## FANDOM

10,673 Pages

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 $$f_{\varphi(\omega,\omega\times 3)}(100)$$

= 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

$$f_{\varphi(\omega\times 2,0)}(100\,000)$$

= 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 $$f_{\varphi(\omega\times 3+93,0)}(100)$$

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

$$f_{\varphi(\omega\times 4,0)}(100)$$

$$f_{\varphi(\omega\times 4,0)}^2(100)$$
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 $$f_{\varphi({\omega}^{5}\times 3,0)}(100)$$

= 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 $$f_{\varphi({\omega}^{6}\times 3,0)}(100)$$

= 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
Community content is available under CC-BY-SA unless otherwise noted.