omega}^3 \times 10,0)}(100)\)
 
|\(f_{\varphi({\omega}^3 \times 10,0)}(100)\)
  +
|-
  +
|tethracubiquinquagintice (50,000,000)
  +
|E100#^^#^####50
  +
|\(f_{\varphi({\omega}^3 \times 50,0)}(100)\)
 
|-
 
|-
 
|(9594) tethraquarticutope (100,000,000)
 
|(9594) tethraquarticutope (100,000,000)
Line 4,312: Line 4,316:
 
|E100#^^(#^#^5)10
 
|E100#^^(#^#^5)10
 
|\(f_{\varphi({\omega}^4\times 10,0)}(100)\)
 
|\(f_{\varphi({\omega}^4\times 10,0)}(100)\)
  +
|-
  +
|tethraquarticutopoquinquagintice (5,000,000,000)
  +
|E100#^^(#^#^5)50
  +
|\(f_{\varphi({\omega}^4 \times 50,0)}(100)\)
  +
|-
  +
|(9605) tethraquinticutope (10^10)
  +
|E100#^^(#^#^5)100
  +
|\(f_{\varphi({\omega}^5,0)}(100)\)
  +
|-
  +
|tethraquinticutopothoth
  +
|E100#^^(#^#^5*#)100
  +
|\(f_{\varphi({\omega}^{5}+1,0)}(100)\)
  +
|-
  +
|tethraquinticutopotope
  +
|E100#^^(#^#^5*#^#)100
  +
|\(f_{\varphi({\omega}^{5}+\omega,0)}(100)\)
  +
|
  +
|-
  +
|(9606) tethraquinticutopoquarticutopocubitopolattitopotope
  +
|E100#^^(#^#^5*#^####*#^###*#^##*#^#)100
  +
|TBA
  +
|-
  +
|(9607) tethraquinticutopodeus
  +
|E100#^^(#^#^5*#^#^5)100
  +
|\(f_{\varphi({\omega}^{5}\times 2,0)}(100)\)
  +
|-
  +
|(9608) tethraquinticutopotruce
  +
|E100#^^(#^#^5*#^#^5*#^#^5)100
  +
|\(f_{\varphi({\omega}^{5}\times 3,0)}(100)\)
  +
|-
  +
|(9609) tethraquinticutopoquad
  +
|E100#^^(#^#^5*#^#^5*#^#^5*#^#^5)100
  +
= E100#^^(#^#^6)4
  +
|\(f_{\varphi({\omega}^{5}\times 4,0)}(100)\)
  +
|-
  +
|(9610) tethraquinticutopoquid
  +
|E100#^^(#^#^6)5
  +
|\(f_{\varphi({\omega}^{5}\times 5,0)}(100)\)
  +
|-
  +
|(9611) tethraquinticutoposid
  +
|E100#^^(#^#^6)6
  +
|\(f_{\varphi({\omega}^{5}\times 6,0)}(100)\)
  +
|-
  +
|(9612) tethraquinticutoposeptuce
  +
|E100#^^(#^#^6)7
  +
|\(f_{\varphi({\omega}^{5}\times 7,0)}(100)\)
  +
|-
  +
|(9613) tethraquinticutopo-octuce
  +
|E100#^^(#^#^6)8
  +
|\(f_{\varphi({\omega}^{5}\times 8,0)}(100)\)
  +
|-
  +
|(9614) tethraquinticutopononuce
  +
|E100#^^(#^#^6)9
  +
|\(f_{\varphi({\omega}^{5}\times 9,0)}(100)\)
  +
|-
  +
|(9615) tethraquinticutopodecuce (10^11)
  +
|E100#^^(#^#^6)10
  +
|\(f_{\varphi({\omega}^{5}\times 10,0)}(100)\)
  +
|-
  +
|dustaculated tethraquinticutopodecuce
  +
|E100#^^(#^#^(6)10>#^#^(6)10)100
  +
|\(f_{\varphi({\omega}^{5}\times 10,\varphi({\omega}^{5}\times 10,0))}(100)\)
  +
|-
  +
|tethraquinticutopodecucithoth
  +
|E100#^^(#^#^(6)10*#)100
  +
|\(f_{\varphi({\omega}^{5}\times 10 + 1,0)}(100)\)
  +
|-
  +
|tethraquinticutopodecucitope
  +
|E100#^^(#^#^(6)10*#^#)100
  +
|\(f_{\varphi({\omega}^{5}\times 10 + \omega,0)}(100)\)
  +
|-
  +
|(9616) tethrasexticutope (10^12)
  +
|E100#^^(#^#^6)100
  +
|\(f_{\varphi({\omega}^{6},0)}(100)\)
  +
|-
  +
|(9617) tethrasexticutopo-quinticutopoquarticutopocubitopolattitopotope
  +
|E100#^^(#^#^6*#^#^5*#^####*#^###*#^##*#^#)100
  +
|TBA
  +
|-
  +
|(9618) tethrasexticutopodeus
  +
|E100#^^(#^#^6*#^#^6)100
  +
|\(f_{\varphi({\omega}^{6}\times 2,0)}(100)\)
  +
|-
  +
|(9619) tethrasexticutopotruce
  +
|E100#^^(#^#^6*#^#^6*#^#^6)100
  +
|\(f_{\varphi({\omega}^{6}\times 3,0)}(100)\)
  +
|-
  +
|(9620) tethrasexticutopoquad
  +
|E100#^^(#^#^6*#^#^6*#^#^6*#^#^6)100
  +
  +
= E100#^^(#^#^7)4
  +
|\(f_{\varphi({\omega}^{6}\times 4,0)}(100)\)
  +
|-
  +
|(9621) tethrasexticutopoquid
  +
|E100#^^(#^#^7)5
  +
|\(f_{\varphi({\omega}^{6}\times 5,0)}(100)\)
  +
|-
  +
|(9622) tethrasexticutoposid
  +
|E100#^^(#^#^7)6
  +
|\(f_{\varphi({\omega}^{6}\times 6,0)}(100)\)
  +
|-
  +
|(9623) tethrasexticutoposeptuce
  +
|E100#^^(#^#^7)7
  +
|\(f_{\varphi({\omega}^{6}\times 7,0)}(100)\)
  +
|-
  +
|(9624) tethrasexticutopo-octuce
  +
|E100#^^(#^#^7)8
  +
|\(f_{\varphi({\omega}^{6}\times 8,0)}(100)\)
  +
|-
  +
|(9625) tethrasexticutopononuce
  +
|E100#^^(#^#^7)9
  +
|\(f_{\varphi({\omega}^{6}\times 9,0)}(100)\)
  +
|-
  +
|(9626) tethrasexticutopodecuce (10^13)
  +
|E100#^^(#^#^7)10
  +
|\(f_{\varphi({\omega}^{6}\times 10,0)}(100)\)
 
|}
 
|}
 
WIP. Feel free to extend this series by adding more googolisms.
 
WIP. Feel free to extend this series by adding more googolisms.

Revision as of 14:52, January 16, 2020

Note: this article is a part of ExE generator of googologisms.

This article provides list of comprehensive googolisms listed in tethratope regiment, which coined using Extended Cascading-E Notation. And also, I'm going to add some of my own googolisms which is not available in original source. [1] The original source has 897 googolisms listed there.

So, let's begin.

Note: E100#^^#^#n = E100#^^#^(n)100

Numbers

Before E100#^^#^#(E100)

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9010) tethrahendekon (E100#^^#^#11) (has recursion level \(f_{\varphi(11,0)}(100)\))
(9011) tethradodekon (E100#^^#^#12) (has recursion level \(f_{\varphi(12,0)}(100)\))
(9012) tethratredekon (E100#^^#^#13) (has recursion level \(f_{\varphi(13,0)}(100)\))
(9013) tethraterdekon (E100#^^#^#14) (has recursion level \(f_{\varphi(14,0)}(100)\))
(9014) tethrapedekon (E100#^^#^#15) (has recursion level \(f_{\varphi(15,0)}(100)\))
(9015) tethra-exdekon (E100#^^#^#16) (has recursion level \(f_{\varphi(16,0)}(100)\))
(9016) tethra-epdekon (E100#^^#^#17) (has recursion level \(f_{\varphi(17,0)}(100)\))
(9017) tethra-ogdekon E100(#^^#^18)100 (has recursion level \(f_{\varphi(18,0)}(100)\))
(9018) tethra-enndekon E100(#^^#^19)100 (has recursion level \(f_{\varphi(19,0)}(100)\))
(9019) tethra-icoson E100(#^^#^20)100 (has recursion level \(f_{\varphi(20,0)}(100)\))
tethra-penicoson E100(#^^#^25)100 (has recursion level \(f_{\varphi(25,0)}(100)\))
tethra-hexicoson E100(#^^#^26)100 (has recursion level \(f_{\varphi(26,0)}(100)\))
tethra-hepticoson E100(#^^#^27)100 (has recursion level \(f_{\varphi(27,0)}(100)\))
tethra-octicoson E100(#^^#^28)100 (has recursion level \(f_{\varphi(28,0)}(100)\))
tethra-ennicoson E100(#^^#^29)100 (has recursion level \(f_{\varphi(29,0)}(100)\))
(9020) tethratrianton E100(#^^#^30)100 (has recursion level \(f_{\varphi(30,0)}(100)\))
(9021) tethrasaranton E100(#^^#^40)100 (has recursion level \(f_{\varphi(40,0)}(100)\))
(9022) tethrapeninton E100(#^^#^50)100 (has recursion level \(f_{\varphi(50,0)}(100)\))
(9023) tethra-exinton E100(#^^#^60)100 (has recursion level \(f_{\varphi(60,0)}(100)\))
(9024) tethra-ebdominton E100(#^^#^70)100 (has recursion level \(f_{\varphi(70,0)}(100)\))
(9025) tethra-ogdonton E100(#^^#^80)100 (has recursion level \(f_{\varphi(80,0)}(100)\))
(9026) tethra-eneninton E100(#^^#^90)100 (has recursion level \(f_{\varphi(90,0)}(100)\))
tethra-heneneninton E100(#^^#^91)100 (has recursion level \(f_{\varphi(91,0)}(100)\))
tethra-doeneninton E100(#^^#^92)100 (has recursion level \(f_{\varphi(92,0)}(100)\))
tethra-tre-eneninton E100(#^^#^93)100 (has recursion level \(f_{\varphi(93,0)}(100)\))
tethra-ter-eneninton E100(#^^#^94)100 (has recursion level \(f_{\varphi(94,0)}(100)\))
tethra-pent-eneninton E100(#^^#^95)100 (has recursion level \(f_{\varphi(95,0)}(100)\))
tethra-ex-eneninton E100(#^^#^96)100 (has recursion level \(f_{\varphi(96,0)}(100)\))
tethra-ep-eneninton E100(#^^#^97)100 (has recursion level \(f_{\varphi(97,0)}(100)\))
tethra-ogdeneninton E100(#^^#^98)100 (has recursion level \(f_{\varphi(98,0)}(100)\))
(9027) tethra-enneneninton E100(#^^#^99)100 (has recursion level \(f_{\varphi(99,0)}(100)\))
(9028) tethrahecton, (9062) tethratope or (9063) tethratopos E100(#^^#^100)100 = E100#^^#^#100 (has recursion level \(f_{\varphi(100,0)}(100) \approx f_{\varphi(\omega,0)}(100)\))
grand tethrahecton E100(#^^#^100)100#2 (has recursion level \(f_{\varphi(100,0)}^2(100)\))
grangol-carta-tethrahecton E100(#^^#^100)100#100 (has recursion level \(f_{\varphi(100,0) + 1}(100)\))
greagol-carta-tethrahecton E100(#^^#^100)100#100#100 (has recursion level \(f_{\varphi(100,0) + 2}(100)\))
gigangol-carta-tethrahecton E100(#^^#^100)100#100#100#100 (has recursion level \(f_{\varphi(100,0) + 3}(100)\))
gugold-carta-tethrahecton E100(#^^#^100)100##100 (has recursion level \(f_{\varphi(100,0) + \omega}(100)\))
throogol-carta-tethrahecton E100(#^^#^100)100###100 (has recursion level \(f_{\varphi(100,0) + \omega^2}(100)\))
tetroogol-carta-tethrahecton E100(#^^#^100)100####100 (has recursion level \(f_{\varphi(100,0) + \omega^3}(100)\))
pentoogol-carta-tethrahecton E100(#^^#^100)100#^(5)100 (has recursion level \(f_{\varphi(100,0) + \omega^4}(100)\))
godgahlah-carta-tethrahecton E100(#^^#^100)100#^#100 (has recursion level \(f_{\varphi(100,0) + \omega^{\omega}}(100)\))
godgathor-carta-tethrahecton E100(#^^#^100)100#^#^#100 (has recursion level \(f_{\varphi(100,0) + \omega^{\omega^{\omega}}}(100)\))
godtothol-carta-tethrahecton E100(#^^#^100)100#^#^#^#100 (has recursion level \(f_{\varphi(100,0) + \omega^{\omega^{\omega^{\omega}}}}(100)\))
godtertol-carta-tethrahecton E100(#^^#^100)100#^^#5 (has recursion level \(f_{\varphi(100,0) + \omega\uparrow\uparrow5}(100)\))
tethrathoth-carta-tethrahecton E100(#^^#^100)100#^^#100 (has recursion level \(f_{\varphi(100,0) + \varepsilon_{0}}(100)\))
tethracross-carta-tethrahecton E100(#^^#^100)100#^^##100 (has recursion level \(f_{\varphi(100,0) + \zeta_{0}}(100)\))
tethracubor-carta-tethrahecton E100(#^^#^100)100#^^###100 (has recursion level \(f_{\varphi(100,0) + \eta_{0}}(100)\))
tethrateron-carta-tethrahecton E100(#^^#^100)100#^^####100 (has recursion level \(f_{\varphi(100,0) + \varphi(4,0)}(100)\))
tethrapeton-carta-tethrahecton E100(#^^#^100)100#^^#^(5)100 (has recursion level \(f_{\varphi(100,0) + \varphi(5,0)}(100)\))
tethrahecton-by-deuteron E100(#^^#^100)100(#^^#^100)100 (has recursion level \(f_{\varphi(100,0) + \varphi(100,0)}(100)\))
grand tethrahecton-by-deuteron E100(#^^#^100)100(#^^#^100)100#2 (has recursion level \(f_{\varphi(100,0) + \varphi(100,0)}^2(100)\))
grangol carta tethrahecton-by-deuteron E100(#^^#^100)100(#^^#^100)100#100 (has recursion level \(f_{\varphi(100,0) + \varphi(100,0) + 1}(100)\))
godgahlah carta tethrahecton-by-deuteron E100(#^^#^100)100(#^^#^100)100#^#100 (has recursion level \(f_{\varphi(100,0) + \varphi(100,0) + \omega^{\omega}}(100)\))
tethrathoth carta tethrahecton-by-deuteron E100(#^^#^100)100(#^^#^100)100#^^#100 (has recursion level \(f_{\varphi(100,0) + \varphi(100,0) + \varepsilon_0}(100)\))
tethracross carta tethrahecton-by-deuteron E100(#^^#^100)100(#^^#^100)100#^^##100 (has recursion level \(f_{\varphi(100,0) + \varphi(100,0) + \zeta_0}(100)\))
tethracubor carta tethrahecton-by-deuteron E100(#^^#^100)100(#^^#^100)100#^^###100 (has recursion level \(f_{\varphi(100,0) + \varphi(100,0) + \eta_0}(100)\))
tethrahecton-by-triton E100(#^^#^100)100(#^^#^100)100(#^^#^100)100 (has recursion level \(f_{\varphi(100,0) + \varphi(100,0) + \varphi(100,0)}(100)\))
grand tethrahecton-by-triton E100(#^^#^100)100(#^^#^100)100(#^^#^100)100#2 (has recursion level \(f_{\varphi(100,0) + \varphi(100,0) + \varphi(100,0)}^2(100)\))
tethrahecton-by-teterton E100(#^^#^100)*#5 (has recursion level \(f_{\varphi(100,0) \times 4}(100)\))
tethrahecton-by-pepton E100(#^^#^100)*#6 (has recursion level \(f_{\varphi(100,0) \times 5}(100)\))
tethrahecton-by-exton E100(#^^#^100)*#7 (has recursion level \(f_{\varphi(100,0) \times 6}(100)\))
tethrahecton-by-epton E100(#^^#^100)*#8 (has recursion level \(f_{\varphi(100,0) \times 7}(100)\))
tethrahecton-by-ogdon E100(#^^#^100)*#9 (has recursion level \(f_{\varphi(100,0) \times 9}(100)\))
tethrahecton-by-enton E100(#^^#^100)*#10 (has recursion level \(f_{\varphi(100,0) \times 10}(100)\))
tethrahecton-by-dekaton E100(#^^#^100)*#11 (has recursion level \(f_{\varphi(100,0) \times 11}(100)\))
tethrahecton-by-hyperion E100(#^^#^100)*#100 (has recursion level \(f_{\varphi(100,0) \times \omega}(100)\))
tethrahecton-by-hyperion-by-deuteron E100(#^^#^100)*##2 (has recursion level \(f_{\varphi(100,0) \times \omega2}(100)\))
tethrahecton-by-hyperion-by-triton E100(#^^#^100)*##3 (has recursion level \(f_{\varphi(100,0) \times \omega3}(100)\))
tethrahecton-by-deuterhyperion E100(#^^#^100)100*##100 (has recursion level \(f_{\varphi(100,0) \times \omega^2}(100)\))
tethrahecton-by-tritohyperion E100(#^^#^100)*###100 (has recursion level \(f_{\varphi(100,0) \times \omega^3}(100)\))
tethrahecton-by-godgahlah E100(#^^#^100)*#^#100 (has recursion level \(f_{\varphi(100,0) \times \omega^{\omega}}(100)\))
tethrahecton-by-godgathor E100(#^^#^100)*#^#^#100 (has recursion level \(f_{\varphi(100,0) \times \omega^{\omega^{\omega}}}(100)\))
tethrahecton-by-godtothol E100(#^^#^100)*#^#^#^#100 (has recursion level \(f_{\varphi(100,0) \times \omega^{\omega^{\omega^{\omega}}}}(100)\))
tethrahecton-by-godtertol E100(#^^#^100)*#^^#5 (has recursion level \(f_{\varphi(100,0) \times \omega\uparrow\uparrow5}(100)\))
tethrahecton-by-tethrathoth E100(#^^#^100)*#^^#100 (has recursion level \(f_{\varphi(100,0) \times \varepsilon_0}(100)\))
tethrahecton-by-tethracross E100(#^^#^100)*#^^##100 (has recursion level \(f_{\varphi(100,0) \times \zeta_0}(100)\))
tethrahecton-by-tethracubor E100(#^^#^100)*#^^###100 (has recursion level \(f_{\varphi(100,0) \times \eta_0}(100)\))
tethrahecton-by-tethrateron E100(#^^#^100)*#^^####100 (has recursion level \(f_{\varphi(100,0) \times \varphi(4,0)}(100)\))
(9148) deutero tethrahecton E100(#^^#^100)*#^^#^(100)100 (has recursion level \(f_{\varphi(100,0)^2}(100)\))
trito tethrahecton E100(#^^#^100)*(#^^#^100)*(#^^#^100)100 (has recursion level \(f_{\varphi(100,0)^3}(100)\))
teterto-tethrahecton E100(#^^#^100)^#4 (has recursion level \(f_{\varphi(100,0)^4}(100)\))
pepto-tethrahecton E100(#^^#^100)^#5 (has recursion level \(f_{\varphi(100,0)^5}(100)\))
exto-tethrahecton E100(#^^#^100)^#6 (has recursion level \(f_{\varphi(100,0)^6}(100)\))
epto-tethrahecton E100(#^^#^100)^#7 (has recursion level \(f_{\varphi(100,0)^7}(100)\))
ogdo-tethrahecton E100(#^^#^100)^#8 (has recursion level \(f_{\varphi(100,0)^8}(100)\))
ento-tethrahecton E100(#^^#^100)^#9 (has recursion level \(f_{\varphi(100,0)^9}(100)\))
dekato-tethrahecton E100(#^^#^100)^#10 (has recursion level \(f_{\varphi(100,0)^{10}}(100)\))
tethrahectonifact E100(#^^#^100)^#100 (has recursion level \(f_{\varphi(100,0)^{\omega}}(100)\))
quadratatethrahecton E100(#^^#^100)^##100 (has recursion level \(f_{\varphi(100,0)^{\omega^{2}}}(100)\))
kubikutethrahecton E100(#^^#^100)^###100 (has recursion level \(f_{\varphi(100,0)^{\omega^{3}}}(100)\))
quarticutethrahecton E100(#^^#^100)^####100 (has recursion level \(f_{\varphi(100,0)^{\omega^{4}}}(100)\))
quinticutethrahecton E100(#^^#^100)^#^#5 (has recursion level \(f_{\varphi(100,0)^{\omega^{5}}}(100)\))
sexticutethrahecton E100(#^^#^100)^#^#6 (has recursion level \(f_{\varphi(100,0)^{\omega^{6}}}(100)\))
septicutethrahecton E100(#^^#^100)^#^#7 (has recursion level \(f_{\varphi(100,0)^{\omega^{7}}}(100)\))
octicutethrahecton E100(#^^#^100)^#^#8 (has recursion level \(f_{\varphi(100,0)^{\omega^{8}}}(100)\))
nonicutethrahecton E100(#^^#^100)^#^#9 (has recursion level \(f_{\varphi(100,0)^{\omega^{9}}}(100)\))
decicutethrahecton E100(#^^#^100)^#^#10 (has recursion level \(f_{\varphi(100,0)^{\omega^{10}}}(100)\))
godgahlah-ipso-tethrahecton E100(#^^#^100)^#^#100 (has recursion level \(f_{\varphi(100,0)^{\omega^{\omega}}}(100)\))
godgathor-ipso-tethrahecton E100(#^^#^100)^#^#^#100 (has recursion level \(f_{\varphi(100,0)^{\omega^{\omega^{\omega}}}}(100)\))
godtothol-ipso-tethrahecton E100(#^^#^100)^#^^#4 (has recursion level \(f_{\varphi(100,0)^{\omega↑↑4}}(100)\))
godtertol-ipso-tethrahecton E100(#^^#^100)^#^^#5 (has recursion level \(f_{\varphi(100,0)^{\omega↑↑5}}(100)\))
tethrathoth-ipso-tethrahecton E100(#^^#^100)^(#^^#)100 (has recursion level \(f_{\varphi(100,0)^{\varepsilon_{0}}}(100)\))
tethracross-ipso-tethrahecton E100(#^^#^100)^(#^^##)100 (has recursion level \(f_{\varphi(100,0)^{\zeta_{0}}}(100)\))
tethracubor-ipso-tethrahecton E100(#^^#^100)^(#^^###)100 (has recursion level \(f_{\varphi(100,0)^{\eta_{0}}}(100)\))
tethrateron-ipso-tethrahecton E100(#^^#^100)^(#^^#^4)100 (has recursion level \(f_{\varphi(100,0)^{\varphi(4,0)}}(100)\))
(9211) dutetrated tethrahecton E100(#^^#^100)^(#^^#^100)100 (has recursion level \(f_{\varphi(100,0)^{\varphi(100,0)}}(100)\))
tritetrated tethrahecton E100(#^^#^100)^(#^^#^100)^(#^^#^100)100 (has recursion level \(f_{\varphi(100,0)^{\varphi(100,0)^{\varphi(100,0)}}}(100)\))
quadratetrated tethrahecton E100(#^^#^100)^^#4 (has recursion level \(f_{\varphi(100,0)^{\varphi(100,0)^{\varphi(100,0)^{\varphi(100,0)}}}}(100)\))
quintatetrated tethrahecton E100(#^^#^100)^^#5 (has recursion level \(f_{\varphi(100,0)↑↑5}(100)\))
sextatetrated tethrahecton E100(#^^#^100)^^#6 (has recursion level \(f_{\varphi(100,0)↑↑6}(100)\))
septatetrated tethrahecton E100(#^^#^100)^^#7 (has recursion level \(f_{\varphi(100,0)↑↑7}(100)\))
octatetrated tethrahecton E100(#^^#^100)^^#8 (has recursion level \(f_{\varphi(100,0)↑↑8}(100)\))
nonatetrated tethrahecton E100(#^^#^100)^^#9 (has recursion level \(f_{\varphi(100,0)↑↑9}(100)\))
decatetrated tethrahecton E100(#^^#^100)^^#10 (has recursion level \(f_{\varphi(100,0)↑↑{10}}(100)\))
terrible tethrahecton E100(#^^#^100)^^#100 (has recursion level \(f_{\varepsilon_{\varphi(100,0) + 1}}(100)\))
territertethrahecton E100(#^^#^100)^^#>#100 (has recursion level \(f_{\varepsilon_{\varphi(100,0) + \omega}}(100)\))
dustaculated territethrahecton E100(#^^#^100)^^#>(#^^#^100)^^#100 (has recursion level \(f_{\varepsilon_{\varepsilon_{\varphi(100,0) + 1}}}(100)\))
terrisquared tethrahecton E100(#^^#^100)^^##100 (has recursion level \(f_{\zeta_{\varphi(100,0) + 1}}(100)\))
terricubed tethrahecton E100(#^^#^100)^^###100 (has recursion level \(f_{\eta_{\varphi(100,0) + 1}}(100)\))
territesserated tethrahecton E100(#^^#^100)^^####100 (has recursion level \(f_{\varphi(4,\varphi(100,0) + 1)}(100)\))
terripenterated tethrahecton E100(#^^#^100)^^#^(5)100 (has recursion level \(f_{\varphi(5,\varphi(100,0) + 1)}(100)\))
terrihexerated tethrahecton E100(#^^#^100)^^#^(6)100 (has recursion level \(f_{\varphi(6,\varphi(100,0) + 1)}(100)\))
terrihepterated tethrahecton E100(#^^#^100)^^#^(7)100 (has recursion level \(f_{\varphi(7,\varphi(100,0) + 1)}(100)\))
terriocterated tethrahecton E100(#^^#^100)^^#^(8)100 (has recursion level \(f_{\varphi(8,\varphi(100,0) + 1)}(100)\))
terriennerated tethrahecton E100(#^^#^100)^^#^(9)100 (has recursion level \(f_{\varphi(9,\varphi(100,0) + 1)}(100)\))
terridekerated tethrahecton E100(#^^#^100)^^#^(10)100 (has recursion level \(f_{\varphi(10,\varphi(100,0) + 1)}(100)\))
tethradeuterhecton E100(#^^#^100)^^#^(100)100 (has recursion level \(f_{\varphi(100,1)}(100)\))
tethratritohecton E100((#^^#^100)^^#^100)^^#^(100)100 (has recursion level \(f_{\varphi(100,2)}(100)\))
tethratetertohecton E100#^^#^(100)>#4 (has recursion level \(f_{\varphi(100,3)}(100)\))
tethrapeptohecton E100#^^#^(100)>#5 (has recursion level \(f_{\varphi(100,4)}(100)\))
tethraextohecton E100#^^#^(100)>#6 (has recursion level \(f_{\varphi(100,5)}(100)\))
tethraeptohecton E100#^^#^(100)>#7 (has recursion level \(f_{\varphi(100,6)}(100)\))
tethraogdohecton E100#^^#^(100)>#8 (has recursion level \(f_{\varphi(100,7)}(100)\))
tethraentohecton E100#^^#^(100)>#9 (has recursion level \(f_{\varphi(100,8)}(100)\))
tethradekatohecton E100#^^#^(100)>#10 (has recursion level \(f_{\varphi(100,9)}(100)\))
tethriterhecton E100#^^#^(100)>#100 (has recursion level \(f_{\varphi(100,\omega)}(100)\))
deuterhyperion-turreted-tethrahecton E100#^^#^(100)>##100 (has recursion level \(f_{\varphi(100,\omega^2)}(100)\))
tritohyperion-turreted-tethrahecton E100#^^#^(100)>###100 (has recursion level \(f_{\varphi(100,\omega^3)}(100)\))
tetertohyperion-turreted-tethrahecton E100#^^#^(100)>####100 (has recursion level \(f_{\varphi(100,\omega^4)}(100)\))
peptohyperion-turreted-tethrahecton E100#^^#^(100)>#^#5 (has recursion level \(f_{\varphi(100,\omega^5)}(100)\))
godgahlah-turreted-tethrahecton E100#^^#^(100)>#^#100 (has recursion level \(f_{\varphi(100,\omega^{\omega})}(100)\))
godgathor-turreted-tethrahecton E100#^^#^(100)>#^#^#100 (has recursion level \(f_{\varphi(100,\omega^{\omega^{\omega}})}(100)\))
godtothol-turreted-tethrahecton E100#^^#^(100)>#^#^#^#100 (has recursion level \(f_{\varphi(100,\omega^{\omega^{\omega^{\omega}}})}(100)\))
tethrathoth-turreted-tethrahecton E100#^^#^(100)>#^^#100 (has recursion level \(f_{\varphi(100,\varepsilon_0)}(100)\))
tethracross-turreted-tethrahecton E100#^^#^(100)>#^^##100 (has recursion level \(f_{\varphi(100,\zeta_0)}(100)\))
tethracubor-turreted-tethrahecton E100#^^#^(100)>#^^###100 (has recursion level \(f_{\varphi(100,\eta_0)}(100)\))
tethrateron-turreted-tethrahecton E100#^^#^(100)>#^^####100 (has recursion level \(f_{\varphi(100,\varphi(4,0))}(100)\))
tethrapeton-turreted-tethrahecton E100#^^#^(100)>#^^#^(5)100 (has recursion level \(f_{\varphi(100,\varphi(5,0))}(100)\))
dustaculated-tethrahecton E100#^^#^(100)>#^^#^(100)100 (has recursion level \(f_{\varphi(100,\varphi(100,0))}(100)\))
tristaculated-tethrahecton E100#^^#^(100)>#^^#^(100)>#^^#^(100)100 (has recursion level \(f_{\varphi(100,\varphi(100,\varphi(100,0)))}(100)\))
tetrastaculated-tethrahecton E100#^^#^(100)>#^^#^(100)>#^^#^(100)>#^^#^(100)100 (has recursion level \(f_{\varphi(100,\varphi(100,\varphi(100,\varphi(100,0))))}(100)\))
pentastaculated-tethrahecton E100#^^#^(101)5 (has recursion level \(f_{\varphi(101,0)[4]}(100)\))
hexastaculated-tethrahecton E100#^^#^(101)6 (has recursion level \(f_{\varphi(101,0)[5]}(100)\))
heptastaculated-tethrahecton E100#^^#^(101)7 (has recursion level \(f_{\varphi(101,0)[6]}(100)\))
octastaculated-tethrahecton E100#^^#^(101)8 (has recursion level \(f_{\varphi(101,0)[7]}(100)\))
ennastaculated-tethrahecton E100#^^#^(101)9 (has recursion level \(f_{\varphi(101,0)[8]}(100)\))
dekastaculated-tethrahecton E100#^^#^(101)10 (has recursion level \(f_{\varphi(101,0)[9]}(100)\))
hecastaculated-tethrahecton or tethrahectothoth E100#^^#^(101)100 (has recursion level \(f_{\varphi(101,0)}(100)\))
tethrahectocross E100#^^#^(102)100 (has recursion level \(f_{\varphi(102,0)}(100)\))
tethrahectocubor E100#^^#^(103)100 (has recursion level \(f_{\varphi(103,0)}(100)\))
tethrahectoteron E100#^^#^(104)100 (has recursion level \(f_{\varphi(104,0)}(100)\))
tethrahectopeton E100#^^#^(105)100 (has recursion level \(f_{\varphi(105,0)}(100)\))
tethrahectohexon E100#^^#^(106)100 (has recursion level \(f_{\varphi(106,0)}(100)\))
tethrahectohepton E100#^^#^(107)100 (has recursion level \(f_{\varphi(107,0)}(100)\))
tethrahecto-ogdon E100#^^#^(108)100 (has recursion level \(f_{\varphi(108,0)}(100)\))
tethrahectennon E100#^^#^(109)100 (has recursion level \(f_{\varphi(109,0)}(100)\))
tethrahectodekon E100#^^#^(110)100 (has recursion level \(f_{\varphi(110,0)}(100)\))
tethrahecto-icoson E100#^^#^(120)100 (has recursion level \(f_{\varphi(120,0)}(100)\))
tethrahecto-trianton E100#^^#^(130)100 (has recursion level \(f_{\varphi(130,0)}(100)\))
tethrahecto-saranton E100#^^#^(140)100 (has recursion level \(f_{\varphi(140,0)}(100)\))
tethrahecto-peninton E100#^^#^(150)100 (has recursion level \(f_{\varphi(150,0)}(100)\))
tethrahecto-exinton E100#^^#^(160)100 (has recursion level \(f_{\varphi(160,0)}(100)\))
tethrahecto-ebdominton E100#^^#^(170)100 (has recursion level \(f_{\varphi(170,0)}(100)\))
tethrahecto-ogdonton E100#^^#^(180)100 (has recursion level \(f_{\varphi(180,0)}(100)\))
tethrahecto-eneninton E100#^^#^(190)100 (has recursion level \(f_{\varphi(190,0)}(100)\))
tethraduhecton E100#^^#^(200)100 (has recursion level \(f_{\varphi(200,0)}(100)\))
tethratrihecton E100#^^#^(300)100 = E100#^^#^#300 (has recursion level \(f_{\varphi(300,0)}(100) \approx f_{\varphi(\omega,0)}(300)\))
tethratetrahecton E100#^^#^#400 (has recursion level \(f_{\varphi(\omega,0)}(400)\))
tethrapentahecton E100#^^#^#500 (has recursion level \(f_{\varphi(\omega,0)}(500)\))
tethratopoding E500#^^#^#500 (has recursion level \(f_{\varphi(\omega,0)}(500)\))
tethrahexahecton E100#^^#^#600 (has recursion level \(f_{\varphi(\omega,0)}(600)\))
tethraheptahecton E100#^^#^#700 (has recursion level \(f_{\varphi(\omega,0)}(700)\))
tethraoctahecton E100#^^#^#800 (has recursion level \(f_{\varphi(\omega,0)}(800)\))
tethranonahecton E100#^^#^#900 (has recursion level \(f_{\varphi(\omega,0)}(900)\))
(9029) tethrachillion
(has recursion level \(f_{\varphi(\omega,0)}(1\,000)\))
tethratopochime E1000#^^#^#1000 (has recursion level \(f_{\varphi(\omega,0)}(1\,000)\))
tethratopobell E5000#^^#^#5000 (has recursion level \(f_{\varphi(\omega,0)}(5\,000)\))
(9030) tethramyrion E100#^^#^#10,000 (has recursion level \(f_{\varphi(\omega,0)}(10\,000)\))
tethratopotoll E10,000#^^#^#10,000 (has recursion level \(f_{\varphi(\omega,0)}(10\,000)\))
tethratoporing E50,000#^^#^#50,000 (has recursion level \(f_{\varphi(\omega,0)}(50\,000)\))
(9031) tethrahecatochillion E100#^^#^#100,000 (has recursion level \(f_{\varphi(\omega,0)}(100\,000)\))
tethratopogong E100,000#^^#^#100,000 (has recursion level \(f_{\varphi(\omega,0)}(100\,000)\))
tethratopoclang E500,000#^^#^#500,000 (has recursion level \(f_{\varphi(\omega,0)}(500\,000)\))
(9032) tethrahecatomyrion or tethramejon E100#^^#^#1,000,000 (has recursion level \(f_{\varphi(\omega,0)}(1\,000\,000)\))
(9033) tethrachilliomyrion E100#^^#^#10,000,000 (has recursion level \(f_{\varphi(\omega,0)}(10\,000\,000)\))
(9034) tethraoctadion E100#^^#^#100,000,000 (has recursion level \(f_{\varphi(\omega,0)}(100\,000\,000)\))
tethratopobong E(108)#^^#^#(108) (has recursion level \(f_{\varphi(\omega,0)}(100\,000\,000)\))
(9035) tethragijon E100#^^#^#1,000,000,000 (has recursion level \(f_{\varphi(\omega,0)}(1\,000\,000\,000)\))
tethratopothrong E(1011)#^^#^#(1011) (has recursion level \(f_{\varphi(\omega,0)}(10^{11})\))
(9036) tethra-aston E100#^^#^#E12 (has recursion level \(f_{\varphi(\omega,0)}(10^{12})\))
(9037) tethralunon E100(#^^#^1,000,000,000,000,000)100 = E100#^^#^#E15 (has recursion level \(f_{\varphi(\omega,0)}(10^{15})\))
(9038) tethrasedenion or (9039) tethrasedenionicor E100#^^#^#E16 = E100(#^^#^10,000,000,000,000,000)100 (has recursion level \(f_{\varphi(\omega,0)}(10^{16})\))
(9040) tethrafirmon E100#^^#^#E18 = E100(#^^#^1,000,000,000,000,000,000)100 (has recursion level \(f_{\varphi(\omega,0)}(10^{18})\))
(9041) tethrajovon E100#^^#^#E21 = E100#^^#^(E21)100 (has recursion level \(f_{\varphi(\omega,0)}(10^{21})\))
(9042) tethrasolon E100#^^#^#E24 = E100#^^#^(E24)100 (has recursion level \(f_{\varphi(\omega,0)}(10^{24})\))
(9043) tethrabeton E100#^^#^#E27 = E100#^^#^(E27)100 (has recursion level \(f_{\varphi(\omega,0)}(10^{27})\))
(9044) tethraglocon E100#^^#^#E30 = E100#^^#^(E30)100 (has recursion level \(f_{\varphi(\omega,0)}(10^{30})\))
(9045) tethragaxon E100#^^#^#E33 = E100#^^#^(E33)100 (has recursion level \(f_{\varphi(\omega,0)}(10^{33})\))
(9046) tethrasupon E100#^^#^#E36 = E100#^^#^(E36)100 (has recursion level \(f_{\varphi(\omega,0)}(10^{36})\))
(9047) tethraverson E100#^^#^#E39 = E100#^^#^(E39)100 (has recursion level \(f_{\varphi(\omega,0)}(10^{39})\))
(9048) tethramulton E100#^^#^#E42 = E100#^^#^(E42)100 (has recursion level \(f_{\varphi(\omega,0)}(10^{42})\))

E100#^^#^#(E100) - E100#^^#^#100#100

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9049) tethra-googolope E100#^^#^(E100)100 \(f_{\varphi(\omega,0)}(10^{100})\)
(9050) tethragrangolope E100#^^#^(E100#100)100 \(f_{\varphi(\omega,0)}(f_{3}(100))\)
tethragugoldope E100#^^#^(E100##100)100 \(f_{\varphi(\omega,0)}(f_{\omega}(100))\)
(9051) tethragodgahlope E100#^^#^(E100#^#100)100 \(f_{\varphi(\omega,0)}(f_{\omega^{\omega}}(100))\)
(9052) tethra-tethrathothope or gigantic tethrathoth E100#^^#^(E100#^^#100)100 \(f_{\varphi(\omega,0)}(f_{\varepsilon_0}(100))\)
tethra-tethraduliath-ope E100#^^#^(E100(#^^#)^(#^^#)100)100 \(f_{\varphi(\omega,0)}(f_{\varepsilon_0^{\varepsilon_0}}(100))\)
tethra-Monster-Giant-ope E100#^^#^(E100(#^^#)^(#^^#)^#100)100 \(f_{\varphi(\omega,0)}(f_{\varepsilon_0^{\varepsilon_0^{\omega}}}(100))\)
tethra-territethrathothope E100#^^#^(E100(#^^#)^^#100)100 \(f_{\varphi(\omega,0)}(f_{\varepsilon_1}(100))\)
tethra-Behemoth-Giant-ope E100#^^#^(E100(#^^#>2)^(#^^#>2)^#100)100 \(f_{\varphi(\omega,0)}(f_{\varepsilon_1^{\varepsilon_1^{\omega}}}(100))\)
tethra-territerritethrathothope E100#^^#^(E100((#^^#)^^#)^^#100)100 \(f_{\varphi(\omega,0)}(f_{\varepsilon_2}(100))\)
tethra-Trihemoth-Giant-ope E100#^^#^(E100(#^^#>3)^(#^^#>3)^#100)100 \(f_{\varphi(\omega,0)}(f_{\varepsilon_2^{\varepsilon_2^{\omega}}}(100))\)
tethra-tethriteratorope E100#^^#^(E100#^^#>#100)100 \(f_{\varphi(\omega,0)}(f_{\varepsilon_\omega}(100))\)
tethra-dustacultethrathothope E100#^^#^(E100#^^#>#^^#100)100 \(f_{\varphi(\omega,0)}(f_{\varepsilon_{\varepsilon_0}}(100))\)
(9053) tethra-tethracrossope or gigantic tethracross E100#^^#^(E100#^^##100)100 \(f_{\varphi(\omega,0)}(f_{\zeta_0}(100))\)
(9054) tethra-tethracuborope or gigantic tethracubor E100#^^#^(E100#^^###100)100 \(f_{\varphi(\omega,0)}(f_{\eta_0}(100))\)
(9055) tethra-tethrateronope or gigantic tethrateron E100#^^#^(E100#^^####100)100 \(f_{\varphi(\omega,0)}(f_{\varphi(4,0)}(100))\)
(9056) tethra-tethrapetonope or gigantic tethrapeton E100#^^#^#(E100#^^#^#5) \(f_{\varphi(\omega,0)}(f_{\varphi(5,0)}(100))\)
(9057) tethra-tethrahexonope or gigantic tethrahexon E100#^^#^#(E100#^^#^#6) \(f_{\varphi(\omega,0)}(f_{\varphi(6,0)}(100))\)
(9058) tethra-tethraheptonope or gigantic tethrahepton E100#^^#^#7#2 = E100#^^#^#(E100#^^#^#7) \(f_{\varphi(\omega,0)}(f_{\varphi(7,0)}(100))\)
(9059) tethra-tethra-ogdonope or gigantic tethra-ogdon E100#^^#^#8#2 = E100#^^#^#(E100#^^#^#8) \(f_{\varphi(\omega,0)}(f_{\varphi(8,0)}(100))\)
(9060) tethra-tethrennonope or gigantic tethrennon E100#^^#^#9#2 = E100#^^#^#(E100#^^#^#9) \(f_{\varphi(\omega,0)}(f_{\varphi(9,0)}(100))\)
(9061) tethra-tethradekonope or gigantic tethradekon E100#^^#^#10#2 = E100#^^#^#(E100#^^#^#10) \(f_{\varphi(\omega,0)}(f_{\varphi(10,0)}(100))\)
tethra-tethra-icosonope or gigantic tethra-icoson E100#^^#^#20#2 = E100#^^#^#(E100#^^#^#20) \(f_{\varphi(\omega,0)}(f_{\varphi(20,0)}(100))\)
tethra-tethra-triantonope or gigantic tethratrianton E100#^^#^#30#2 = E100#^^#^#(E100#^^#^#30) \(f_{\varphi(\omega,0)}(f_{\varphi(30,0)}(100))\)
tethra-tethra-sarantonope or gigantic tethrasaranton E100#^^#^#40#2 = E100#^^#^#(E100#^^#^#40) \(f_{\varphi(\omega,0)}(f_{\varphi(40,0)}(100))\)
tethra-tethra-penintonope or gigantic tethrapeninton E100#^^#^#50#2 = E100#^^#^#(E100#^^#^#50) \(f_{\varphi(\omega,0)}(f_{\varphi(50,0)}(100))\)
tethra-tethra-exintonope or gigantic tethraexinton E100#^^#^#60#2 = E100#^^#^#(E100#^^#^#60) \(f_{\varphi(\omega,0)}(f_{\varphi(60,0)}(100))\)
tethra-tethra-ebdomintonope or gigantic tethraebdominton E100#^^#^#70#2 = E100#^^#^#(E100#^^#^#70) \(f_{\varphi(\omega,0)}(f_{\varphi(70,0)}(100))\)
tethra-tethra-ogdontonope or gigantic tethraogdonton E100#^^#^#80#2 = E100#^^#^#(E100#^^#^#80) \(f_{\varphi(\omega,0)}(f_{\varphi(80,0)}(100))\)
tethra-tethra-enenintonope or gigantic tethraeneninton E100#^^#^#90#2 = E100#^^#^#(E100#^^#^#90) \(f_{\varphi(\omega,0)}(f_{\varphi(90,0)}(100))\)
(9064) grand tethratope or gigantic tethrahecton E100#^^#^#100#2 \(f_{\varphi(\omega,0)}(f_{\varphi(100,0)}(100))\)
grand tethratopochime E1000#^^#^#1000#2 \(f_{\varphi(\omega,0)}^2(1\,000)\)
grand tethratopotoll E10,000#^^#^#10,000#2 \(f_{\varphi(\omega,0)}^2(10\,000)\)
grand tethratopogong E100,000#^^#^#100,000#2 \(f_{\varphi(\omega,0)}^2(100\,000)\)
(9065) grand grand tethratope E100#^^#^#100#3 \(f_{\varphi(\omega,0)}^3(100)\)
(9066) grand grand grand tethratope E100#^^#^#100#4 \(f_{\varphi(\omega,0)}^4(100)\)
(9067) grand grand grand grand tethratope E100#^^#^#100#5 \(f_{\varphi(\omega,0)}^5(100)\)
(9068) grand grand grand grand grand tethratope (five-ex-grand-tethratope) E100#^^#^#100#6 \(f_{\varphi(\omega,0)}^6(100)\)
six-ex-grand-tethratope E100#^^#^#100#7 \(f_{\varphi(\omega,0)}^7(100)\)
seven-ex-grand-tethratope E100#^^#^#100#8 \(f_{\varphi(\omega,0)}^8(100)\)
eight-ex-grand-tethratope E100#^^#^#100#9 \(f_{\varphi(\omega,0)}^9(100)\)
nine-ex-grand-tethratope E100#^^#^#100#10 \(f_{\varphi(\omega,0)}^{10}(100)\)
ten-ex-grand-tethratope E100#^^#^#100#11 \(f_{\varphi(\omega,0)}^{11}(100)\)
twenty-ex-grand-tethratope E100#^^#^#100#21 \(f_{\varphi(\omega,0)}^{21}(100)\)
thirty-ex-grand-tethratope E100#^^#^#100#31 \(f_{\varphi(\omega,0)}^{31}(100)\)
forty-ex-grand-tethratope E100#^^#^#100#41 \(f_{\varphi(\omega,0)}^{41}(100)\)
fifty-ex-grand-tethratope E100#^^#^#100#51 \(f_{\varphi(\omega,0)}^{51}(100)\)
sixty-ex-grand-tethratope E100#^^#^#100#61 \(f_{\varphi(\omega,0)}^{61}(100)\)
seventy-ex-grand-tethratope E100#^^#^#100#71 \(f_{\varphi(\omega,0)}^{71}(100)\)
eighty-ex-grand-tethratope E100#^^#^#100#81 \(f_{\varphi(\omega,0)}^{81}(100)\)
ninety-ex-grand-tethratope E100#^^#^#100#91 \(f_{\varphi(\omega,0)}^{91}(100)\)

E100#^^#^#100#100 - E100#^^#^#*#3

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9069) grangol-carta-tethratope E100#^^#^#100#100 \(f_{\varphi(\omega,0)+1}(100)\)
hundred-ex-grand-tethratope E100#^^#^#100#101 \(f_{\varphi(\omega,0)+1}(101)\)
googol-ex-grand-tethratope E100#^^#^#100#(googol + 1) \(f_{\varphi(\omega,0)+1}(10^{100})\)
giggol-ex-grand-tethratope E100#^^#^#100#(giggol + 1) \(f_{\varphi(\omega,0)+1}(f_3(100))\)
grangol-ex-grand-tethratope E100#^^#^#100#(grangol + 1) \(f_{\varphi(\omega,0)+1}(f_3(100))\)
gaggol-ex-grand-tethratope E100#^^#^#100#(gaggol + 1) \(f_{\varphi(\omega,0)+1}(f_4(100))\)
greagol-ex-grand-tethratope E100#^^#^#100#(greagol + 1) \(f_{\varphi(\omega,0)+1}(f_4(100))\)
geegol-ex-grand-tethratope E100#^^#^#100#(geegol + 1) \(f_{\varphi(\omega,0)+1}(f_5(100))\)
gigangol-ex-grand-tethratope E100#^^#^#100#(gigangol + 1) \(f_{\varphi(\omega,0)+1}(f_5(100))\)
boogol-ex-grand-tethratope E100#^^#^#100#(boogol + 1) \(f_{\varphi(\omega,0)+1}(f_{\omega}(100))\)
gugold-ex-grand-tethratope E100#^^#^#100#(gugold + 1) \(f_{\varphi(\omega,0)+1}(f_{\omega}(100))\)
throogol-ex-grand-tethratope E100#^^#^#100#(throogol + 1) \(f_{\varphi(\omega,0)+1}(f_{\omega^{2}}(100))\)
troogol-ex-grand-tethratope E100#^^#^#100#(troogol + 1) \(f_{\varphi(\omega,0)+1}(f_{\omega^{2}}(100))\)
tetroogol-ex-grand-tethratope E100#^^#^#100#(tetroogol + 1) \(f_{\varphi(\omega,0)+1}(f_{\omega^{3}}(100))\)
quadroogol-ex-grand-tethratope E100#^^#^#100#(quadroogol + 1) \(f_{\varphi(\omega,0)+1}(f_{\omega^{3}}(100))\)
goobol-ex-grand-tethratope E100#^^#^#100#(goobol + 1) \(f_{\varphi(\omega,0)+1}(f_{\omega^{\omega}}(100))\)
godgahlah-ex-grand-tethratope E100#^^#^#100#(godgahlah + 1) \(f_{\varphi(\omega,0)+1}(f_{\omega^{\omega}}(100))\)
godgathor-ex-grand-tethratope E100#^^#^#100#(godgathor + 1) \(f_{\varphi(\omega,0)+1}(f_{\omega^{\omega^{\omega}}}(100))\)
godtothol-ex-grand-tethratope E100#^^#^#100#(E100#^#^#^#100+1) \(f_{\varphi(\omega,0)+1}(f_{\omega^{\omega^{\omega^{\omega}}}}(100))\)
godtertol-ex-grand-tethratope E100#^^#^#100#(E100#^^#5+1) \(f_{\varphi(\omega,0)+1}(f_{\omega↑↑5}(100))\)
tethrathoth-ex-grand-tethratope E100#^^#^#100#(E100#^^#100+1) \(f_{\varphi(\omega,0)+1}(f_{\varepsilon_0}(100))\)
tethracross-ex-grand-tethratope E100#^^#^#100#(E100#^^##100+1) \(f_{\varphi(\omega,0)+1}(f_{\zeta_0}(100))\)
tethracubor-ex-grand-tethratope E100#^^#^#100#(E100#^^###100+1) \(f_{\varphi(\omega,0)+1}(f_{\eta_0}(100))\)
tethrateron-ex-grand-tethratope E100#^^#^#100#(E100#^^####100+1) \(f_{\varphi(\omega,0)+1}(f_{\varphi(4,0)}(100))\)
tethrapeton-ex-grand-tethratope E100#^^#^#100#(E100#^^(#^5)100+1) \(f_{\varphi(\omega,0)+1}(f_{\varphi(5,0)}(100))\)
tethrahexon-ex-grand-tethratope E100#^^#^#100#(E100#^^(#^6)100+1) \(f_{\varphi(\omega,0)+1}(f_{\varphi(6,0)}(100))\)
tethrahepton-ex-grand-tethratope E100#^^#^#100#(E100#^^(#^7)100+1) \(f_{\varphi(\omega,0)+1}(f_{\varphi(7,0)}(100))\)
tethra-ogdon-ex-grand-tethratope E100#^^#^#100#(E100#^^(#^8)100+1) \(f_{\varphi(\omega,0)+1}(f_{\varphi(8,0)}(100))\)
tethrennon-ex-grand-tethratope E100#^^#^#100#(E100#^^(#^9)100+1) \(f_{\varphi(\omega,0)+1}(f_{\varphi(9,0)}(100))\)
tethradekon-ex-grand-tethratope E100#^^#^#100#(E100#^^(#^10)100+1) \(f_{\varphi(\omega,0)+1}(f_{\varphi(10,0)}(100))\)
tethratope-minus-one-ex-grand-tethratope E100#^^#^#100#1#2 \(f_{\varphi(\omega,0)+1}(f_{\varphi(\omega,0)}(100))\)
tethratope-ex-grand-tethratope E100#^^#^#100#(E100#^^#^#100+1) \(f_{\varphi(\omega,0)+1}(f_{\varphi(\omega,0)}(100))\)
grand grangol-carta-tethratope E100#^^#^#100#100#2 \(f_{\varphi(\omega,0)+1}^2(100)\)
(9070) greagol-carta-tethratope E100#^^#^#100#100#100 \(f_{\varphi(\omega,0)+2}(100)\)
(9071) gigangol-carta-tethratope E100#^^#^#100#100#100#100 \(f_{\varphi(\omega,0)+3}(100)\)
gorgegol-carta-tethratope E100#^^#^#100##5 \(f_{\varphi(\omega,0)+4}(100)\)
(9072) gugold-carta-tethratope E100#^^#^#100##100 \(f_{\varphi(\omega,0)+\omega}(100)\)
gugolthra-carta-tethratope E100#^^#^#100##100##100 \(f_{\varphi(\omega,0)+\omega2}(100)\)
gugoltesla-carta-tethratope E100#^^#^#100##100##100##100 \(f_{\varphi(\omega,0)+\omega3}(100)\)
gugolpeta-carta-tethratope E100#^^#^#100###5 \(f_{\varphi(\omega,0)+\omega4}(100)\)
(9073) throogol-carta-tethratope E100#^^#^#100###100 \(f_{\varphi(\omega,0)+\omega^{2}}(100)\)
(9074) tetroogol-carta-tethratope E100#^^#^#100####100 \(f_{\varphi(\omega,0)+\omega^{3}}(100)\)
pentoogol-carta-tethratope E100#^^#^#100#^(5)100 \(f_{\varphi(\omega,0)+\omega^{4}}(100)\)
(9075) godgahlah-carta-tethratope E100#^^#^#100#^#100 \(f_{\varphi(\omega,0)+\omega^{\omega}}(100)\)
gridgahlah-carta-tethratope E100#^^#^#100#^##100 \(f_{\varphi(\omega,0)+\omega^{\omega^{2}}}(100)\)
kubikahlah-carta-tethratope E100#^^#^#100#^###100 \(f_{\varphi(\omega,0)+\omega^{\omega^{3}}}(100)\)
quarticahlah-carta-tethratope E100#^^#^#100#^####100 \(f_{\varphi(\omega,0)+\omega^{\omega^{4}}}(100)\)
(9076) godgathor-carta-tethratope E100#^^#^#100#^#^#100 \(f_{\varphi(\omega,0)+\omega^{\omega^{\omega}}}(100)\)
(9077) godtothol-carta-tethratope E100#^^#^#100#^#^#^#100 \(f_{\varphi(\omega,0)+\omega^{\omega^{\omega^{\omega}}}}(100)\)
godtertol-carta-tethratope E100#^^#^#100#^^#5 \(f_{\varphi(\omega,0)+\omega\uparrow\uparrow5}(100)\)
(9078) tethrathoth-carta-tethratope E100#^^#^#100#^^#100 \(f_{\varphi(\omega,0)+\varepsilon_{0}}(100)\)
(9079) Monster-Giant-carta-tethratope E100#^^#^#100(#^^#)^(#^^#)^#100 \(f_{\varphi(\omega,0)+{\varepsilon_{0}^{\varepsilon_{0}^{\omega}}}}(100)\)
(9080) territethrathoth-carta-tethratope E100#^^#^#100(#^^#)^^#100 \(f_{\varphi(\omega,0)+\varepsilon_{1}}(100)\)
(9081) Behemoth-Giant-carta-tethratope E100#^^#^#100(#^^#>2)^(#^^#>2)^#100 \(f_{\varphi(\omega,0)+{\varepsilon_{1}^{\varepsilon_{1}^{\omega}}}}(100)\)
(9082) territerritethrathoth-carta-tethratope E100#^^#^#100((#^^#)^^#)^^#100 \(f_{\varphi(\omega,0)+\varepsilon_{2}}(100)\)
(9083) Trihemoth-Giant-carta-tethratope E100#^^#^#100(#^^#>3)^(#^^#>3)^#100 \(f_{\varphi(\omega,0)+{\varepsilon_{2}^{\varepsilon_{2}^{\omega}}}}(100)\)
territerriterritethrathoth-carta-tethratope E100#^^#^#100(((#^^#)^^#)^^#)^^#100 \(f_{\varphi(\omega,0)+\varepsilon_{3}}(100)\)
(9084) tethriterator-carta-tethratope E100#^^#^#100#^^#>#100 \(f_{\varphi(\omega,0)+\varepsilon_{\omega}}(100)\)
(9085) dustacultethrathoth-carta-tethratope E100#^^#^#100#^^#>#^^#100 \(f_{\varphi(\omega,0)+\varepsilon_{\varepsilon_{0}}}(100)\)
tristacultethrathoth-carta-tethratope E100#^^#^#100#^^#>#^^#>#^^#100 \(f_{\varphi(\omega,0)+\varepsilon_{\varepsilon_{\varepsilon_{0}}}}(100)\)
tetrastacultethrathoth-carta-tethratope E100#^^#^#100#^^##4 \(f_{\varphi(\omega,0)+\zeta_{0}[4]}(100)\)
(9086) tethracross-carta-tethratope E100#^^#^#100#^^##100 \(f_{\varphi(\omega,0)+\zeta_{0}}(100)\)
(9087) tethracubor-carta-tethratope E100#^^#^#100#^^###100 \(f_{\varphi(\omega,0)+\eta_{0}}(100)\)
(9088) tethrateron-carta-tethratope E100#^^#^#100#^^####100 \(f_{\varphi(\omega,0)+\varphi(4,0)}(100)\)
(9089) tethrapeton-carta-tethratope E100#^^#^#100(#^^#^5)100 \(f_{\varphi(\omega,0)+\varphi(5,0)}(100)\)
(9090) tethrahexon-carta-tethratope E100#^^#^#100(#^^#^6)100 \(f_{\varphi(\omega,0)+\varphi(6,0)}(100)\)
(9091) tethrahepton-carta-tethratope E100#^^#^#100(#^^#^7)100 \(f_{\varphi(\omega,0)+\varphi(7,0)}(100)\)
(9092) tethra-ogdon-carta-tethratope E100#^^#^#100(#^^#^8)100 \(f_{\varphi(\omega,0)+\varphi(8,0)}(100)\)
(9093) tethrennon-carta-tethratope E100#^^#^#100(#^^#^9)100 \(f_{\varphi(\omega,0)+\varphi(9,0)}(100)\)
(9094) tethradekon-carta-tehtratope E100#^^#^#100(#^^#^10)100 \(f_{\varphi(\omega,0)+\varphi(10,0)}(100)\)

E100#^^#^#*#3 - E100#^^#^#*#^^#^#100

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9095) tethratope-carta-tehtratope, (9097) tethratope-by-deuteron E100#^^#^#100#^^#^#100 \(f_{\varphi(\omega,0)+\varphi(\omega,0)}(100)\)
N/A E100#^^#^#100#^^#^(tethratope)100 \(f_{\varphi(\omega,0)+\varphi(\omega,0)}(f_{\varphi(\omega,0)}(100))\)
(9096) grand tethratope-carta-tethratope, grand tethratope-by-deuteron E100#^^#^#100#^^#^#100#2 = E100#^^#^#100#^^#^(tethratope-carta-tethratope)100 \(f_{\varphi(\omega,0)+\varphi(\omega,0)}^2(100)\)
grangol-carta-tethratope-carta-tethratope E100#^^#^#100#^^#^#100#100 \(f_{\varphi(\omega,0)+\varphi(\omega,0)+1}(100)\)
gugold-carta-tethratope-carta-tethratope E100#^^#^#100#^^#^#100##100 \(f_{\varphi(\omega,0)+\varphi(\omega,0)+\omega}(100)\)
godgahlah-carta-tethratope-carta-tethratope E100#^^#^#100#^^#^#100#^#100 \(f_{\varphi(\omega,0)+\varphi(\omega,0)+\omega^{\omega}}(100)\)
tethrathoth-carta-tethratope-carta-tethratope E100#^^#^#100#^^#^#100#^^#100 \(f_{\varphi(\omega,0)+\varphi(\omega,0)+\varepsilon_{0}}(100)\)
tethracross-carta-tethratope-carta-tethratope E100#^^#^#100#^^#^#100#^^##100 \(f_{\varphi(\omega,0)+\varphi(\omega,0)+\zeta_{0}}(100)\)
tethracubor-carta-tethratope-carta-tethratope E100#^^#^#100#^^#^#100#^^###100 \(f_{\varphi(\omega,0)+\varphi(\omega,0)+\eta_{0}}(100)\)
(9098) tethratope-by-triton E100#^^#^#100#^^#^#100#^^#^#100 \(f_{\varphi(\omega,0)3}(100)\)
(9099) grand tethratope-by-triton E100#^^#^#100#^^#^#100#^^#^#100#2 \(f_{\varphi(\omega,0)3}^2(100)\)
grangol-carta-tethratope-by-triton E100#^^#^#100#^^#^#100#^^#^#100#100 \(f_{\varphi(\omega,0)3+1}(100)\)
gugold-carta-tethratope-by-triton E100#^^#^#100#^^#^#100#^^#^#100##100 \(f_{\varphi(\omega,0)3+\omega}(100)\)
godgahlah-carta-tethratope-by-triton E100#^^#^#100#^^#^#100#^^#^#100#^#100 \(f_{\varphi(\omega,0)3+\omega^{\omega}}(100)\)
tethrathoth-carta-tethratope-by-triton E100#^^#^#100#^^#^#100#^^#^#100#^^#100 \(f_{\varphi(\omega,0)3+\varepsilon_0}(100)\)
tethracross-carta-tethratope-by-triton E100#^^#^#100#^^#^#100#^^#^#100#^^##100 \(f_{\varphi(\omega,0)3+\zeta_0}(100)\)
tethracubor-carta-tethratope-by-triton E100#^^#^#100#^^#^#100#^^#^#100#^^###100 \(f_{\varphi(\omega,0)3+\eta_0}(100)\)
(9100) tethratope-by-teterton E100#^^#^#*#5 \(f_{\varphi(\omega,0)4}(100)\)
(9101) tethratope-by-pepton E100#^^#^#*#6 \(f_{\varphi(\omega,0)5}(100)\)
(9102) tethratope-by-exton E100#^^#^#*#7 \(f_{\varphi(\omega,0)6}(100)\)
(9103) tethratope-by-epton E100#^^#^#*#8 \(f_{\varphi(\omega,0)7}(100)\)
(9104) tethratope-by-ogdon E100#^^#^#*#9 \(f_{\varphi(\omega,0)8}(100)\)
(9105) tethratope-by-enton E100#^^#^#*#10 \(f_{\varphi(\omega,0)9}(100)\)
(9106) tethratope-by-dekaton E100#^^#^#*#11 \(f_{\varphi(\omega,0)10}(100)\)
(9107) tethratope-by-hyperion E100#^^#^#*#100 \(f_{\varphi(\omega,0)\omega}(100)\)
(9108) tethratope-by-deutero-hyperion E100#^^#^#*##100 \(f_{\varphi(\omega,0)\omega^{2}}(100)\)
(9109) tethratope-by-trito-hyperion E100#^^#^#*###100 \(f_{\varphi(\omega,0)\omega^{3}}(100)\)
(9110) tethratope-by-teterto-hyperion E100#^^#^#*####100 \(f_{\varphi(\omega,0)\omega^{4}}(100)\)
(9111) tethratope-by-pepto-hyperion E100#^^#^#*#^#5 \(f_{\varphi(\omega,0)\omega^{5}}(100)\)
(9112) tethratope-by-exto-hyperion E100#^^#^#*#^#6 \(f_{\varphi(\omega,0)\omega^{6}}(100)\)
(9113) tethratope-by-epto-hyperion E100#^^#^#*#^#7 \(f_{\varphi(\omega,0)\omega^{7}}(100)\)
(9114) tethratope-by-ogdo-hyperion E100#^^#^#*#^#8 \(f_{\varphi(\omega,0)\omega^{8}}(100)\)
(9115) tethratope-by-ento-hyperion E100#^^#^#*#^#9 \(f_{\varphi(\omega,0)\omega^{9}}(100)\)
(9116) tethratope-by-dekato-hyperion E100#^^#^#*#^#10 \(f_{\varphi(\omega,0)\omega^{10}}(100)\)
(9117) tethratope-by-godgahlah E100#^^#^#*#^#100 \(f_{\varphi(\omega,0)\omega^{\omega}}(100)\)
(9118) tethratope-by-gridgahlah E100#^^#^#*#^##100 \(f_{\varphi(\omega,0)\omega^{\omega^{2}}}(100)\)
tethratope-by-kubikahlah E100#^^#^#*#^###100 \(f_{\varphi(\omega,0)\omega^{\omega^{3}}}(100)\)
tethratope-by-quarticahlah E100#^^#^#*#^####100 \(f_{\varphi(\omega,0)\omega^{\omega^{4}}}(100)\)
(9119) tethratope-by-godgathor E100#^^#^#*#^#^#100 \(f_{\varphi(\omega,0)\omega^{\omega^{\omega}}}(100)\)
(9120) tethratope-by-gralgathor E100#^^#^#*#^#^##100 \(f_{\varphi(\omega,0)\omega^{\omega^{\omega^{2}}}}(100)\)
(9121) tethratope-by-godtothol E100#^^#^#*#^#^#^#100 \(f_{\varphi(\omega,0)\omega^{\omega^{\omega^{\omega}}}}(100)\)
(9122) tethratope-by-godtertol E100#^^#^#*#^#^#^#^#100 \(f_{\varphi(\omega,0)\omega↑↑5}(100)\)
tethratope-by-godtopol E100#^^#^#*#^^#6 \(f_{\varphi(\omega,0)\omega↑↑6}(100)\)
(9123) tethratope-by-tethrathoth E100#^^#^#*#^^#100 \(f_{\varphi(\omega,0)\varepsilon_0}(100)\)
(9124) tethratope-by-Monster-Giant E100#^^#^#*(#^^#)^(#^^#)^#100 fφ(ω,0)ε0ε0ω(100)
(9125) tethratope-by-territethrathoth E100#^^#^#*(#^^#)^^#100 \(f_{\varphi(\omega,0)\varepsilon_1}(100)\)
(9126) tethratope-by-Behemoth-Giant E100#^^#^#*(#^^#>2)^(#^^#>2)^#100 fφ(ω,0)ε1ε1ω(100)
(9127) tethratope-by-territerritethrathoth E100#^^#^#*((#^^#)^^#)^^#100 \(f_{\varphi(\omega,0)\varepsilon_2}(100)\)
(9128) tethratope-by-Trihemoth-Giant E100#^^#^#*(#^^#>3)^(#^^#>3)^#100 fφ(ω,0)ε2ε2ω(100)
(9129) tethratope-by-tethriterator E100#^^#^#*#^^#>#100 \(f_{\varphi(\omega,0)\varepsilon_{\omega}}(100)\)
tethratope-by-dustacultethrathoth E100#^^#^#*#^^#>#^^#100 \(f_{\varphi(\omega,0)\varepsilon_{\varepsilon_0}}(100)\)
(9130) tethratope-by-tethracross E100#^^#^#*#^^##100 \(f_{\varphi(\omega,0)\zeta_0}(100)\)
(9131) tethratope-by-tethracubor E100#^^#^#*#^^###100 \(f_{\varphi(\omega,0)\eta_0}(100)\)
(9132) tethratope-by-tethrateron E100#^^#^#*#^^####100 \(f_{\varphi(\omega,0)\varphi(4,0)}(100)\)
(9133) tethratope-by-tethrapeton E100#^^#^#*(#^^#^5)100 \(f_{\varphi(\omega,0)\varphi(5,0)}(100)\)
(9134) tethratope-by-tethrahexon E100#^^#^#*(#^^#^6)100 \(f_{\varphi(\omega,0)\varphi(6,0)}(100)\)
(9135) tethratope-by-tethrahepton E100#^^#^#*(#^^#^7)100 \(f_{\varphi(\omega,0)\varphi(7,0)}(100)\)
(9136) tethratope-by-tethra-ogdon E100#^^#^#*(#^^#^8)100 \(f_{\varphi(\omega,0)\varphi(8,0)}(100)\)
(9137) tethratope-by-tethrennon E100#^^#^#*(#^^#^9)100 \(f_{\varphi(\omega,0)\varphi(9,0)}(100)\)
(9138) tethratope-by-tethradekon E100#^^#^#*(#^^#^10)100 \(f_{\varphi(\omega,0)\varphi(10,0)}(100)\)
(9139) tethratope-by-tethra-icoson E100#^^#^#*(#^^#^20)100 \(f_{\varphi(\omega,0)\varphi(20,0)}(100)\)
(9140) tethratope-by-tethratrianton E100#^^#^#*(#^^#^30)100 \(f_{\varphi(\omega,0)\varphi(30,0)}(100)\)
(9141) tethratope-by-tethrasaranton E100#^^#^#*(#^^#^40)100 \(f_{\varphi(\omega,0)\varphi(40,0)}(100)\)
(9142) tethratope-by-tethrapeninton E100#^^#^#*(#^^#^50)100 \(f_{\varphi(\omega,0)\varphi(50,0)}(100)\)
(9143) tethratope-by-tethra-exinton E100#^^#^#*(#^^#^60)100 \(f_{\varphi(\omega,0)\varphi(60,0)}(100)\)
(9144) tethratope-by-tethra-ebdominton E100#^^#^#*(#^^#^70)100 \(f_{\varphi(\omega,0)\varphi(70,0)}(100)\)
(9145) tethratope-by-tethra-ogdonton E100#^^#^#*(#^^#^80)100 \(f_{\varphi(\omega,0)\varphi(80,0)}(100)\)
(9146) tethratope-by-tethra-eneninton E100#^^#^#*(#^^#^90)100 \(f_{\varphi(\omega,0)\varphi(90,0)}(100)\)

E100#^^#^#*#^^#^#100 - E100(#^^#^#)^#^#100

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9147) tethratope-by-tethratope or (9150) deutero-tethratope E100#^^#^#*#^^#^#100 \(f_{\varphi(\omega,0)^{2}}(100)\)
N/A E100#^^#^#*#^^#^(tethratope)100 \(f_{\varphi(\omega,0)^{2}}(f_{\varphi(\omega,0)}(100))\)
(9149) grand tethratope-by-tethratope E100#^^#^#*#^^#^#100#2 \(f_{\varphi(\omega,0)^{2}}^2(100)\)
grangol-carta-deutero-tethratope E100#^^#^#*#^^#^#100#100 \(f_{\varphi(\omega,0)^{2}+1}(100)\)
godgahlah-carta-deutero-tethratope E100#^^#^#*#^^#^#100#^#100 \(f_{\varphi(\omega,0)^{2}+\omega^{\omega}}(100)\)
tethrathoth-carta-deutero-tethratope E100#^^#^#*#^^#^#100#^^#100 \(f_{\varphi(\omega,0)^{2}+\varepsilon_{0}}(100)\)
tethratope-carta-deutero-tethratope E100#^^#^#*#^^#^#100#^^#^#100 \(f_{\varphi(\omega,0)^{2}+\varphi(\omega,0)}(100)\)
(deutero-tethratope)-by-deuteron E100#^^#^#*#^^#^#*#3 \(f_{\varphi(\omega,0)^{2}2}(100)\)
(deutero-tethratope)-by-hyperion E100#^^#^#*#^^#^#*#100 \(f_{\varphi(\omega,0)^{2}\omega}(100)\)
(deutero-tethratope)-by-godgahlah E100#^^#^#*#^^#^#*#^#100 \(f_{\varphi(\omega,0)^{2}\omega^{\omega}}(100)\)
(deutero-tethratope)-by-tethrathoth E100#^^#^#*#^^#^#*#^^#100 \(f_{\varphi(\omega,0)^{2}\varepsilon_{0}}(100)\)
(9151) trito-tethratope or (deutero-tethratope)-by-tethratope E100#^^#^#*#^^#^#*#^^#^#100 \(f_{\varphi(\omega,0)^{3}}(100)\)
(9152) grand trito-tethratope E100#^^#^#*#^^#^#*#^^#^#100#2

= E100#^^#^#*#^^#^#*#^^#^(trito-tethratope)100

\(f_{\varphi(\omega,0)^{3}}^2(100)\)
grangol-carta-trito-tethratope E100#^^#^#*#^^#^#*#^^#^#100#100 \(f_{\varphi(\omega,0)^{3}+1}(100)\)
(trito-tethratope)-by-deuteron E100#^^#^#*#^^#^#*#^^#^#*#3 \(f_{\varphi(\omega,0)^{3}2}(100)\)
(9153) teterto-tethratope or (trito-tethratope)-by-tethratope E100#^^#^#*#^^#^#*#^^#^#*#^^#^#100 = E100(#^^#^#)^#4 \(f_{\varphi(\omega,0)^{4}}(100)\)
(9154) pepto-tethratope E100(#^^#^#)^#5 \(f_{\varphi(\omega,0)^{5}}(100)\)
(9155) exto-tethratope E100(#^^#^#)^#6 \(f_{\varphi(\omega,0)^{6}}(100)\)
(9156) epto-tethratope E100(#^^#^#)^#7 \(f_{\varphi(\omega,0)^{7}}(100)\)
(9157) ogdo-tethratope E100(#^^#^#)^#8 \(f_{\varphi(\omega,0)^{8}}(100)\)
(9158) ento-tethratope E100(#^^#^#)^#9 \(f_{\varphi(\omega,0)^{9}}(100)\)
(9159) dekato-tethratope E100(#^^#^#)^#10 \(f_{\varphi(\omega,0)^{10}}(100)\)
(9160) isosto-tethratope E100(#^^#^#)^#20 \(f_{\varphi(\omega,0)^{20}}(100)\)
(9161) trianto-tethratope E100(#^^#^#)^#30 \(f_{\varphi(\omega,0)^{30}}(100)\)
(9162) saranto-tethratope E100(#^^#^#)^#40 \(f_{\varphi(\omega,0)^{40}}(100)\)
(9163) peninto-tethratope E100(#^^#^#)^#50 \(f_{\varphi(\omega,0)^{50}}(100)\)
(9164) exinto-tethratope E100(#^^#^#)^#60 \(f_{\varphi(\omega,0)^{60}}(100)\)
(9165) ebdominto-tethratope E100(#^^#^#)^#70 \(f_{\varphi(\omega,0)^{70}}(100)\)
(9166) ogdonto-tethratope E100(#^^#^#)^#80 \(f_{\varphi(\omega,0)^{80}}(100)\)
(9167) eneninto-tethratope E100(#^^#^#)^#90 \(f_{\varphi(\omega,0)^{90}}(100)\)
(9168) hecato-tethratope or (9169) tethratopofact E100(#^^#^#)^#100 \(f_{\varphi(\omega,0)^{\omega}}(100)\)
grand tethratopofact E100(#^^#^#)^#100#2 \(f_{\varphi(\omega,0)^{\omega}}^2(100)\)
grangol-carta-tethratopofact E100(#^^#^#)^#100#100 \(f_{\varphi(\omega,0)^{\omega}+1}(100)\)
tethratopofact-by-deuteron E100(#^^#^#)^#100(#^^#^#)^#100 \(f_{\varphi(\omega,0)^{\omega}2}(100)\)
tethratopofact-by-tethratope E100(#^^#^#)^#*#^^#^#100 \(f_{\varphi(\omega,0)^{\omega+1}}(100)\)
tethratopofact-by-deuterotethratope E100(#^^#^#)^#*#^^#^#*#^^#^#100 \(f_{\varphi(\omega,0)^{\omega+2}}(100)\)
deutero-tethratopofact E100(#^^#^#)^#*(#^^#^#)^#100 \(f_{\varphi(\omega,0)^{\omega\times2}}(100)\)
(9170) quadratatethratope E100(#^^#^#)^##100 \(f_{\varphi(\omega,0)^{\omega^{2}}}(100)\)
(9171) kubikutethratope E100(#^^#^#)^###100 \(f_{\varphi(\omega,0)^{\omega^{3}}}(100)\)
(9172) quarticutethratope E100(#^^#^#)^####100 \(f_{\varphi(\omega,0)^{\omega^{4}}}(100)\)
(9173) quinticutethratope E100(#^^#^#)^#^#5 \(f_{\varphi(\omega,0)^{\omega^{5}}}(100)\)
(9174) sexticutethratope E100(#^^#^#)^#^#6 \(f_{\varphi(\omega,0)^{\omega^{6}}}(100)\)
(9175) septicutethratope E100(#^^#^#)^#^#7 \(f_{\varphi(\omega,0)^{\omega^{7}}}(100)\)
(9176) octicutethratope E100(#^^#^#)^#^#8 \(f_{\varphi(\omega,0)^{\omega^{8}}}(100)\)
(9177) nonicutethratope E100(#^^#^#)^#^#9 \(f_{\varphi(\omega,0)^{\omega^{9}}}(100)\)
(9178) decicutethratope E100(#^^#^#)^#^#10 \(f_{\varphi(\omega,0)^{\omega^{10}}}(100)\)

E100(#^^#^#)^#^#100 - E100(#^^#^#)^^#100

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9179) centicutethratope or (9180) tethratope-ipso-godgahlah E100(#^^#^#)^#^#100 \(f_{\varphi(\omega,0)^{\omega^{\omega}}}(100)\)
(9181) tethratope-ipso-gridgahlah E100(#^^#^#)^#^##100 \(f_{\varphi(\omega,0)^{\omega^{\omega^2}}}(100)\)
(9182) tethratope-ipso-godgathor E100(#^^#^#)^#^#^#100 \(f_{\varphi(\omega,0)^{\omega^{\omega^{\omega}}}}(100)\)
(9183) tethratope-ipso-gralgathor E100(#^^#^#)^#^#^##100 \(f_{\varphi(\omega,0)^{\omega^{\omega^{\omega^2}}}}(100)\)
(9184) tethratope-ipso-godtothol E100(#^^#^#)^#^#^#^#100 \(f_{\varphi(\omega,0)^{\omega↑↑4}}(100)\)
(9185) tethratope-ipso-godtertol E100(#^^#^#)^#^^#5 \(f_{\varphi(\omega,0)^{\omega↑↑5}}(100)\)
tethratope-ipso-godtopol E100(#^^#^#)^#^^#6 \(f_{\varphi(\omega,0)^{\omega↑↑6}}(100)\)
(9186) tethratope-ipso-tethrathoth E100(#^^#^#)^#^^#100 \(f_{\varphi(\omega,0)^{\varepsilon_0}}(100)\)
(9187) tethratope-ipso-Monster-Giant E100(#^^#^#)^(#^^#)^(#^^#)^#100 fφ(ω,0)ε0ε0ω(100)
(9188) tethratope-ipso-territethrathoth E100(#^^#^#)^(#^^#)^^#100 \(f_{\varphi(\omega,0)^{\varepsilon_1}}(100)\)
(9189) tethratope-ipso-Behemoth-Giant E100(#^^#^#)^(#^^#>2)^(#^^#>2)^#100 fφ(ω,0)ε1ε1ω(100)
(9190) tethratope-ipso-territerritethrathoth E100(#^^#^#)^((#^^#)^^#)^^#100 \(f_{\varphi(\omega,0)^{\varepsilon_2}}(100)\)
(9191) tethratope-ipso-Trihemoth-Giant E100(#^^#^#)^(#^^#>3)^(#^^#>3)^#100 fφ(ω,0)ε2ε2ω(100)
(9192) tethratope-ipso-tethriterator E100(#^^#^#)^#^^#>#100 \(f_{\varphi(\omega,0)^{\varepsilon_\omega}}(100)\)
tethratope-ipso-dustacultethrathoth E100(#^^#^#)^#^^#>#^^#100 \(f_{\varphi(\omega,0)^{\varepsilon_{\varepsilon_0}}}(100)\)
(9193) tethratope-ipso-tethracross E100(#^^#^#)^#^^##100 \(f_{\varphi(\omega,0)^{\zeta_0}}(100)\)
(9194) tethratope-ipsotethracubor E100(#^^#^#)^#^^###100 \(f_{\varphi(\omega,0)^{\eta_0}}(100)\)
(9195) tethratope-ipso-tethrateron E100(#^^#^#)^#^^####100 \(f_{\varphi(\omega,0)^{\varphi(4,0)}}(100)\)
(9196) tethratope-ipso-tethrapeton E100(#^^#^#)^(#^^#^5)100 \(f_{\varphi(\omega,0)^{\varphi(5,0)}}(100)\)
(9197) tethratope-ipso-tethrahexon E100(#^^#^#)^(#^^#^6)100 \(f_{\varphi(\omega,0)^{\varphi(6,0)}}(100)\)
(9198) tethratope-ipso-tethrahepton E100(#^^#^#)^(#^^#^7)100 \(f_{\varphi(\omega,0)^{\varphi(7,0)}}(100)\)
(9199) tethratope-ipso-tethra-ogdon E100(#^^#^#)^(#^^#^8)100 \(f_{\varphi(\omega,0)^{\varphi(8,0)}}(100)\)
(9200) tethratope-ipso-tethrennon E100(#^^#^#)^(#^^#^9)100 \(f_{\varphi(\omega,0)^{\varphi(9,0)}}(100)\)
(9201) tethratope-ipso-tethradekon E100(#^^#^#)^(#^^#^10)100 \(f_{\varphi(\omega,0)^{\varphi(10,0)}}(100)\)
(9202) tethratope-ipso-tethra-icoson E100(#^^#^#)^(#^^#^20)100 \(f_{\varphi(\omega,0)^{\varphi(20,0)}}(100)\)
(9203) tethratope-ipso-tethratrianton E100(#^^#^#)^(#^^#^30)100 \(f_{\varphi(\omega,0)^{\varphi(30,0)}}(100)\)
(9204) tethratope-ipso-tethrasaranton E100(#^^#^#)^(#^^#^40)100 \(f_{\varphi(\omega,0)^{\varphi(40,0)}}(100)\)
(9205) tethratope-ipso-tethrapeninton E100(#^^#^#)^(#^^#^50)100 \(f_{\varphi(\omega,0)^{\varphi(50,0)}}(100)\)
(9206) tethratope-ipso-tethra-exinton E100(#^^#^#)^(#^^#^60)100 \(f_{\varphi(\omega,0)^{\varphi(60,0)}}(100)\)
(9207) tethratope-ipso-ebdominton E100(#^^#^#)^(#^^#^70)100 \(f_{\varphi(\omega,0)^{\varphi(70,0)}}(100)\)
(9208) tethratope-ipso-ogdonton E100(#^^#^#)^(#^^#^80)100 \(f_{\varphi(\omega,0)^{\varphi(80,0)}}(100)\)
(9209) tethratope-ipso-eneninton E100(#^^#^#)^(#^^#^90)100 \(f_{\varphi(\omega,0)^{\varphi(90,0)}}(100)\)
(9210) tethratope-ipso-tethratope or (9213) dutetrated-tethratope E100(#^^#^#)^(#^^#^#)100 \(f_{\varphi(\omega,0)^{\varphi(\omega,0)}}(100)\)
(9212) grand tethratope-ipso-tethratope E100(#^^#^#)^(#^^#^#)100#2 \(f_{\varphi(\omega,0)^{\varphi(\omega,0)}}^2(100)\)
dutetrated tethratopofact E100(#^^#^#)^(#^^#^#)^#100 \(f_{\varphi(\omega,0)^{\varphi(\omega,0)^{\omega}}}(100)\)
dutetrated tethratope-ipso-tethratope or (9214) tritetrated-tethratope E100(#^^#^#)^(#^^#^#)^(#^^#^#)100 \(f_{\varphi(\omega,0)^{\varphi(\omega,0)^{\varphi(\omega,0)}}}(100)\)
(9215) grand tritetrated-tethratope E100(#^^#^#)^(#^^#^#)^(#^^#^#)100#2 \(f_{\varphi(\omega,0)^{\varphi(\omega,0)^{\varphi(\omega,0)}}}^2(100)\)
tritetrated tethratopofact E100(#^^#^#)^(#^^#^#)^(#^^#^#)^#100 \(f_{\varphi(\omega,0)^{\varphi(\omega,0)^{\varphi(\omega,0)^{\omega}}}}(100)\)
(9216) quadratetrated-tethratope E100(#^^#^#)^^#4 \(f_{\varphi(\omega,0)↑↑4}(100)\)
(9217) quinquatetrated-tethratope E100(#^^#^#)^^#5 \(f_{\varphi(\omega,0)↑↑5}(100)\)
(9218) sexatetrated-tethratope E100(#^^#^#)^^#6 \(f_{\varphi(\omega,0)↑↑6}(100)\)
(9219) septatetrated-tethratope E100(#^^#^#)^^#7 \(f_{\varphi(\omega,0)↑↑7}(100)\)
(9220) octatetrated-tethratope E100(#^^#^#)^^#8 \(f_{\varphi(\omega,0)↑↑8}(100)\)
(9221) nonatetrated-tethratope E100(#^^#^#)^^#9 \(f_{\varphi(\omega,0)↑↑9}(100)\)
(9222) decatetrated-tethratope E100(#^^#^#)^^#10 \(f_{\varphi(\omega,0)↑↑{10}}(100)\)

E100(#^^#^#)^^#100 - E100(#^^#^#)^^##100

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9223) terrible tethratope E100(#^^#^#)^^#100 \(f_{\varepsilon_{\varphi(\omega,0)+1}}(100)\)
grand terrible tethratope E100(#^^#^#)^^#100#2 \(f_{\varepsilon_{\varphi(\omega,0)+1}}^2(100)\)
(9224) terrible terrible tethratope E100((#^^#^#)^^#)^^#100 \(f_{\varepsilon_{\varphi(\omega,0)+2}}(100)\)
(9225) three-ex-terrible tethratope E100(((#^^#^#)^^#)^^#)^^#100 \(f_{\varepsilon_{\varphi(\omega,0)+3}}(100)\)
(9226) four-ex-terrible tethratope E100((((#^^#^#)^^#)^^#)^^#)^^#100 = E100(#^^#^#)^^#>(4)100 \(f_{\varepsilon_{\varphi(\omega,0)+4}}(100)\)
(9227) five-ex-terrible tethratope E100(#^^#^#)^^#>(5)100 \(f_{\varepsilon_{\varphi(\omega,0)+5}}(100)\)
(9228) six-ex-terrible tethratope E100(#^^#^#)^^#>(6)100 \(f_{\varepsilon_{\varphi(\omega,0)+6}}(100)\)
(9229) seven-ex-terrible tethratope E100(#^^#^#)^^#>(7)100 \(f_{\varepsilon_{\varphi(\omega,0)+7}}(100)\)
(9230) eight-ex-terrible tethratope E100(#^^#^#)^^#>(8)100 \(f_{\varepsilon_{\varphi(\omega,0)+8}}(100)\)
(9231) nine-ex-terrible tethratope E100(#^^#^#)^^#>(9)100 \(f_{\varepsilon_{\varphi(\omega,0)+9}}(100)\)
(9232) ten-ex-terrible tethratope E100(#^^#^#)^^#>(10)100 \(f_{\varepsilon_{\varphi(\omega,0)+{10}}}(100)\)
20-ex-terrible tethratope E100(#^^#^#)^^#>(20)100 \(f_{\varepsilon_{\varphi(\omega,0)+{20}}}(100)\)
(9233) territertethratope E100(#^^#^#)^^#>#100 \(f_{\varepsilon_{\varphi(\omega,0)+{\omega}}}(100)\)
double-hyperion-turreted-tethratope E100(#^^#^#)^^#>##100 \(f_{\varepsilon_{\varphi(\omega,0)+{\omega^2}}}(100)\)
(9234) godgahlah-turreted-territethratope E100(#^^#^#)^^#>#^#100 \(f_{\varepsilon_{\varphi(\omega,0)+{\omega^{\omega}}}}(100)\)
(9235) tethrathoth-turreted-territethratope E100(#^^#^#)^^#>#^^#100 \(f_{\varepsilon_{\varphi(\omega,0)+{\varepsilon_{0}}}}(100)\)
(9236) tethracross-turreted-territethratope E100(#^^#^#)^^#>#^^##100 \(f_{\varepsilon_{\varphi(\omega,0)+{\zeta_{0}}}}(100)\)
(9237) tethracubor-turreted-territethratope E100(#^^#^#)^^#>#^^###100 \(f_{\varepsilon_{\varphi(\omega,0)+{\eta_{0}}}}(100)\)
(9238) tethrateron-turreted-territethratope E100(#^^#^#)^^#>#^^####100 \(f_{\varepsilon_{\varphi(\omega,0)+{\varphi(4,0)}}}(100)\)
(9239) tethrapeton-turreted-territethratope E100(#^^#^#)^^#>(#^^#^5)100 \(f_{\varepsilon_{\varphi(\omega,0)+{\varphi(5,0)}}}(100)\)
(9240) tethrahexon-turreted-territethratope E100(#^^#^#)^^#>(#^^#^6)100 \(f_{\varepsilon_{\varphi(\omega,0)+{\varphi(6,0)}}}(100)\)
(9241) tethrahepton-turreted-territethratope E100(#^^#^#)^^#>(#^^#^7)100 \(f_{\varepsilon_{\varphi(\omega,0)+{\varphi(7,0)}}}(100)\)
(9242) tethra-ogdon-turreted-territethratope E100(#^^#^#)^^#>(#^^#^8)100 \(f_{\varepsilon_{\varphi(\omega,0)+{\varphi(8,0)}}}(100)\)
(9243) tethrennon-turreted-territethratope E100(#^^#^#)^^#>(#^^#^9)100 \(f_{\varepsilon_{\varphi(\omega,0)+{\varphi(9,0)}}}(100)\)
(9244) tethradekon-turreted-territethratope E100(#^^#^#)^^#>(#^^#^10)100 \(f_{\varepsilon_{\varphi(\omega,0)+{\varphi(10,0)}}}(100)\)
tethraicoson-turreted-territethratope E100(#^^#^#)^^#>(#^^#^20)100 \(f_{\varepsilon_{\varphi(\omega,0)+{\varphi(20,0)}}}(100)\)
(9245) tethratope-turreted-territethratope E100(#^^#^#)^^#>#^^#^#100 = E100(#^^#^#)^^#>(#^^#^100)100 \(f_{\varepsilon_{\varphi(\omega,0)2}}(100)\)
(9246) grand tethratope-turreted-territethratope E100(#^^#^#)^^#>#^^#^#100#2

= E100(#^^#^#)^^#>#^^#^(tethratope-turreted-territethratope)100

\(f_{\varepsilon_{\varphi(\omega,0)2}}^2(100)\)
N/A E100(#^^#^#)^^#>#^^#^#100#100 \(f_{\varepsilon_{\varphi(\omega,0)2}+1}(100)\)
N/A E100(#^^#^#)^^#>#^^#^#100*#3 \(f_{\varepsilon_{\varphi(\omega,0)2}2}(100)\)
N/A E100(#^^#^#)^^#>#^^#^#100*#100 \(f_{\varepsilon_{\varphi(\omega,0)2}\omega}(100)\)
N/A E100(#^^#^#)^^#>#^^#^#*(#^^#^#)^^#>#^^#^#100 \(f_{\varepsilon_{\varphi(\omega,0)2}^2}(100)\)
N/A E100((#^^#^#)^^#>#^^#^#)^#100 \(f_{\varepsilon_{\varphi(\omega,0)2}^{\omega}}(100)\)
N/A E100((#^^#^#)^^#>#^^#^#)^^#100 \(f_{\varepsilon_{\varphi(\omega,0)2+1}}(100)\)
N/A E100(#^^#^#)^^#>(#^^#^#+#)100 \(f_{\varepsilon_{\varphi(\omega,0)2+\omega}}(100)\)
N/A E100(#^^#^#)^^#>(#^^#^#+#^^#^#)100 \(f_{\varepsilon_{\varphi(\omega,0)3}}(100)\)
N/A E100(#^^#^#)^^#>(#^^#^#*#)100 \(f_{\varepsilon_{\varphi(\omega,0)\omega}}(100)\)
N/A E100(#^^#^#)^^#>((#^^#^#)^#)100 \(f_{\varepsilon_{\varphi(\omega,0)^{\omega}}}(100)\)
(9247) dustaculated-territethratope E100(#^^#^#)^^#>(#^^#^#)^^#100 \(f_{\varepsilon_{\varepsilon_{\varphi(\omega,0)+1}}}(100)\)
(9248) tristaculated-territethratope E100(#^^#^#)^^#>(#^^#^#)^^#>(#^^#^#)^^#100 \(f_{\varepsilon_{\varepsilon_{\varepsilon_{\varphi(\omega,0)+1}}}}(100)\)
(9249) tetrastaculated-territethratope E100(#^^#^#)^^#>(#^^#^#)^^#>(#^^#^#)^^#>(#^^#^#)^^#100 = E100(#^^#^#)^^##4 \(f_{\zeta_{\varphi(\omega,0)+1}[4]}(100)\)
(9250) pentastaculated-territethratope E100(#^^#^#)^^##5 \(f_{\zeta_{\varphi(\omega,0)+1}[5]}(100)\)
(9251) hexastaculated-territethratope E100(#^^#^#)^^##6 \(f_{\zeta_{\varphi(\omega,0)+1}[6]}(100)\)
(9252) heptastaculated-territethratope E100(#^^#^#)^^##7 \(f_{\zeta_{\varphi(\omega,0)+1}[7]}(100)\)
(9253) ogdastaculated-territethratope E100(#^^#^#)^^##8 \(f_{\zeta_{\varphi(\omega,0)+1}[8]}(100)\)
(9254) ennastaculated-territethratope E100(#^^#^#)^^##9 \(f_{\zeta_{\varphi(\omega,0)+1}[9]}(100)\)
(9255) dekastaculated-territethratope E100(#^^#^#)^^##10 \(f_{\zeta_{\varphi(\omega,0)+1}[10]}(100)\)

E100(#^^#^#)^^##100 - E100#^^(#^#)>#100

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9256) terrisquared tethratope E100(#^^#^#)^^##100 \(f_{\zeta_{\varphi(\omega,0)+1}}(100)\)
dustaculated terrisquared tethratope E100(#^^#^#)^^##>(#^^#^#)^^##100 \(f_{\zeta_{\zeta_{\varphi(\omega,0)+1}}}(100)\)
(9257) terricubed tethratope E100(#^^#^#)^^###100 \(f_{\eta_{\varphi(\omega,0)+1}}(100)\)
dustaculated terricubed tethratope E100(#^^#^#)^^###>(#^^#^#)^^###100 \(f_{\eta_{\eta_{\varphi(\omega,0)+1}}}(100)\)
(9258) territesserated tethratope E100(#^^#^#)^^####100 \(f_{\varphi(4,\varphi(\omega,0)+1)}(100)\)
dustaculated territesserated tethratope E100(#^^#^#)^^####>(#^^#^#)^^####100 \(f_{\varphi(4,\varphi(4,\varphi(\omega,0)+1))}(100)\)
(9259) terripenterated tethratope E100((#^^#^#)^^#^5)100 \(f_{\varphi(5,\varphi(\omega,0)+1)}(100)\)
dustaculated terripenterated tethratope E100(#^^#^#)^^#^5>(#^^#^#)^^#^(5)100 \(f_{\varphi(5,\varphi(5,\varphi(\omega,0)+1))}(100)\)
(9260) terrihexerated tethratope E100((#^^#^#)^^#^6)100 \(f_{\varphi(6,\varphi(\omega,0)+1)}(100)\)
(9261) terrihepterated tethratope E100((#^^#^#)^^#^7)100 \(f_{\varphi(7,\varphi(\omega,0)+1)}(100)\)
(9262) terriogderated tethratope E100((#^^#^#)^^#^8)100 \(f_{\varphi(8,\varphi(\omega,0)+1)}(100)\)
(9263) terriennerated tethratope E100((#^^#^#)^^#^9)100 \(f_{\varphi(9,\varphi(\omega,0)+1)}(100)\)
(9264) terridekerated tethratope E100((#^^#^#)^^#^10)100 \(f_{\varphi(10,\varphi(\omega,0)+1)}(100)\)
terri-20-ated tethratope E100((#^^#^#)^^#^20)100 \(f_{\varphi(20,\varphi(\omega,0)+1)}(100)\)
terri-25-ated tethratope E100((#^^#^#)^^#^25)100 \(f_{\varphi(25,\varphi(\omega,0)+1)}(100)\)
terri-30-ated tethratope E100((#^^#^#)^^#^30)100 \(f_{\varphi(30,\varphi(\omega,0)+1)}(100)\)
terri-40-ated tethratope E100((#^^#^#)^^#^40)100 \(f_{\varphi(40,\varphi(\omega,0)+1)}(100)\)
terri-50-ated tethratope E100((#^^#^#)^^#^50)100 \(f_{\varphi(50,\varphi(\omega,0)+1)}(100)\)
terri-60-ated tethratope E100((#^^#^#)^^#^60)100 \(f_{\varphi(60,\varphi(\omega,0)+1)}(100)\)
terri-70-ated tethratope E100((#^^#^#)^^#^70)100 \(f_{\varphi(70,\varphi(\omega,0)+1)}(100)\)
terri-80-ated tethratope E100((#^^#^#)^^#^80)100 \(f_{\varphi(80,\varphi(\omega,0)+1)}(100)\)
terri-90-ated tethratope E100((#^^#^#)^^#^90)100 \(f_{\varphi(90,\varphi(\omega,0)+1)}(100)\)
(9265) tethradeutertope or (9266) tethradutope E100(#^^#^#)^^#^#100 \(f_{\varphi(\omega,1)}(100)\)
tethradeutertopogong E100000(#^^#^#)^^#^#100000 \(f_{\varphi(\omega,1)}(100\,000)\)
(9267) grand tethradeutertope E100(#^^#^#)^^#^#100#2 = E100(#^^#^#)^^#^(tethradeutertope)100 \(f_{\varphi(\omega,1)}^2(100)\)
grangol-carta-tethradeutertope E100(#^^#^#)^^#^#100#100 \(f_{\varphi(\omega,1)+1}(100)\)
grangol-carta-tethradeutertope E100(#^^#^#)^^#^#100#100 \(f_{\varphi(\omega,1)+1}(100)\)
N/A E100(#^^#^#)^^#^#*#3 \(f_{\varphi(\omega,1)+\varphi(\omega,1)}(100)\)
N/A E100(#^^#^#)^^#^#*(#^^#^#)^^#^#100 \(f_{\varphi(\omega,1)^2}(100)\)
N/A E100((#^^#^#)^^#^#)^#100 \(f_{\varphi(\omega,1)^{\omega}}(100)\)
(9268) terrible tethradeutertope E100((#^^#^#)^^#^#)^^#100 \(f_{\varepsilon_{\varphi(\omega,1)}+1}(100)\)
(9269) terrisquared tethradeutertope E100((#^^#^#)^^#^#)^^##100 \(f_{\zeta_{\varphi(\omega,1)}+1}(100)\)
(9270) terricubed tethradeutertope E100((#^^#^#)^^#^#)^^###100 \(f_{\eta_{\varphi(\omega,1)}+1}(100)\)
(9271) territesserated tethradeutertope E100((#^^#^#)^^#^#)^^####100 \(f_{\varphi(4,\varphi(\omega,1)+1)}(100)\)
(9272) terripenterated tethradeutertope E100(((#^^#^#)^^#^#)^^#^5)100 \(f_{\varphi(5,\varphi(\omega,1)+1)}(100)\)
(9273) terrihexerated tethradeutertope E100(((#^^#^#)^^#^#)^^#^6)100 \(f_{\varphi(6,\varphi(\omega,1)+1)}(100)\)
(9274) terrihepterated tethradeutertope E100(((#^^#^#)^^#^#)^^#^7)100 \(f_{\varphi(7,\varphi(\omega,1)+1)}(100)\)
(9275) terriogderated tethradeutertope E100(((#^^#^#)^^#^#)^^#^8)100 \(f_{\varphi(8,\varphi(\omega,1)+1)}(100)\)
(9276) terriennerated tethradeutertope E100(((#^^#^#)^^#^#)^^#^9)100 \(f_{\varphi(9,\varphi(\omega,1)+1)}(100)\)
(9277) terridekerated tethradeutertope E100(((#^^#^#)^^#^#)^^#^10)100 \(f_{\varphi(10,\varphi(\omega,1)+1)}(100)\)
terri-20-ated tethradeutertope E100(((#^^#^#)^^#^#)^^#^20)100 \(f_{\varphi(20,\varphi(\omega,1)+1)}(100)\)
(9278) tethratritotope or (9279) tethratritope E100((#^^#^#)^^#^#)^^#^#100 \(f_{\varphi(\omega,2)}(100)\)
(9280) tethratetertotope or (9281) tethratetratope E100(((#^^#^#)^^#^#)^^#^#)^^#^#100 = E100#^^(#^#)>#4 \(f_{\varphi(\omega,3)}(100)\)
(9282) tethrapeptotope or (9283) tethrapentatope E100#^^(#^#)>#5 \(f_{\varphi(\omega,4)}(100)\)
(9284) tethra-extotope or (9285) tethrahexatope E100#^^(#^#)>#6 \(f_{\varphi(\omega,5)}(100)\)
(9286) tethra-eptotope or (9287) tethraheptatope E100#^^(#^#)>#7 \(f_{\varphi(\omega,6)}(100)\)
(9288) tethra-ogdotope or (9289) tethra-octatope E100#^^(#^#)>#8 \(f_{\varphi(\omega,7)}(100)\)
(9290) tethra-entotope or (9291) tethra-ennatope E100#^^(#^#)>#9 \(f_{\varphi(\omega,8)}(100)\)
(9292) tethra-dekatotope or (9293) tethradekatope E100#^^(#^#)>#10 \(f_{\varphi(\omega,9)}(100)\)
(9294) tethra-endekatope E100#^^(#^#)>#11 \(f_{\varphi(\omega,10)}(100)\)
(9295) tethra-dodekatope E100#^^(#^#)>#12 \(f_{\varphi(\omega,11)}(100)\)
tethra-tridekatope E100#^^(#^#)>#13 \(f_{\varphi(\omega,12)}(100)\)
tethra-tetradekatope E100#^^(#^#)>#14 \(f_{\varphi(\omega,13)}(100)\)
tethra-pentadekatope E100#^^(#^#)>#15 \(f_{\varphi(\omega,14)}(100)\)
tethra-hexadekatope E100#^^(#^#)>#16 \(f_{\varphi(\omega,15)}(100)\)
tethra-heptadekatope E100#^^(#^#)>#17 \(f_{\varphi(\omega,16)}(100)\)
tethra-octadekatope E100#^^(#^#)>#18 \(f_{\varphi(\omega,17)}(100)\)
tethra-ennadekatope E100#^^(#^#)>#19 \(f_{\varphi(\omega,18)}(100)\)
(9296) tethra-icosatope E100#^^(#^#)>#20 \(f_{\varphi(\omega,19)}(100)\)

E100#^^(#^#)>#100 - E100#^^(#^#*#)100

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9297) tethritertope E100#^^(#^#)>#100 \(f_{\varphi(\omega,\omega)}(100)\)
tethritertopogong E100000#^^(#^#)>#100000 \(f_{\varphi(\omega,\omega)}(100\,000)\)
(9298) terrible tethritertope E100(#^^(#^#)>#)^^#100 \(f_{\varepsilon_{\varphi(\omega,\omega)}+1}(100)\)
(9299) terrisquared tethritertope E100(#^^(#^#)>#)^^##100 \(f_{\zeta_{\varphi(\omega,\omega)}+1}(100)\)
(9300) terricubed tethritertope E100(#^^(#^#)>#)^^###100 \(f_{\eta_{\varphi(\omega,\omega)}+1}(100)\)
(9301) territesserated tethritertope E100(#^^(#^#)>#)^^####100 \(f_{\varphi(4,{\varphi(\omega,\omega)}+1)}(100)\)
(9302) terripenterated tethritertope E100((#^^(#^#)>#)^^#^5)100 \(f_{\varphi(5,{\varphi(\omega,\omega)}+1)}(100)\)
(9303) terrihexerated tethritertope E100((#^^(#^#)>#)^^#^6)100 \(f_{\varphi(6,{\varphi(\omega,\omega)}+1)}(100)\)
(9304) terrihepterated tethritertope E100((#^^(#^#)>#)^^#^7)100 \(f_{\varphi(7,{\varphi(\omega,\omega)}+1)}(100)\)
(9305) terriocterated tethritertope E100((#^^(#^#)>#)^^#^8)100 \(f_{\varphi(8,{\varphi(\omega,\omega)}+1)}(100)\)
(9306) terriennerated tethritertope E100((#^^(#^#)>#)^^#^9)100 \(f_{\varphi(9,{\varphi(\omega,\omega)}+1)}(100)\)
(9307) terridekerated tethritertope E100((#^^(#^#)>#)^^#^10)100 \(f_{\varphi(10,{\varphi(\omega,\omega)+1)}}(100)\)
(9308) territoped tethritertope E100(#^^(#^#)>#)^^#^#100 \(f_{\varphi(\omega,{\varphi(\omega,\omega)+1)}}(100) = f_{\varphi(\omega,\omega+1)}(100)\)
(9309) grand territoped tethritertope E100(#^^(#^#)>#)^^#^#100#2 = E100(#^^(#^#)>#)^^#^(territoped tethritertope)100 \(f_{\varphi(\omega,{\varphi(\omega,\omega)+1)}}^2(100) = f_{\varphi(\omega,\omega+1)}^2(100)\)
terrible territoped tethritertope E100((#^^(#^#)>#)^^#^#)^^#100 \(f_{\varepsilon_{\varphi(\omega,{\varphi(\omega,\omega)+1)}}+1}(100)\)
terrisquared territoped tethritertope E100((#^^(#^#)>#)^^#^#)^^##100 \(f_{\zeta_{\varphi(\omega,{\varphi(\omega,\omega)+1)}}+1}(100)\)
terricubed territoped tethritertope E100((#^^(#^#)>#)^^#^#)^^###100 \(f_{\eta_{\varphi(\omega,{\varphi(\omega,\omega)+1)}}+1}(100)\)
(9310) territoped territoped tethritertope E100((#^^(#^#)>#)^^#^#)^^#^#100 = E100#^^(#^#)>(#+#)2 \(f_{\varphi(\varphi(\omega,{\varphi(\omega,\omega)+1)}+1)}(100) = f_{\varphi(\omega,\omega+2)}(100)\)
(9311) three-ex-territoped tethritertope E100(((#^^(#^#)>#)^^#^#)^^#^#)^^#^#100 \(f_{\varphi(\omega,\omega+3)}(100)\)
(9312) four-ex-territoped tethritertope E100#^^(#^#)>(#+#)4 \(f_{\varphi(\omega,\omega+4)}(100)\)
(9313) five-ex-territoped tethritertope E100#^^(#^#)>(#+#)5 \(f_{\varphi(\omega,\omega+5)}(100)\)
(9314) six-ex-territoped tethritertope E100#^^(#^#)>(#+#)6 \(f_{\varphi(\omega,\omega+6)}(100)\)
(9315) seven-ex-territoped tethritertope E100#^^(#^#)>(#+#)7 \(f_{\varphi(\omega,\omega+7)}(100)\)
(9316) eight-ex-territoped tethritertope E100#^^(#^#)>(#+#)8 \(f_{\varphi(\omega,\omega+8)}(100)\)
(9317) nine-ex-territoped tethritertope E100#^^(#^#)>(#+#)9 \(f_{\varphi(\omega,\omega+9)}(100)\)
(9318) ten-ex-territoped tethritertope E100#^^(#^#)>(#+#)10 \(f_{\varphi(\omega,\omega+10)}(100)\)
20-ex-territoped tethritertope E100#^^(#^#)>(#+#)20 \(f_{\varphi(\omega,\omega+20)}(100)\)
(9319) tethriditertope E100#^^(#^#)>(#+#)100 \(f_{\varphi(\omega,\omega\times 2)}(100)\)
(9320) tethritritertope E100#^^(#^#)>(#+#+#)100 \(f_{\varphi(\omega,\omega\times 3)}(100)\)
(9321) tethriquaditertope E100#^^(#^#)>(#+#+#+#)100

= E100#^^(#^#)>##4

\(f_{\varphi(\omega,\omega\times 4)}(100)\)
(9322) tethriquiditertope E100#^^(#^#)>##5 \(f_{\varphi(\omega,\omega\times 5)}(100)\)
(9323) tethrisiditertope E100#^^(#^#)>##6 \(f_{\varphi(\omega,\omega\times 6)}(100)\)
(9324) tethrisepitertope E100#^^(#^#)>##7 \(f_{\varphi(\omega,\omega\times 7)}(100)\)
(9325) tethriogditertope E100#^^(#^#)>##8 \(f_{\varphi(\omega,\omega\times 8)}(100)\)
(9326) tethrinonitertope E100#^^(#^#)>##9 \(f_{\varphi(\omega,\omega\times 9)}(100)\)
(9327) tethridecitertope E100#^^(#^#)>##10 \(f_{\varphi(\omega,\omega\times 10)}(100)\)
(9328) tethrigriditertope E100#^^(#^#)>##100 \(f_{\varphi(\omega,\omega^2)}(100)\)
(9329) tethricubicultope E100#^^(#^#)>###100 \(f_{\varphi(\omega,\omega^3)}(100)\)
(9330) tethriquarticultope E100#^^(#^#)>####100 \(f_{\varphi(\omega,\omega^4)}(100)\)
(9331) tethriquinticultope E100#^^(#^#)>#^#5 \(f_{\varphi(\omega,\omega^5)}(100)\)
(9332) tethrisexticultope E100#^^(#^#)>#^#6 \(f_{\varphi(\omega,\omega^6)}(100)\)
(9333) tethrisepticultope E100#^^(#^#)>#^#7 \(f_{\varphi(\omega,\omega^7)}(100)\)
(9334) tethriocticultope E100#^^(#^#)>#^#8 \(f_{\varphi(\omega,\omega^8)}(100)\)
(9335) tethrinonicultope E100#^^(#^#)>#^#9 \(f_{\varphi(\omega,\omega^9)}(100)\)
(9336) tethridecicultope E100#^^(#^#)>#^#10 \(f_{\varphi(\omega,\omega^{10})}(100)\)
(9337) godgahlah-turreted-tethratope E100#^^(#^#)>#^#100 \(f_{\varphi(\omega,\omega^{\omega})}(100)\)
(9338) godgahlah-ipso-deuteron-turreted-tethratope E100#^^(#^#)>(#^#*#^#)100 \(f_{\varphi(\omega,\omega^{\omega\times 2})}(100)\)
(9339) gridgahlah-turreted-tethratope E100#^^(#^#)>#^##100 \(f_{\varphi(\omega,\omega^{\omega^2})}(100)\)
(9340) kubikahlah-turreted-tethratope E100#^^(#^#)>#^###100 \(f_{\varphi(\omega,\omega^{\omega^3})}(100)\)
(9341) quarticahlah-turreted-tethratope E100#^^(#^#)>#^####100 \(f_{\varphi(\omega,\omega^{\omega^4})}(100)\)
quinticahlah-turreted-tethratope E100#^^(#^#)>#^#^#5 \(f_{\varphi(\omega,\omega^{\omega^5})}(100)\)
(9342) godgathor-turreted-tethratope E100#^^(#^#)>#^#^#100 \(f_{\varphi(\omega,\omega^{\omega^{\omega}})}(100)\)
(9343) godtothol-turreted-tethratope E100#^^(#^#)>#^#^#^#100 \(f_{\varphi(\omega,\omega^{\omega^{\omega^{\omega}}})}(100)\)
godtertol-turreted-tethratope E100#^^(#^#)>#^^#5 \(f_{\varphi(\omega,\omega↑↑5)}(100)\)
(9344) tethrathoth-turreted-tethratope E100#^^(#^#)>#^^#100 \(f_{\varphi(\omega,\varepsilon_{0})}(100)\)
(9345) terrible tethrathoth-turreted-tethratope E100(#^^(#^#)>#^^#)^^#100 \(f_{\varepsilon_{\varphi(\omega,\varepsilon_{0})}+1}(100)\)
terrisquared tethrathoth-turreted-tethratope E100(#^^(#^#)>#^^#)^^##100 \(f_{\zeta_{\varphi(\omega,\varepsilon_{0})}+1}(100)\)
terricubed tethrathoth-turreted-tethratope E100(#^^(#^#)>#^^#)^^###100 \(f_{\eta_{\varphi(\omega,\varepsilon_{0})}+1}(100)\)
(9346) territoped tethrathoth-turreted-tethratope E100(#^^(#^#)>#^^#)^^#^#100 \(f_{\varphi(\omega,\varepsilon_{0}+1)}(100)\)
(9347) territoped territoped tethrathoth-turreted-tethratope E100((#^^(#^#)>#^^#)^^#^#)^^#^#100 \(f_{\varphi(\omega,\varepsilon_{0}+2)}(100)\)
(9348) hundred-ex-territoped tethrathoth-turreted-tethratope E100#^^(#^#)>(#^^#+#)100 \(f_{\varphi(\omega,\varepsilon_{0}+\omega)}(100)\)
n/a E100#^^(#^#)>(#^^#+##)100 \(f_{\varphi(\omega,\varepsilon_{0}+\omega^2)}(100)\)
n/a E100#^^(#^#)>(#^^#+#^#)100 \(f_{\varphi(\omega,\varepsilon_{0}+\omega^{\omega})}(100)\)
n/a E100#^^(#^#)>(#^^#+#^^#)100 \(f_{\varphi(\omega,\varepsilon_{0}\times 2)}(100)\)
n/a E100#^^(#^#)>(#^^#*#^^#)100 \(f_{\varphi(\omega,\varepsilon_{0}^{2})}(100)\)
n/a E100#^^(#^#)>(#^^#)^^#100 \(f_{\varphi(\omega,\varepsilon_{0}^{\omega})}(100)\)
(9349) Monster-Giant-turreted-tethratope E100#^^(#^#)>(#^^#)^(#^^#)^#100 \(f_{\varphi(\omega,\varepsilon_{0}^{\varepsilon_{0}^{\omega}})}(100)\)
(9350) territethrathoth-turreted-tethratope E100#^^(#^#)>(#^^#)^^#100 \(f_{\varphi(\omega,\varepsilon_{1})}(100)\)
(9351) Behemoth-Giant-turreted-tethratope E100#^^(#^#)>(#^^#>2)^(#^^#>2)^#100 \(f_{\varphi(\omega,\varepsilon_{1}^{\varepsilon_{1}^{\omega}})}(100)\)
(9352) territerritethrathoth-turreted-tethratope E100#^^(#^#)>((#^^#)^^#)^^#100 \(f_{\varphi(\omega,\varepsilon_{2})}(100)\)
(9353) Trihemoth-Giant-turreted-tethratope E100#^^(#^#)>(#^^#>3)^(#^^#>3)^#100 \(f_{\varphi(\omega,\varepsilon_{2}^{\varepsilon_{2}^{\omega}})}(100)\)
(9354) tethriterator-turreted-tethratope E100#^^(#^#)>#^^#>#100 \(f_{\varphi(\omega,\varepsilon_\omega)}(100)\)
(9355) dustacultethrathoth-turreted-tethratope E100#^^(#^#)>#^^#>#^^#100 \(f_{\varphi(\omega,\varepsilon_{\varepsilon_0})}(100)\)
tristacultethrathoth-turreted-tethratope E100#^^(#^#)>#^^#>#^^#>#^^#100 \(f_{\varphi(\omega,\varepsilon_{\varepsilon_{\varepsilon_0}})}(100)\)
(9356) tethracross-turreted-tethratope E100#^^(#^#)>#^^##100 \(f_{\varphi(\omega,\zeta_0)}(100)\)
(9357) tethracubor-turreted-tethratope E100#^^(#^#)>#^^###100 \(f_{\varphi(\omega,\eta_0)}(100)\)
(9358) tethrateron-turreted-tethratope E100#^^(#^#)>#^^####100 \(f_{\varphi(\omega,\varphi(4,0))}(100)\)
(9359) tethrapeton-turreted-tethratope E100#^^(#^#)>(#^^#^5)100 \(f_{\varphi(\omega,\varphi(5,0))}(100)\)
(9360) tethrahexon-turreted-tethratope E100#^^(#^#)>(#^^#^6)100 \(f_{\varphi(\omega,\varphi(6,0))}(100)\)
(9361) tethrahepton-turreted-tethratope E100#^^(#^#)>(#^^#^7)100 \(f_{\varphi(\omega,\varphi(7,0))}(100)\)
(9362) tethra-ogdon-turreted-tethratope E100#^^(#^#)>(#^^#^8)100 \(f_{\varphi(\omega,\varphi(8,0))}(100)\)
(9363) tethrennon-turreted-tethratope E100#^^(#^#)>(#^^#^9)100 \(f_{\varphi(\omega,\varphi(9,0))}(100)\)
(9364) tethradekon-turreted-tethratope E100#^^(#^#)>(#^^#^10)100 \(f_{\varphi(\omega,\varphi(10,0))}(100)\)
(9365) dustaculated-tethratope E100#^^(#^#)>#^^(#^#)100 \(f_{\varphi(\omega,\varphi(\omega,0))}(100)\)
(9366) tristaculated-tethratope E100#^^(#^#)>#^^(#^#)>#^^(#^#)100 \(f_{\varphi(\omega,\varphi(\omega,\varphi(\omega,0)))}(100)\)
(9367) tetrastaculated-tethratope E100#^^(#^#)>#^^(#^#)>#^^(#^#)>#^^(#^#)100

= E100#^^(#^#*#)4

\(f_{\varphi(\omega,\varphi(\omega,\varphi(\omega,\varphi(\omega,0))))}(100) = f_{\varphi(\omega+1,0)[4]}(100)\)
(9368) pentastaculated-tethratope E100#^^(#^#*#)5 \(f_{\varphi(\omega+1,0)[5]}(100)\)
(9369) hexastaculated-tethratope E100#^^(#^#*#)6 \(f_{\varphi(\omega+1,0)[6]}(100)\)
(9370) heptastaculated-tethratope E100#^^(#^#*#)7 \(f_{\varphi(\omega+1,0)[7]}(100)\)
(9371) ogdastaculated-tethratope E100#^^(#^#*#)8 \(f_{\varphi(\omega+1,0)[8]}(100)\)
(9372) ennastaculated-tethratope E100#^^(#^#*#)9 \(f_{\varphi(\omega+1,0)[9]}(100)\)
(9373) dekastaculated-tethratope E100#^^(#^#*#)10 \(f_{\varphi(\omega+1,0)[10]}(100)\)

E100#^^(#^#*#)100 - E100#^^(#^#*#^#)100

Extension step 1: tethratopothoth
2: tethratopocross etc.

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9374) tethratopothoth E100#^^(#^#*#)100 \(f_{\varphi(\omega+1,0)}(100)\)
tethratopothothigong E100000#^^(#^#*#)100000 \(f_{\varphi(\omega+1,0)}(100\,000)\)
terrible tethratopothoth E100(#^^(#^#*#))^^#100 \(f_{\varepsilon_{\varphi(\omega+1,0)}+1}(100)\)
territoped tethratopothoth E100(#^^(#^#*#))^^(#^#)100 \(f_{\varphi(\omega,{\varphi(\omega+1,0)}+1)}(100)\)
tethradeutertopothoth E100(#^^(#^#*#))^^(#^#*#)100 \(f_{\varphi(\omega+1,1)}(100)\)
tethritertopothoth E100#^^(#^#*#)>#100 \(f_{\varphi(\omega+1,\omega)}(100)\)
tethratope turreted tethratopothoth E100#^^(#^#*#)>#^^(#^#)100 \(f_{\varphi(\omega+1,\varphi(\omega,0))}(100)\)
(9375) dustaculated-tethratopothoth E100#^^(#^#*#)>#^^(#^#*#)100 \(f_{\varphi(\omega+1,\varphi(\omega+1,0))}(100)\)
(9376) tristaculated-tethratopothoth E100#^^(#^#*#)>#^^(#^#*#)>#^^(#^#*#)100

= E100#^^(#^#*##)3

\(f_{\varphi(\omega+1,\varphi(\omega+1,\varphi(\omega+1,0)))}(100)\)
(9377) tetrastaculated-tethratopothoth E100#^^(#^#*#)>#^^(#^#*#)>#^^(#^#*#)>#^^(#^#*#)100

= E100#^^(#^#*##)4

\(f_{\varphi(\omega+2,0)[4]}(100)\)
(9378) pentastaculated-tethratopothoth E100#^^(#^#*##)5 \(f_{\varphi(\omega+2,0)[5]}(100)\)
(9379) hexastaculated-tethratopothoth E100#^^(#^#*##)6 \(f_{\varphi(\omega+2,0)[6]}(100)\)
(9380) heptastaculated-tethratopothoth E100#^^(#^#*##)7 \(f_{\varphi(\omega+2,0)[7]}(100)\)
(9381) ogdastaculated-tethratopothoth E100#^^(#^#*##)8 \(f_{\varphi(\omega+2,0)[8]}(100)\)
(9382) ennastaculated-tethratopothoth E100#^^(#^#*##)9 \(f_{\varphi(\omega+2,0)[9]}(100)\)
(9383) dekastaculated-tethratopothoth E100#^^(#^#*##)10 \(f_{\varphi(\omega+2,0)[10]}(100)\)
(extension step 2) (9384) tethratopocross E100#^^(#^#*##)100 \(f_{\varphi(\omega+2,0)}(100)\)
territopothothated tethratopocross E100(#^^(#^#*##))^^(#^#*#)100 \(f_{\varphi(\omega+1,{\varphi(\omega+2,0)}+1)}(100)\)
(9385) tethradutopocross E100(#^^(#^#*##))^^(#^#*##)100 \(f_{\varphi(\omega+2,1)}(100)\)
(9386) tethritertopocross E100#^^(#^#*##)>#100 \(f_{\varphi(\omega+2,\omega)}(100)\)
(9387) godgahlah-turreted-tethratopocross E100#^^(#^#*##)>#^#100 \(f_{\varphi(\omega+2,\omega^{\omega})}(100)\)
tethrathoth-turreted-tethratopocross E100#^^(#^#*##)>#^^#100 \(f_{\varphi(\omega+2,\varepsilon_0)}(100)\)
(9388) dustaculated-tethratopocross E100#^^(#^#*##)>#^^(#^#*##)100 \(f_{\varphi(\omega+2,\varphi(\omega+2,0))}(100)\)
(9389) tristaculated-tethratopocross E100#^^(#^#*##)>#^^(#^#*##)>#^^(#^#*##)100

= E100#^^(#^#*###)3

\(f_{\varphi(\omega+2,\varphi(\omega+2,\varphi(\omega+2,0)))}(100)\)
(9390) tetrastaculated-tethratopocross E100#^^(#^#*##)>#^^(#^#*##)>#^^(#^#*##)>#^^(#^#*##)100

= E100#^^(#^#*###)4

\(f_{\varphi(\omega+3,0)[4]}(100)\)
(9391) pentastaculated-tethratopocross E100#^^(#^#*###)5 \(f_{\varphi(\omega+3,0)[5]}(100)\)
(9392) hexastaculated-tethratopocross E100#^^(#^#*###)6 \(f_{\varphi(\omega+3,0)[6]}(100)\)
(9393) heptastaculated-tethratopocross E100#^^(#^#*###)7 \(f_{\varphi(\omega+3,0)[7]}(100)\)
(9394) ogdastaculated-tethratopocross E100#^^(#^#*###)8 \(f_{\varphi(\omega+3,0)[8]}(100)\)
(9395) ennastaculated-tethratopocross E100#^^(#^#*###)9 \(f_{\varphi(\omega+3,0)[9]}(100)\)
(9396) dekastaculated-tethratopocross E100#^^(#^#*###)10 \(f_{\varphi(\omega+3,0)[10]}(100)\)
(Step 3) (9397) tethratopocubor E100#^^(#^#*###)100 \(f_{\varphi(\omega+3,0)}(100)\)
territoposquared tethratopocubor E100(#^^(#^#*###))^^(#^#*##)100 \(f_{\varphi(\omega+2,{\varphi(\omega+3,0)}+1)}(100)\)
(9398) tethradutopocubor E100(#^^(#^#*###))^^(#^#*###)100 \(f_{\varphi(\omega+3,1)}(100)\)
tethratritopocubor E100((#^^(#^#*###))^^(#^#*###))^^(#^#*###)100 \(f_{\varphi(\omega+3,2)}(100)\)
(9399) tethritertopocubor E100#^^(#^#*###)>#100 \(f_{\varphi(\omega+3,\omega)}(100)\)
(9400) godgahlah-turreted-tethratopocubor E100#^^(#^#*###)>#^#100 \(f_{\varphi(\omega+3,\omega^{\omega})}(100)\)
tethrathoth-turreted-tethratopocubor E100#^^(#^#*###)>#^^#100 \(f_{\varphi(\omega+3,\varepsilon_0)}(100)\)
(9401) dustaculated-tethratopocubor E100#^^(#^#*###)>#^^(#^#*###)100 \(f_{\varphi(\omega+3,\varphi(\omega+3,0))}(100)\)
(9402) tristaculated-tethratopocubor E100#^^(#^#*###)>#^^(#^#*###)>#^^(#^#*###)100

= E100#^^(#^#*####)3

\(f_{\varphi(\omega+3,\varphi(\omega+3,\varphi(\omega+3,0)))}(100)\)
(9403) tetrastaculated-tethratopocubor E100#^^(#^#*###)>#^^(#^#*###)>#^^(#^#*###)>#^^(#^#*###)100

= E100#^^(#^#*####)4

\(f_{\varphi(\omega+4,0)[4]}(100)\)
(9404) pentastaculated-tethratopocubor E100#^^(#^#*####)5 \(f_{\varphi(\omega+4,0)[5]}(100)\)
(9405) hexastaculated-tethratopocubor E100#^^(#^#*####)6 \(f_{\varphi(\omega+4,0)[6]}(100)\)
(9406) heptastaculated-tethratopocubor E100#^^(#^#*####)7 \(f_{\varphi(\omega+4,0)[7]}(100)\)
(9407) ogdastaculated-tethratopocubor E100#^^(#^#*####)8 \(f_{\varphi(\omega+4,0)[8]}(100)\)
(9408) ennastaculated-tethratopocubor E100#^^(#^#*####)9 \(f_{\varphi(\omega+4,0)[9]}(100)\)
(9409) dekastaculated-tethratopocubor E100#^^(#^#*####)10 \(f_{\varphi(\omega+4,0)[10]}(100)\)
(9410) tethratopoteron (extension step 4) E100#^^(#^#*####)100 \(f_{\varphi(\omega+4,0)}(100)\)
territopocubed tethratopoteron E100(#^^(#^#*####))^^(#^#*###)100 \(f_{\varphi(\omega+3,{\varphi(\omega+4,0)}+1)}(100)\)
tethradutopoteron E100(#^^(#^#*####))^^(#^#*####)100 \(f_{\varphi(\omega+4,1)}(100)\)
tethritertopoteron E100#^^(#^#*####)>#100 \(f_{\varphi(\omega+4,\omega)}(100)\)
(9411) dustaculated-tethratopoteron E100#^^(#^#*####)>#^^(#^#*####)100 \(f_{\varphi(\omega+4,\varphi(\omega+4,0))}(100)\)
(9412) tristaculated-tethratopoteron E100#^^(#^#*####)>#^^(#^#*####)>#^^(#^#*####)100 \(f_{\varphi(\omega+4,\varphi(\omega+4,\varphi(\omega+4,0)))}(100)\)
(9413) tetrastaculated-tethratopoteron E100#^^(#^#*####)>#^^(#^#*####)>#^^(#^#*####)>#^^(#^#*####)100

= E100#^^(#^#*#^5)4

\(f_{\varphi(\omega+5,0)[4]}(100)\)
(9414) pentastaculated-tethratopoteron E100#^^(#^#*#^5)5 \(f_{\varphi(\omega+5,0)[5]}(100)\)
(9415) hexastaculated-tethratopoteron E100#^^(#^#*#^5)6 \(f_{\varphi(\omega+5,0)[6]}(100)\)
(9416) heptastaculated-tethratopoteron E100#^^(#^#*#^5)7 \(f_{\varphi(\omega+5,0)[7]}(100)\)
(9417) ogdastaculated-tethratopoteron E100#^^(#^#*#^5)8 \(f_{\varphi(\omega+5,0)[8]}(100)\)
(9418) ennastaculated-tethratopoteron E100#^^(#^#*#^5)9 \(f_{\varphi(\omega+5,0)[9]}(100)\)
(9419) dekastaculated-tethratopoteron E100#^^(#^#*#^5)10 \(f_{\varphi(\omega+5,0)[10]}(100)\)
(9420) tethratopopeton (step 5) E100#^^(#^#*#^5)100 \(f_{\varphi(\omega+5,0)}(100)\)
territopotesserated tethratopopeton E100(#^^(#^#*#^5))^^(#^#*####)100 \(f_{\varphi(\omega+4,{\varphi(\omega+5,0)}+1)}(100)\)
tethridutopopeton E100(#^^(#^#*#^5))^^(#^#*#^5)100 \(f_{\varphi(\omega+5,1)}(100)\)
tethritertopopeton E100#^^(#^#*#^5)>#100 \(f_{\varphi(\omega+5,\omega)}(100)\)
(9421) dustaculated-tethratopopeton E100#^^(#^#*#^5)>#^^(#^#*#^5)100 \(f_{\varphi(\omega+5,\varphi(\omega+5,0))}(100)\)
(9422) tristaculated-tethratopopeton E100#^^(#^#*#^5)>#^^(#^#*#^5)>#^^(#^#*#^5)100 \(f_{\varphi(\omega+5,\varphi(\omega+5,\varphi(\omega+5,0)))}(100)\)
(9423) tetrastaculated-tethratopopeton E100#^^(#^#*#^5)>#^^(#^#*#^5)>#^^(#^#*#^5)>#^^(#^#*#^5)100

= E100#^^(#^#*#^6)4

\(f_{\varphi(\omega+6,0)[4]}(100)\)
(9424) pentastaculated-tethratopopeton E100#^^(#^#*#^6)5 \(f_{\varphi(\omega+6,0)[5]}(100)\)
(9425) hexastaculated-tethratopopeton E100#^^(#^#*#^6)6 \(f_{\varphi(\omega+6,0)[6]}(100)\)
(9426) heptastaculated-tethratopopeton E100#^^(#^#*#^6)7 \(f_{\varphi(\omega+6,0)[7]}(100)\)
(9427) ogdastaculated-tethratopopeton E100#^^(#^#*#^6)8 \(f_{\varphi(\omega+6,0)[8]}(100)\)
(9428) ennastaculated-tethratopopeton E100#^^(#^#*#^6)9 \(f_{\varphi(\omega+6,0)[9]}(100)\)
(9429) dekastaculated-tethratopopeton E100#^^(#^#*#^6)10 \(f_{\varphi(\omega+6,0)[10]}(100)\)
(9430) tethratopohexon (step 6) E100#^^(#^#*#^6)100 \(f_{\varphi(\omega+6,0)}(100)\)
territopopenterated tethratopohexon E100(#^^(#^#*#^6))^^(#^#*#^5)100 \(f_{\varphi(\omega+5,{\varphi(\omega+6,0)}+1)}(100)\)
tethradutopohexon E100(#^^(#^#*#^6))^^(#^#*#^6)100 \(f_{\varphi(\omega+6,1)}(100)\)
tethritertopohexon E100#^^(#^#*#^6)>#100 \(f_{\varphi(\omega+6,\omega)}(100)\)
(9431) dustaculated-tethratopohexon E100#^^(#^#*#^6)>#^^(#^#*#^6)100 \(f_{\varphi(\omega+6,\varphi(\omega+6,0))}(100)\)
(9432) tristaculated-tethratopohexon E100#^^(#^#*#^6)>#^^(#^#*#^6)>#^^(#^#*#^6)100 \(f_{\varphi(\omega+6,\varphi(\omega+6,\varphi(\omega+6,0)))}(100)\)
(9433) tetrastaculated-tethratopohexon E100#^^(#^#*#^6)>#^^(#^#*#^6)>#^^(#^#*#^6)>#^^(#^#*#^6)100

= E100#^^(#^#*#^7)4

\(f_{\varphi(\omega+7,0)[4]}(100)\)
(9434) pentastaculated-tethratopohexon E100#^^(#^#*#^7)5 \(f_{\varphi(\omega+7,0)[5]}(100)\)
(9435) hexastaculated-tethratopohexon E100#^^(#^#*#^7)6 \(f_{\varphi(\omega+7,0)[6]}(100)\)
(9436) heptastaculated-tethratopohexon E100#^^(#^#*#^7)7 \(f_{\varphi(\omega+7,0)[7]}(100)\)
(9437) ogdastaculated-tethratopohexon E100#^^(#^#*#^7)8 \(f_{\varphi(\omega+7,0)[8]}(100)\)
(9438) ennastaculated-tethratopohexon E100#^^(#^#*#^7)9 \(f_{\varphi(\omega+7,0)[9]}(100)\)
(9439) dekastaculated-tethratopohexon E100#^^(#^#*#^7)10 \(f_{\varphi(\omega+7,0)[10]}(100)\)
(9440) tethratopohepton (step 7) E100#^^(#^#*#^7)100 \(f_{\varphi(\omega+7,0)}(100)\)
territopohexerated tethratopohepton E100(#^^(#^#*#^7))^^(#^#*#^6)100 \(f_{\varphi(\omega+6,{\varphi(\omega+7,0)}+1)}(100)\)
tethradutopohepton E100(#^^(#^#*#^7))^^(#^#*#^7)100 \(f_{\varphi(\omega+7,1)}(100)\)
tethritertopohepton E100#^^(#^#*#^7)>#100 \(f_{\varphi(\omega+7,\omega)}(100)\)
(9441) dustaculated-tethratopohepton E100#^^(#^#*#^7)>#^^(#^#*#^7)100 \(f_{\varphi(\omega+7,\varphi(\omega+7,0))}(100)\)
(9442) tristaculated-tethratopohepton E100#^^(#^#*#^7)>#^^(#^#*#^7)>#^^(#^#*#^7)100 \(f_{\varphi(\omega+7,\varphi(\omega+7,\varphi(\omega+7,0)))}(100)\)
(9443) tetrastaculated-tethratopohepton E100#^^(#^#*#^7)>#^^(#^#*#^7)>#^^(#^#*#^7)>#^^(#^#*#^7)100

= E100#^^(#^#*#^8)4

\(f_{\varphi(\omega+8,0)[4]}(100)\)
(9444) pentastaculated-tethratopohepton E100#^^(#^#*#^8)5 \(f_{\varphi(\omega+8,0)[5]}(100)\)
(9445) hexastaculated-tethratopohepton E100#^^(#^#*#^8)6 \(f_{\varphi(\omega+8,0)[6]}(100)\)
(9446) heptastaculated-tethratopohepton E100#^^(#^#*#^8)7 \(f_{\varphi(\omega+8,0)[7]}(100)\)
(9447) ogdastaculated-tethratopohepton E100#^^(#^#*#^8)8 \(f_{\varphi(\omega+8,0)[8]}(100)\)
(9448) ennastaculated-tethratopohepton E100#^^(#^#*#^8)9 \(f_{\varphi(\omega+8,0)[9]}(100)\)
(9449) dekastaculated-tethratopohepton E100#^^(#^#*#^8)10 \(f_{\varphi(\omega+8,0)[10]}(100)\)
(9450) tethratopo-ogdon or tethratopo-octon (step 8) E100#^^(#^#*#^8)100 \(f_{\varphi(\omega+8,0)}(100)\)
territopohepterated tethratopo-ogdon E100(#^^(#^#*#^8))^^(#^#*#^7)100 \(f_{\varphi(\omega+7,{\varphi(\omega+8,0)}+1)}(100)\)
tethradutopo-ogdon or territopoocterated tethratopo-ogdon E100(#^^(#^#*#^8))^^(#^#*#^8)100 \(f_{\varphi(\omega+8,1)}(100)\)
tethritertopo-ogdon E100#^^(#^#*#^8)>#100 \(f_{\varphi(\omega+8,\omega)}(100)\)
(9451) dustaculated-tethratopo-ogdon E100#^^(#^#*#^8)>#^^(#^#*#^8)100 \(f_{\varphi(\omega+8,\varphi(\omega+8,0))}(100)\)
(9452) tristaculated-tethratopo-ogdon E100#^^(#^#*#^8)>#^^(#^#*#^8)>#^^(#^#*#^8)100 \(f_{\varphi(\omega+8,\varphi(\omega+8,\varphi(\omega+8,0)))}(100)\)
(9453) tetrastaculated-tethratopo-ogdon E100#^^(#^#*#^8)>#^^(#^#*#^8)>#^^(#^#*#^8)>#^^(#^#*#^8)100

= E100#^^(#^#*#^9)4

\(f_{\varphi(\omega+9,0)[4]}(100)\)
(9454) pentastaculated-tethratopo-ogdon E100#^^(#^#*#^9)5 \(f_{\varphi(\omega+9,0)[5]}(100)\)
(9455) hexastaculated-tethratopo-ogdon E100#^^(#^#*#^9)6 \(f_{\varphi(\omega+9,0)[6]}(100)\)
(9456) heptastaculated-tethratopo-ogdon E100#^^(#^#*#^9)7 \(f_{\varphi(\omega+9,0)[7]}(100)\)
(9457) ogdastaculated-tethratopo-ogdon E100#^^(#^#*#^9)8 \(f_{\varphi(\omega+9,0)[8]}(100)\)
(9458) ennastaculated-tethratopo-ogdon E100#^^(#^#*#^9)9 \(f_{\varphi(\omega+9,0)[9]}(100)\)
(9459) dekastaculated-tethratopo-ogdon E100#^^(#^#*#^9)10 \(f_{\varphi(\omega+9,0)[10]}(100)\)
(9460) tethratopo-ennon (step 9) E100#^^(#^#*#^9)100 \(f_{\varphi(\omega+9,0)}(100)\)
territopoocterated tethratopo-ennon E100(#^^(#^#*#^9))^^(#^#*#^8)100 \(f_{\varphi(\omega+8,{\varphi(\omega+9,0)}+1)}(100)\)
tethradutopo-ennon or territopononerated tethratopo-ennon E100(#^^(#^#*#^9))^^(#^#*#^9)100 \(f_{\varphi(\omega+9,1)}(100)\)
tethritertopo-ennon E100#^^(#^#*#^9)>#100 \(f_{\varphi(\omega+9,\omega)}(100)\)
(9461) dustaculated-tethratopo-ennon E100#^^(#^#*#^9)>#^^(#^#*#^9)100 \(f_{\varphi(\omega+9,\varphi(\omega+9,0))}(100)\)
(9462) tristaculated-tethratopo-ennon E100#^^(#^#*#^9)>#^^(#^#*#^9)>#^^(#^#*#^9)100 \(f_{\varphi(\omega+9,\varphi(\omega+9,\varphi(\omega+9,0)))}(100)\)
(9463) tetrastaculated-tethratopo-ennon E100#^^(#^#*#^9)>#^^(#^#*#^9)>#^^(#^#*#^9)>#^^(#^#*#^9)100

= E100#^^(#^#*#^10)4

\(f_{\varphi(\omega+10,0)[4]}(100)\)
(9464) pentastaculated-tethratopo-ennon E100#^^(#^#*#^10)5 \(f_{\varphi(\omega+10,0)[5]}(100)\)
(9465) hexastaculated-tethratopo-ennon E100#^^(#^#*#^10)6 \(f_{\varphi(\omega+10,0)[6]}(100)\)
(9466) heptastaculated-tethratopo-ennon E100#^^(#^#*#^10)7 \(f_{\varphi(\omega+10,0)[7]}(100)\)
(9467) ogdastaculated-tethratopo-ennon E100#^^(#^#*#^10)8 \(f_{\varphi(\omega+10,0)[8]}(100)\)
(9468) ennastaculated-tethratopo-ennon E100#^^(#^#*#^10)9 \(f_{\varphi(\omega+10,0)[9]}(100)\)
(9469) dekastaculated-tethratopo-ennon E100#^^(#^#*#^10)10 \(f_{\varphi(\omega+10,0)[10]}(100)\)
(9470) tethratopodekon (step 10) E100#^^(#^#*#^10)100 \(f_{\varphi(\omega+10,0)}(100)\)
territopononerated tethratopodekon E100(#^^(#^#*#^10))^^(#^#*#^9)100 \(f_{\varphi(\omega+9,{\varphi(\omega+10,0)}+1)}(100)\)
tethradutopodekon or territopodekerated tethratopodekon E100(#^^(#^#*#^10))^^(#^#*#^10)100 \(f_{\varphi(\omega+10,1)}(100)\)
tethritertopodekon E100#^^(#^#*#^10)>#100 \(f_{\varphi(\omega+10,\omega)}(100)\)
(9471) dustacuated-tethratopodekon E100#^^(#^#*#^10)>#^^(#^#*#^10)100 \(f_{\varphi(\omega+10,\varphi(\omega+10,0))}(100)\)
(9472) tristaculated-tethratopodekon E100#^^(#^#*#^10)>#^^(#^#*#^10)>#^^(#^#*#^10)100 \(f_{\varphi(\omega+10,\varphi(\omega+10,\varphi(\omega+10,0)))}(100)\)
(9473) tetrastaculated-tethratopodekon E100#^^(#^#*#^10)>#^^(#^#*#^10)>#^^(#^#*#^10)>#^^(#^#*#^10)100

= E100#^^(#^#*#^11)4

\(f_{\varphi(\omega+11,0)[4]}(100)\)
(9474) pentastaculated-tethratopodekon E100#^^(#^#*#^11)5 \(f_{\varphi(\omega+11,0)[5]}(100)\)
(9475) hexastaculated-tethratopodekon E100#^^(#^#*#^11)6 \(f_{\varphi(\omega+11,0)[6]}(100)\)
(9476) heptastaculated-tethratopodekon E100^^(#^#*#^11)7 \(f_{\varphi(\omega+11,0)[7]}(100)\)
(9477) ogdastaculated-tethratopodekon E100#^^(#^#*#^11)8 \(f_{\varphi(\omega+11,0)[8]}(100)\)
(9478) ennastaculated-tethratopodekon E100#^^(#^#*#^11)9 \(f_{\varphi(\omega+11,0)[9]}(100)\)
(9479) dekastaculated-tethratopodekon E100#^^(#^#*#^11)10 \(f_{\varphi(\omega+11,0)[10]}(100)\)
(9480) tethratopohendekon (step 11) E100#^^(#^#*#^11)100 \(f_{\varphi(\omega+11,0)}(100)\)
(9481) tethratopododekon (step 12) E100#^^(#^#*#^12)100 \(f_{\varphi(\omega+12,0)}(100)\)
(9482) tethratopotredekon E100#^^(#^#*#^13)100 \(f_{\varphi(\omega+13,0)}(100)\)
(9483) tethratopoterdekon (not to be confused with no. 9482) E100#^^(#^#*#^14)100 \(f_{\varphi(\omega+14,0)}(100)\)
(9484) tethratopopedekon E100#^^(#^#*#^15)100 \(f_{\varphi(\omega+15,0)}(100)\)
(9485) tethratopo-exdekon E100#^^(#^#*#^16)100 \(f_{\varphi(\omega+16,0)}(100)\)
(9486) tethratopo-epdekon E100#^^(#^#*#^17)100 \(f_{\varphi(\omega+17,0)}(100)\)
(9487) tethratopo-ogdekon E100#^^(#^#*#^18)100 \(f_{\varphi(\omega+18,0)}(100)\)
(9488) tethratopo-enndekon E100#^^(#^#*#^19)100 \(f_{\varphi(\omega+19,0)}(100)\)
(9489) tethratopo-icoson (step 20) E100#^^(#^#*#^20)100 \(f_{\varphi(\omega+20,0)}(100)\)
(9490) tethratopotrianton E100#^^(#^#*#^30)100 \(f_{\varphi(\omega+30,0)}(100)\)
(9491) tethratoposaranton E100#^^(#^#*#^40)100 \(f_{\varphi(\omega+40,0)}(100)\)
(9492) tethratopopeninton E100#^^(#^#*#^50)100 \(f_{\varphi(\omega+50,0)}(100)\)
(9493) tethratopo-exinton E100#^^(#^#*#^60)100 \(f_{\varphi(\omega+60,0)}(100)\)
(9494) tethratopo-ebdominton E100#^^(#^#*#^70)100 \(f_{\varphi(\omega+70,0)}(100)\)
(9495) tethratopo-ogdonton E100#^^(#^#*#^80)100 \(f_{\varphi(\omega+80,0)}(100)\)
(9496) tethratopo-eneninton E100#^^(#^#*#^90)100 \(f_{\varphi(\omega+90,0)}(100)\)

E100#^^(#^#*#^#)100 - E100#^^#^##100

Level 1: tethrathoth
Level 2: tethracross
...
Level 100: tethratope
level 101: tethratopothoth
...
etc.
Level 200:

Now entering: tethratopodeus. The suffix -deus has been used in Cascading-E notation, and reused in this notation.

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9497) tethratopodeus or tethratopohecton (level 200) E100#^^(#^#*#^#)100

= E100#^^(#^#*#^100)100

\(f_{\varphi(\omega+100,0)}(100) = f_{\varphi(\omega\times 2,0)}(100)\)
tethratopochillion or tethratopokalon E100#^^(#^#*#^#)1000

= E100#^^(#^#*#^1,000)100

\(f_{\varphi(\omega\times 2,0)}(1\,000)\)
tethratopomyrion or tethratopodakalon E100#^^(#^#*#^#)10000

= E100#^^(#^#*#^10,000)100

\(f_{\varphi(\omega\times 2,0)}(10\,000)\)
tethratopohecatochillion or tethratopohotalon E100#^^(#^#*#^#)100000

= E100#^^(#^#*#^100,000)100

\(f_{\varphi(\omega\times 2,0)}(100\,000)\)
tethratopodeusigong E100,000#^^(#^#*#^#)100000

= E100,000#^^(#^#*#^100,000)100,000

\(f_{\varphi(\omega\times 2,0)}(100\,000)\)
tethratopo-octadion E100#^^(#^#*#^#)10^8

= E100#^^(#^#*#^E8)100

\(f_{\varphi(\omega\times 2,0)}(10^{8})\)
tethratopo-googolope E100#^^(#^#*#^#)10^100

= E100#^^(#^#*#^E100)100

\(f_{\varphi(\omega\times 2,0)}(10^{100})\)
tethratopo-grangolope E100#^^(#^#*#^#)(E100#100) \(f_{\varphi(\omega\times 2,0)}(f_3(100))\)
tethratopo-greagolope E100#^^(#^#*#^#)(E100#100#100) \(f_{\varphi(\omega\times 2,0)}(f_4(100))\)
tethratopo-gugoldope E100#^^(#^#*#^#)(E100##100) \(f_{\varphi(\omega\times 2,0)}(f_{\omega}(100))\)
tethratopo-throogolope E100#^^(#^#*#^#)(E100###100) \(f_{\varphi(\omega\times 2,0)}(f_{\omega^2}(100))\)
tethratopo-godgahlah E100#^^(#^#*#^#)(E100#^#100) \(f_{\varphi(\omega\times 2,0)}(f_{\omega^\omega}(100))\)
tethratopo-godgathor E100#^^(#^#*#^#)(E100#^#^#100) \(f_{\varphi(\omega\times 2,0)}(f_{\omega^{\omega^{\omega}}}(100))\)
tethratopo-tethrathoth E100#^^(#^#*#^#)(E100#^^#100) \(f_{\varphi(\omega\times 2,0)}(f_{\varepsilon_0}(100))\)
tethratopo-tethracross E100#^^(#^#*#^#)(E100#^^##100) \(f_{\varphi(\omega\times 2,0)}(f_{\zeta_0}(100))\)
tethratopo-tethratope E100#^^(#^#*#^#)(E100#^^#^#100) \(f_{\varphi(\omega\times 2,0)}(f_{\varphi(\omega,0)}(100))\)
(9498) grand tethratopodeus or tethratopo-tethratopo-hecton E100#^^(#^#*#^#)100#2

= E100#^^(#^#*#^tethratopodeus)100

\(f_{\varphi(\omega\times 2,0)}^2(100)\)
grand grand tethratopodeus or tethratopo-tethratopo-tethratopo-hecton E100#^^(#^#*#^#)100#3 \(f_{\varphi(\omega\times 2,0)}^3(100)\)
grangol-carta-tethratopodeus E100#^^(#^#*#^#)100#100 \(f_{\varphi(\omega\times 2,0)+1}(100)\)
tethratopodeus-by-deuteron E100#^^(#^#*#^#)100#^^(#^#*#^#)100 \(f_{\varphi(\omega\times 2,0)\times 2}(100)\)
deutero tethratopodeus E100#^^(#^#*#^#)*#^^(#^#*#^#)100 \(f_{\varphi(\omega\times 2,0)^2}(100)\)
tethratopodeusifact E100(#^^(#^#*#^#))^#100 \(f_{\varphi(\omega\times 2,0)^\omega}(100)\)
dutetrated-tethratopodeus E100(#^^(#^#*#^#))^(#^^(#^#*#^#))100 \(f_{\varphi(\omega\times 2,0)^{\varphi(\omega\times 2,0)}}(100)\)
terrible tethratopodeus E100(#^^(#^#*#^#))^^#100 \(f_{\varepsilon_{\varphi(\omega\times 2,0)+1}}(100)\)
territoped tethratopodeus E100(#^^(#^#*#^#))^^(#^#)100 \(f_{\varphi(\omega,\varphi(\omega\times 2,0)+1)}(100)\)
territopothothated tethratopodeus E100(#^^(#^#*#^#))^^(#^#*#)100 \(f_{\varphi(\omega+1,\varphi(\omega\times 2,0)+1)}(100)\)
territopodeusated tethratopodeus E100(#^^(#^#*#^#))^^(#^#*#^#)100 \(f_{\varphi(\omega\times 2,1)}(100)\)
two ex territopodeusated tethratopodeus E100((#^^(#^#*#^#))^^(#^#*#^#))^^(#^#*#^#)100 \(f_{\varphi(\omega\times 2,2)}(100)\)
tethritertopodeus E100#^^(#^#*#^#)>#100 \(f_{\varphi(\omega\times 2,\omega)}(100)\)
tethratope-turreted-tethratopodeus E100#^^(#^#*#^#)>#^^(#^#)100 \(f_{\varphi(\omega\times 2,\varphi(\omega,0))}(100)\)
dustaculated-tethratopodeus E100#^^(#^#*#^#)>#^^(#^#*#^#)100 \(f_{\varphi(\omega\times 2,\varphi(\omega\times 2,0))}(100)\)
(9499) tethratopodeusithoth (201) E100#^^(#^#*#^#*#)100 \(f_{\varphi(\omega\times 2+1,0)}(100)\)
territopodeusated tethratopodeusithoth E100(#^^(#^#*#^#*#))^^(#^#*#^#)100 \(f_{\varphi(\omega\times 2,\varphi(\omega\times 2+1,0)+1)}(100)\)
territopodeusithothated tethratopodeusithoth E100(#^^(#^#*#^#*#))^^(#^#*#^#*#)100 \(f_{\varphi(\omega\times 2+1,1)}(100)\)
dustaculated-tethratopodeusithoth E100#^^(#^#*#^#*#)>#^^(#^#*#^#*#)100 \(f_{\varphi(\omega\times 2+1,\varphi(\omega\times 2+1,0))}(100)\)
(9500) tethratopodeusicross (202) E100^^(#^#*#^#*##)100 \(f_{\varphi(\omega\times 2+2,0)}(100)\)
territopodeusisquared tethratopodeusicross E100(#^^(#^#*#^#*##))^^(#^#*#^#*##)100 \(f_{\varphi(\omega\times 2+2,1)}(100)\)
dustaculated-tethratopodeusicross E100#^^(#^#*#^#*##)>#^^(#^#*#^#*##)100 \(f_{\varphi(\omega\times 2+2,\varphi(\omega\times 2+2,0))}(100)\)
(9501) tethratopodeusicubor (level 103) E100#^^(#^#*#^#*###)100 \(f_{\varphi(\omega\times 2+3,0)}(100)\)
territopodeusicubed tethratopodeusicubor E100(#^^(#^#*#^#*###))^^(#^#*#^#*###)100 \(f_{\varphi(\omega\times 2+3,1)}(100)\)
dustaculated-tethratopodeusicubor E100#^^(#^#*#^#*###)>#^^(#^#*#^#*###)100 \(f_{\varphi(\omega\times 2+3,\varphi(\omega\times 2+3,0))}(100)\)
(9502) tethratopodeusiteron (level 104) E100#^^(#^#*#^#*####)100 \(f_{\varphi(\omega\times 2+4,0)}(100)\)
territopodeusitesserated tethratopodeusiteron E100(#^^(#^#*#^#*####))^^(#^#*#^#*####)100 \(f_{\varphi(\omega\times 2+4,1)}(100)\)
dustaculated-tethratopodeusiteron E100#^^(#^#*#^#*####)>#^^(#^#*#^#*####)100 \(f_{\varphi(\omega\times 2+4,\varphi(\omega\times 2+4,0))}(100)\)
(9503) tethratopodeusipeton (level 205) E100#^^(#^#*#^#*#^5)100 \(f_{\varphi(\omega\times 2+5,0)}(100)\)
territopodeusipenterated tethratopodeusipeton E100(#^^(#^#*#^#*#^5))^^(#^#*#^#*#^5)100 \(f_{\varphi(\omega\times 2+5,1)}(100)\)
(9504) tethratopodeusihexon (level 206) E100#^^(#^#*#^#*#^6)100 \(f_{\varphi(\omega\times 2+6,0)}(100)\)
territopodeusihexerated tethratopodeusihexon E100(#^^(#^#*#^#*#^6))^^(#^#*#^#*#^6)100 \(f_{\varphi(\omega\times 2+6,1)}(100)\)
(9505) tethratopodeusihepton (level 207) E100#^^(#^#*#^#*#^7)100 \(f_{\varphi(\omega\times 2+7,0)}(100)\)
(9506) tethratopodeusi-ogdon (level 208) E100#^^(#^#*#^#*#^8)100 \(f_{\varphi(\omega\times 2+8,0)}(100)\)
(9507) tethratopodeusi-ennon (level 209) E100#^^(#^#*#^#*#^9)100 \(f_{\varphi(\omega\times 2+9,0)}(100)\)
(9508) tethratopodeusidekon (level 210) E100#^^(#^#*#^#*#^10)100 \(f_{\varphi(\omega\times 2+10,0)}(100)\)
tethratopodeusi-icoson (level 220) E100#^^(#^#*#^#*#^20)100 \(f_{\varphi(\omega\times 2+20,0)}(100)\)
tethratopodeusi-trianton (level 230) E100#^^(#^#*#^#*#^20)100 \(f_{\varphi(\omega\times 2+20,0)}(100)\)
(9509) tethratopotruce (level 300) E100#^^(#^#*#^#*#^#)100

= E100#^^(#^#*#^#*#^100)100

\(f_{\varphi(\omega\times 3,0)}(100)\)
(9510) grand tethratopotruce E100#^^(#^#*#^#*#^#)100#2

= E100#^^(#^#*#^#*#^tethratopotruce)100

\(f_{\varphi(\omega\times 3,0)}^2(100)\)
terrible tethratopotruce E100(#^^(#^#*#^#*#^#))^^#100 \(f_{\varepsilon_{\varphi(\omega\times 3,0)+1}}(100)\)
territopotrucated tethratopotruce E100(#^^(#^#*#^#*#^#))^^(#^#*#^#*#^#)100 \(f_{\varphi(\omega\times 3,1)}(100)\)
(9511) tethratopotrucithoth (level 301) E100#^^(#^#*#^#*#^#*#)100 \(f_{\varphi(\omega\times 3+1,0)}(100)\)
(9512) tethratopotrucicross (level 302) E100#^^(#^#*#^#*#^#*##)100 \(f_{\varphi(\omega\times 3+2,0)}(100)\)
(9513) tethratopotrucicubor (level 303) E100#^^(#^#*#^#*#^#*###)100 \(f_{\varphi(\omega\times 3+3,0)}(100)\)
(9514) tethratopotruciteron (level 304) E100#^^(#^#*#^#*#^#*####)100 \(f_{\varphi(\omega\times 3+4,0)}(100)\)
(9515) tethratopotrucipeton (level 305) E100#^^(#^#*#^#*#^#*#^5)100 \(f_{\varphi(\omega\times 3+5,0)}(100)\)
(9516) tethratopotrucihexon (level 306) E100#^^(#^#*#^#*#^#*#^6)100 \(f_{\varphi(\omega\times 3+6,0)}(100)\)
(9517) tethratopotrucihepton (level 307) E100#^^(#^#*#^#*#^#*#^7)100 \(f_{\varphi(\omega\times 3+7,0)}(100)\)
(9518) tethratopotruci-ogdon (level 308) E100#^^(#^#*#^#*#^#*#^8)100 \(f_{\varphi(\omega\times 3+8,0)}(100)\)
(9519) tethratopotruci-ennon (level 309) E100#^^(#^#*#^#*#^#*#^9)100 \(f_{\varphi(\omega\times 3+9,0)}(100)\)
(9520) tethratopotrucidekon (level 310) E100#^^(#^#*#^#*#^#*#^10)100 \(f_{\varphi(\omega\times 3+10,0)}(100)\)
tethratopotrucitre-eneninton (level 393) E100#^^(#^#*#^#*#^#*#^93)100 \(f_{\varphi(\omega\times 3+93,0)}(100)\)
(9521) tethratopoquad (level 400) E100#^^(#^#*#^#*#^#*#^#)100

= E100#^^(#^#*#^#*#^#*#^100)100

\(f_{\varphi(\omega\times 4,0)}(100)\)
(9522) grand tethratopoquad E100#^^(#^#*#^#*#^#*#^#)100#2

= E100#^^(#^#*#^#*#^#*#^tethratopoquad)100

\(f_{\varphi(\omega\times 4,0)}^2(100)\)
terrible tethratopoquad E100(#^^(#^#*#^#*#^#*#^#))^^#100 \(f_{\varepsilon_{\varphi(\omega\times 4,0)+1}}(100)\)
territopoquadated tethratopoquad or tethradeutertopoquad E100(#^^(#^#*#^#*#^#*#^#))^^(#^#*#^#*#^#*#^#)100 \(f_{\varphi(\omega\times 4,1)}(100)\)
dustaculated tethratopoquad E100#^^(#^#*#^#*#^#*#^#)>(#^#*#^#*#^#*#^#)100 \(f_{\varphi(\omega\times 4,\varphi(\omega\times 4,1))}(100)\)
(9523) tethratopoquadithoth (level 401) E100#^^(#^#*#^#*#^#*#^#*#)100 \(f_{\varphi(\omega\times 4+1,0)}(100)\)
(9524) tethratopoquadicross (level 402) E100#^^(#^#*#^#*#^#*#^#*##)100 \(f_{\varphi(\omega\times 4+2,0)}(100)\)
(9525) tethratopoquadicubor (level 403) E100#^^(#^#*#^#*#^#*#^#*###)100 \(f_{\varphi(\omega\times 4+3,0)}(100)\)
(9526) tethratopoquaditeron (level 404) E100#^^(#^#*#^#*#^#*#^#*####)100 \(f_{\varphi(\omega\times 4+4,0)}(100)\)
(9527) dustaculated-tethratopoquaditeron E100#^^(#^#*#^#*#^#*#^#*####)>#^^(#^#*#^#*#^#*#^#*####)100 \(f_{\varphi(\omega\times 4+4,\varphi(\omega\times 4+4,0))}(100)\)
(9528) tethratopoquadipeton (level 405) E100#^^(#^#*#^#*#^#*#^#*#^5)100 \(f_{\varphi(\omega\times 4+5,0)}(100)\)
(9529) tethratopoquadihexon (level 406) E100#^^(#^#*#^#*#^#*#^#*#^6)100 \(f_{\varphi(\omega\times 4+6,0)}(100)\)
(9530) tethratopoquadihepton (level 407) E100#^^(#^#*#^#*#^#*#^#*#^7)100 \(f_{\varphi(\omega\times 4+7,0)}(100)\)
(9531) tethratopoquadi-ogdon (level 408) E100#^^(#^#*#^#*#^#*#^#*#^8)100 \(f_{\varphi(\omega\times 4+8,0)}(100)\)
(9532) tethratopoquadi-ennon (level 409) E100#^^(#^#*#^#*#^#*#^#*#^9)100 \(f_{\varphi(\omega\times 4+9,0)}(100)\)
(9533) tethratopoquadidekon (level 410) E100#^^(#^#*#^#*#^#*#^#*#^10)100 \(f_{\varphi(\omega\times 4+10,0)}(100)\)
tethratopoquadi-hexaogdonton (level 486) E100#^^(#^#*#^#*#^#*#^#*#^86)100 \(f_{\varphi(\omega\times 4+86,0)}(100)\)
(9534) tethratopoquid (level 500) E100#^^#^##5

= E100#^^(#^#*#^#*#^#*#^#*#^#)100

= E100#^^(#^#*#^#*#^#*#^#*#^100)100

\(f_{\varphi(\omega\times 5,0)}(100)\)
(9535) grand tethratopoquid = E100#^^(#^#*#^#*#^#*#^#*#^#)100#2

= E100#^^(#^#*#^#*#^#*#^#*#^tethratopoquid)100

\(f_{\varphi(\omega\times 5,0)}^2(100)\)
tethradeutertopoquid E100(#^^(#^#*#^#*#^#*#^#*#^#))^^(#^#*#^#*#^#*#^#*#^#)100 \(f_{\varphi(\omega\times 5,1)}(100)\)
tethratopoquidithoth (level 501) E100#^^(#^#*#^#*#^#*#^#*#^#*#)100 \(f_{\varphi(\omega\times 5+1,0)}(100)\)
tethratopoquiditetratrianton (level 534) E100#^^(#^#*#^#*#^#*#^#*#^#*#^34)100 \(f_{\varphi(\omega\times 5+34,0)}(100)\)
(9536) tethratoposid (level 600) E100#^^#^##6 \(f_{\varphi(\omega\times 6,0)}(100)\)
tethratoposidi-henexinton (level 661) E100#^^(#^#*#^#*#^#*#^#*#^#*#^#*#^61)100 \(f_{\varphi(\omega\times 6+61,0)}(100)\)
(9537) tethratoposeptuce (level 700) E100#^^#^##7 \(f_{\varphi(\omega\times 7,0)}(100)\)
tethratoposeptuci-hensaranton (level 741) E100#^^(#^#*#^#*#^#*#^#*#^#*#^#*#^#*#^41)100 \(f_{\varphi(\omega\times 7+41,0)}(100)\)
(9538) tethratopo-octuce (level 800) E100#^^#^##8 \(f_{\varphi(\omega\times 8,0)}(100)\)
tethratopooctuci-heptapeninton (level 857) E100#^^((#^##[8])*#^57)100 \(f_{\varphi(\omega\times 8+57,0)}(100)\)
(9539) tethratopononuce (level 900) E100#^^#^##9 \(f_{\varphi(\omega\times 9,0)}(100)\)
tethratoponoci-saranton (level 940) E100#^^((#^##[9])*#^40)100 \(f_{\varphi(\omega\times 9+40,0)}(100)\)
(9540) tethratopodecuce (level 1000) E100#^^#^##10 \(f_{\varphi(\omega\times {10},0)}(100)\)
tethratopodeci-hendekon (level 1011) E100#^^((#^##[10])*#^11)100 \(f_{\varphi(\omega\times {10}+11,0)}(100)\)
(9541) tethratopovigintice (level 2000) E100#^^#^##20 \(f_{\varphi(\omega\times {20},0)}(100)\)
(9542) tethratopotrigintice (level 3000) E100#^^#^##30 \(f_{\varphi(\omega\times {30},0)}(100)\)
(9543) tethratopoquadragintice (level 4000) E100#^^#^##40 \(f_{\varphi(\omega\times {40},0)}(100)\)
tethratopounquadragintice (level 4100) E100#^^#^##41 \(f_{\varphi(\omega\times {41},0)}(100)\)
(9544) tethratopoquinquagintice (level 5000) E100#^^#^##50 \(f_{\varphi(\omega\times {50},0)}(100)\)
(9545) tethratoposexagintice (level 6000) E100#^^#^##60 \(f_{\varphi(\omega\times {60},0)}(100)\)
(9546) tethratoposeptuagintice (level 7000) E100#^^#^##70 \(f_{\varphi(\omega\times {70},0)}(100)\)
(9547) tethratopo-octogintice (level 8000) E100#^^#^##80 \(f_{\varphi(\omega\times {80},0)}(100)\)
(9548) tethratopononagintice (level 9000) E100#^^#^##90 \(f_{\varphi(\omega\times {90},0)}(100)\)
tethratopononaginticeithoth (level 9001, over 9000) E100#^^((#^##[90])*#)100 \(f_{\varphi(\omega\times {90}+1,0)}(100)\)
tethratoponovemnonagintice (level 9900) E100#^^#^##99 \(f_{\varphi(\omega\times {99},0)}(100)\)
tethratoponovemnonagintici-enneneninton (level 9999) E100#^^((#^##[99])*#^99)100 \(f_{\varphi(\omega\times {99}+99,0)}(100)\)

E100#^^#^##100 - E100#^^#^###100

Continuing the trend, the tethra- naming scheme is now at level 10000.

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9549) tethralattitope (level 10,000) E100#^^#^##100 \(f_{\varphi(\omega^2,0)}(100)\)
tethratopomillice E100#^^#^##1000 \(f_{\varphi(\omega^2,0)}(1\,000)\)
tethratopomicrice E100#^^#^##(10^6) \(f_{\varphi(\omega^2,0)}(10^6)\)
tethratopogoogolice E100#^^#^##10^100 \(f_{\varphi(\omega^2,0)}(10^{100})\)
tethratopokillice E100#^^#^##(10^3,000) \(f_{\varphi(\omega^2,0)}(10^{3\,000})\)
tethratopodakallice E100#^^#^##(10^(3*10^30)) \(f_{\varphi(\omega^2,0)}(10^{3\times 10^{30}})\)
tethratopokallice E100#^^#^##(10^(3*10^3000)) \(f_{\varphi(\omega^2,0)}(10^{3\times 10^{3\,000}})\)
tethratopomultice E100#^^#^##(103*103*1042) TBC
(9550) grand tethralattitope E100#^^#^##100#2 \(f_{\varphi(\omega^2,0)}^2(100)\)
terrible tethralattitope E100(#^^#^##)^^#100 \(f_{\varepsilon_{\varphi(\omega^2,0)+1}}(100)\)
tethriterlattitope E100#^^(#^##)>#100 \(f_{\varphi(\omega^2,\omega)}(100)\)
dustaculated tethralattitope E100#^^(#^##)>#^^(#^##)100 \(f_{\varphi(\omega^2,\varphi(\omega^2,0))}(100)\)
(9551) tethralattitopothoth E100#^^(#^##*#)100 \(f_{\varphi(\omega^2+1,0)}(100)\)
(9552) tethralattitopocross E100#^^(#^##*##)100 \(f_{\varphi(\omega^2+2,0)}(100)\)
(9553) tethralattitopocubor E100#^^(#^##*###)100 \(f_{\varphi(\omega^2+3,0)}(100)\)
(9554) tethralattitopoteron E100#^^(#^##*####)100 \(f_{\varphi(\omega^2+4,0)}(100)\)
(9555) tethralattitopopeton E100#^^(#^##*#^5)100 \(f_{\varphi(\omega^2+5,0)}(100)\)
(9556) tethralattitopohexon E100#^^(#^##*#^6)100 \(f_{\varphi(\omega^2+6,0)}(100)\)
(9557) tethralattitopohepton E100#^^(#^##*#^7)100 \(f_{\varphi(\omega^2+7,0)}(100)\)
(9558) tethralattitopo-ogdon E100#^^(#^##*#^8)100 \(f_{\varphi(\omega^2+8,0)}(100)\)
(9559) tethralattitopo-ennon E100#^^(#^##*#^9)100 \(f_{\varphi(\omega^2+9,0)}(100)\)
(9560) tethralattitopodekon E100#^^(#^##*#^10)100 \(f_{\varphi({\omega}^2+{10},0)}(100)\)
(9561) tethralattitopotope E100#^^(#^##*#^#)100 \(f_{\varphi({\omega}^2+{\omega},0)}(100)\)
(9562) grand tethralattitopotope E100#^^(#^##*#^#)100#2 \(f_{\varphi({\omega}^2+{\omega},0)}^2(100)\)
tethriterlattitopotope E100#^^(#^##*#^#)>#100 \(f_{\varphi(\omega^2+{\omega},\omega)}(100)\)
(9563) tethralattitopotopothoth E100#^^(#^##*#^#*#)100 \(f_{\varphi({\omega}^2+{\omega+1},0)}(100)\)
(9564) tethralattitopotopocross E100#^^(#^##*#^#*##)100 \(f_{\varphi({\omega}^2+{\omega+2},0)}(100)\)
(9565) tethralattitopotopodeus (10200) E100#^^(#^##*#^#*#^#)100 \(f_{\varphi({\omega}^2+{\omega\times 2},0)}(100)\)
(9566) tethralattitopotopotruce (10300) E100#^^(#^##*#^#*#^#*#^#)100 \(f_{\varphi({\omega}^2+{\omega\times 3},0)}(100)\)
(9567) tethralattitopotopoquad (10400) E100#^^(#^##*#^#*#^#*#^#*#^#)100 \(f_{\varphi({\omega}^2+{\omega\times 4},0)}(100)\)
(9568) tethralattitopotopoquid (10500) E100#^^(#^##*#^##)5 \(f_{\varphi({\omega}^2+{\omega\times 5},0)}(100)\)
(9569) tethralattitopotoposid (10600) E100#^^(#^##*#^##)6 \(f_{\varphi({\omega}^2+{\omega\times 6},0)}(100)\)
(9570) tethralattitopotoposeptuce (10700) E100#^^(#^##*#^##)7 \(f_{\varphi({\omega}^2+{\omega\times 7},0)}(100)\)
(9571) tethralattitopotopo-octuce (10800) E100#^^(#^##*#^##)8 \(f_{\varphi({\omega}^2+{\omega\times 8},0)}(100)\)
(9572) tethralattitopotopononuce (10900) E100#^^(#^##*#^##)9 \(f_{\varphi({\omega}^2+{\omega\times 9},0)}(100)\)
(9573) tethralattitopotopodecuce (11000) E100#^^(#^##*#^##)10 \(f_{\varphi({\omega}^2+{\omega\times 10},0)}(100)\)
(9574) tethralattitopodeus (20000) E100#^^(#^##*#^##)100 \(f_{\varphi({\omega}^2 \times 2,0)}(100)\)
tethralattitopodeusitope (20100) E100#^^(#^##*#^##*#^#)100 \(f_{\varphi({\omega}^2 \times 2+{\omega},0)}(100)\)
tethralattitopodeusitopodeus (20200) E100#^^(#^##*#^##*#^#*#^#)100 \(f_{\varphi({\omega}^2 \times 2+{\omega\times 2},0)}(100)\)
(9575) tethralattitopotruce (30000) E100#^^(#^##*#^##*#^##)100 \(f_{\varphi({\omega}^2 \times 3,0)}(100)\)
(9576) tethralattitopoquad (40000) E100#^^(#^##*#^##*#^##*#^##)100 \(f_{\varphi({\omega}^2 \times 4,0)}(100)\)
(9577) tethralattitopoquid (50000) E100#^^#^###5 \(f_{\varphi({\omega}^2 \times 5,0)}(100)\)
(9578) tethralattitoposid (60000) E100#^^#^###6 \(f_{\varphi({\omega}^2 \times 6,0)}(100)\)
(9579) tethralattitoposeptuce (70000) E100#^^#^###7 \(f_{\varphi({\omega}^2 \times 7,0)}(100)\)
(9580) tethralattitopo-octuce (80000) E100#^^#^###8 \(f_{\varphi({\omega}^2 \times 8,0)}(100)\)
(9581) tethralattitopononuce (90000) E100#^^#^###9 \(f_{\varphi({\omega}^2 \times 9,0)}(100)\)
(9582) tethralattitopodecuce (100,000) E100#^^#^###10 \(f_{\varphi({\omega}^2 \times {10},0)}(100)\)

E100#^^#^###100 - E100#^^(#^#^7)100

Now at level 1,000,000, prepare to blast off for even more absurd levels!

name of ExE number Extended Cascading-E Notation (definition) Fast-growing hierarchy (approximation)
(9583) tethracubitope E100#^^#^###100 \(f_{\varphi({\omega}^3,0)}(100)\)
tethracubitopotope (1,000,100) E100#^^(#^###*#^#)100 \(f_{\varphi({\omega}^3+{\omega},0)}(100)\)
tethracubitopolattitope (1,010,000) E100#^^(#^###*#^##)100 \(f_{\varphi({\omega}^3+{\omega}^2,0)}(100)\)
(9584) tethracubitopolattitopotope (1,010,100) E100#^^(#^###*#^##*#^#)100 \(f_{\varphi({\omega}^3+{\omega}^2+{\omega},0)}(100)\)
tethracubitopolattitopodeus (1,020,000) E100#^^(#^###*#^##*#^##)100 \(f_{\varphi({\omega}^3+{\omega}^2\times 2,0)}(100)\)
tethracubitopolattitopodecuce (1,100,000) E100#^^(#^###*#^###)10 \(f_{\varphi({\omega}^3+{\omega}^2\times 10,0)}(100)\)
(9585) tethracubitopodeus (2,000,000) E100#^^(#^###*#^###)100 \(f_{\varphi({\omega}^3 \times 2,0)}(100)\)
tethracubitopodeusilattitopoquinquagintice (2,500,000) E100#^^(#^###*#^###*#^###(50))100 TBA
(9586) tethracubitopotruce (3,000,000) E100#^^(#^###*#^###*#^###)100 \(f_{\varphi({\omega}^3 \times 3,0)}(100)\)
(9587) tethracubitopoquad (4,000,000) E100#^^(#^###*#^###*#^###*#^###)100 \(f_{\varphi({\omega}^3 \times 4,0)}(100)\)
(9588) tethracubitopoquid (5,000,000) E100#^^#^####5 \(f_{\varphi({\omega}^3 \times 5,0)}(100)\)
(9589) tethracubitoposid (6,000,000) E100#^^#^####6 \(f_{\varphi({\omega}^3 \times 6,0)}(100)\)
(9590) tethracubitoposeptuce (7,000,000) E100#^^#^####7 \(f_{\varphi({\omega}^3 \times 7,0)}(100)\)
(9591) tethracubitopo-octuce (8,000,000) E100#^^#^####8 \(f_{\varphi({\omega}^3 \times 8,0)}(100)\)
(9592) tethracubitopononuce (9,000,000) E100#^^#^####9 \(f_{\varphi({\omega}^3 \times 9,0)}(100)\)
(9593) tethracubitopodecuce (10,000,000) E100#^^#^####10 \(f_{\varphi({\omega}^3 \times 10,0)}(100)\)
tethracubiquinquagintice (50,000,000) E100#^^#^####50 \(f_{\varphi({\omega}^3 \times 50,0)}(100)\)
(9594) tethraquarticutope (100,000,000) E100#^^#^####100 \(f_{\varphi({\omega}^4,0)}(100)\)
(9595) tethraquarticutopocubitopolattitopotope (101,010,100) E100#^^(#^####*#^###*#^##*#^#)100 TBA
(9596) tethraquarticutopodeus (200,000,000) E100#^^(#^####*#^####)100 \(f_{\varphi({\omega}^4\times 2,0)}(100)\)
(9597) tethraquarticutopotruce E100#^^(#^####*#^####*#^####)100 \(f_{\varphi({\omega}^4\times 3,0)}(100)\)
(9598) tethraquarticutopoquad E100#^^(#^####*#^####*#^####*#^####)100 \(f_{\varphi({\omega}^4\times 4,0)}(100)\)
(9599) tethraquarticutopoquid E100#^^(#^#^5)5 \(f_{\varphi({\omega}^4\times 5,0)}(100)\)
(9600) tethraquarticutoposid E100#^^(#^#^5)6 \(f_{\varphi({\omega}^4\times 6,0)}(100)\)
(9601) tethraquarticutoposeptuce E100#^^(#^#^5)7 \(f_{\varphi({\omega}^4\times 7,0)}(100)\)
(9602) tethraquarticutopo-octuce E100#^^(#^#^5)8 \(f_{\varphi({\omega}^4\times 8,0)}(100)\)
(9603) tethraquarticutopononuce E100#^^(#^#^5)9 \(f_{\varphi({\omega}^4\times 9,0)}(100)\)
(9604) tethraquarticutopodecuce (1,000,000,000) E100#^^(#^#^5)10 \(f_{\varphi({\omega}^4\times 10,0)}(100)\)
tethraquarticutopoquinquagintice (5,000,000,000) E100#^^(#^#^5)50 \(f_{\varphi({\omega}^4 \times 50,0)}(100)\)
(9605) tethraquinticutope (10^10) E100#^^(#^#^5)100 \(f_{\varphi({\omega}^5,0)}(100)\)
tethraquinticutopothoth E100#^^(#^#^5*#)100 \(f_{\varphi({\omega}^{5}+1,0)}(100)\)
tethraquinticutopotope E100#^^(#^#^5*#^#)100 \(f_{\varphi({\omega}^{5}+\omega,0)}(100)\)
(9606) tethraquinticutopoquarticutopocubitopolattitopotope E100#^^(#^#^5*#^####*#^###*#^##*#^#)100 TBA
(9607) tethraquinticutopodeus E100#^^(#^#^5*#^#^5)100 \(f_{\varphi({\omega}^{5}\times 2,0)}(100)\)
(9608) tethraquinticutopotruce E100#^^(#^#^5*#^#^5*#^#^5)100 \(f_{\varphi({\omega}^{5}\times 3,0)}(100)\)
(9609) tethraquinticutopoquad E100#^^(#^#^5*#^#^5*#^#^5*#^#^5)100

= E100#^^(#^#^6)4

\(f_{\varphi({\omega}^{5}\times 4,0)}(100)\)
(9610) tethraquinticutopoquid E100#^^(#^#^6)5 \(f_{\varphi({\omega}^{5}\times 5,0)}(100)\)
(9611) tethraquinticutoposid E100#^^(#^#^6)6 \(f_{\varphi({\omega}^{5}\times 6,0)}(100)\)
(9612) tethraquinticutoposeptuce E100#^^(#^#^6)7 \(f_{\varphi({\omega}^{5}\times 7,0)}(100)\)
(9613) tethraquinticutopo-octuce E100#^^(#^#^6)8 \(f_{\varphi({\omega}^{5}\times 8,0)}(100)\)
(9614) tethraquinticutopononuce E100#^^(#^#^6)9 \(f_{\varphi({\omega}^{5}\times 9,0)}(100)\)
(9615) tethraquinticutopodecuce (10^11) E100#^^(#^#^6)10 \(f_{\varphi({\omega}^{5}\times 10,0)}(100)\)
dustaculated tethraquinticutopodecuce E100#^^(#^#^(6)10>#^#^(6)10)100 \(f_{\varphi({\omega}^{5}\times 10,\varphi({\omega}^{5}\times 10,0))}(100)\)
tethraquinticutopodecucithoth E100#^^(#^#^(6)10*#)100 \(f_{\varphi({\omega}^{5}\times 10 + 1,0)}(100)\)
tethraquinticutopodecucitope E100#^^(#^#^(6)10*#^#)100 \(f_{\varphi({\omega}^{5}\times 10 + \omega,0)}(100)\)
(9616) tethrasexticutope (10^12) E100#^^(#^#^6)100 \(f_{\varphi({\omega}^{6},0)}(100)\)
(9617) tethrasexticutopo-quinticutopoquarticutopocubitopolattitopotope E100#^^(#^#^6*#^#^5*#^####*#^###*#^##*#^#)100 TBA
(9618) tethrasexticutopodeus E100#^^(#^#^6*#^#^6)100 \(f_{\varphi({\omega}^{6}\times 2,0)}(100)\)
(9619) tethrasexticutopotruce E100#^^(#^#^6*#^#^6*#^#^6)100 \(f_{\varphi({\omega}^{6}\times 3,0)}(100)\)
(9620) tethrasexticutopoquad E100#^^(#^#^6*#^#^6*#^#^6*#^#^6)100

= E100#^^(#^#^7)4

\(f_{\varphi({\omega}^{6}\times 4,0)}(100)\)
(9621) tethrasexticutopoquid E100#^^(#^#^7)5 \(f_{\varphi({\omega}^{6}\times 5,0)}(100)\)
(9622) tethrasexticutoposid E100#^^(#^#^7)6 \(f_{\varphi({\omega}^{6}\times 6,0)}(100)\)
(9623) tethrasexticutoposeptuce E100#^^(#^#^7)7 \(f_{\varphi({\omega}^{6}\times 7,0)}(100)\)
(9624) tethrasexticutopo-octuce E100#^^(#^#^7)8 \(f_{\varphi({\omega}^{6}\times 8,0)}(100)\)
(9625) tethrasexticutopononuce E100#^^(#^#^7)9 \(f_{\varphi({\omega}^{6}\times 9,0)}(100)\)
(9626) tethrasexticutopodecuce (10^13) E100#^^(#^#^7)10 \(f_{\varphi({\omega}^{6}\times 10,0)}(100)\)

WIP. Feel free to extend this series by adding more googolisms.

Sources

  1. Original source
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