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The heptaelgathor regiment is a series of numbers from E100(#^#^#^7)100 to E100(#^#^#^8)90 defined using Cascading-E notation (i.e. beginning from heptaelgathor and up to heptaelgathornonagintice).[1] The numbers were coined by Sbiis Saibian.

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List of numbers of the regiment

Name of number Cascading-E notation (definition) Fast-growing hierarchy (approximation)
heptaelgathor E100#^#^#######100 = E100(#^#^#^7)100 \(f_{\omega^{\omega^{\omega^7}}}(100)\)
grand heptaelgathor E100(#^#^#^7)100#2 \(f_{\omega^{\omega^{\omega^7}}}^2(100)\)
grangol-carta-heptaelgathor E100(#^#^#^7)100#100 \(f_{\omega^{\omega^{\omega^7}}+1}(100)\)
godgahlah-carta-heptaelgathor E100(#^#^#^7)100#^#100 \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega}}(100)\)
godgathor-carta-heptaelgathor E100(#^#^#^7)100#^#^#100 \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^\omega}}(100)\)
gralgathor-carta-heptaelgathor E100(#^#^#^7)100#^#^##100 \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^{\omega^2}}}(100)\)
thraelgathor-carta-heptaelgathor E100(#^#^#^7)100#^#^###100 \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^{\omega^3}}}(100)\)
terinngathor-carta-heptaelgathor E100(#^#^#^7)100#^#^####100 \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^{\omega^4}}}(100)\)
pentaelgathor-carta-heptaelgathor E100(#^#^#^7)100(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^{\omega^5}}}(100)\)
hexaelgathor-carta-heptaelgathor E100(#^#^#^7)100(#^#^#^6)100 \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^{\omega^6}}}(100)\)
heptaeltrigathor E100(#^#^#^7)100(#^#^#^7)100 \(f_{\omega^{\omega^{\omega^7}}2}(100)\)
heptaeltergathor E100(#^#^#^7)*#4 \(f_{\omega^{\omega^{\omega^7}}3}(100)\)
heptaelpeggathor E100(#^#^#^7)*#5 \(f_{\omega^{\omega^{\omega^7}}4}(100)\)
heptaelhexgathor E100(#^#^#^7)*#6 \(f_{\omega^{\omega^{\omega^7}}5}(100)\)
heptaelhepgathor E100(#^#^#^7)*#7 \(f_{\omega^{\omega^{\omega^7}}6}(100)\)
heptael-ahtgathor E100(#^#^#^7)*#8 \(f_{\omega^{\omega^{\omega^7}}7}(100)\)
heptael-enngathor E100(#^#^#^7)*#9 \(f_{\omega^{\omega^{\omega^7}}8}(100)\)
heptaeldekagathor E100(#^#^#^7)*#10 \(f_{\omega^{\omega^{\omega^7}}9}(100)\)
heptaelgathor-by-hyperion E100(#^#^#^7)*#100 \(f_{\omega^{\omega^{\omega^7}+1}}(100)\)
heptaelgathor-by-godgahlah E100(#^#^#^7)*#^#100 \(f_{\omega^{\omega^{\omega^7}+\omega}}(100)\)
heptaelgathor-by-godgathor E100(#^#^#^7)*#^#^#100 \(f_{\omega^{\omega^{\omega^7}+\omega^\omega}}(100)\)
heptaelgathor-by-gralgathor E100(#^#^#^7)*#^#^##100 \(f_{\omega^{\omega^{\omega^7}+\omega^{\omega^2}}}(100)\)
heptaelgathor-by-thraelgathor E100(#^#^#^7)*#^#^###100 \(f_{\omega^{\omega^{\omega^7}+\omega^{\omega^3}}}(100)\)
heptaelgathor-by-terinngathor E100(#^#^#^7)*#^#^####100 \(f_{\omega^{\omega^{\omega^7}+\omega^{\omega^4}}}(100)\)
heptaelgathor-by-pentaelgathor E100(#^#^#^7)*(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^7}+\omega^{\omega^5}}}(100)\)
heptaelgathor-by-hexaelgathor E100(#^#^#^7)*(#^#^#^6)100 \(f_{\omega^{\omega^{\omega^7}+\omega^{\omega^6}}}(100)\)
deutero-heptaelgathor E100(#^#^#^7)*(#^#^#^7)100 \(f_{\omega^{\omega^{\omega^7}2}}(100)\)
trito-heptaelgathor E100(#^#^#^7)*(#^#^#^7)*(#^#^#^7)100 \(f_{\omega^{\omega^{\omega^7}3}}(100)\)
teterto-heptaelgathor E100#^(#^#^7*#)4 \(f_{\omega^{\omega^{\omega^7}4}}(100)\)
pepto-heptaelgathor E100#^(#^#^7*#)5 \(f_{\omega^{\omega^{\omega^7}5}}(100)\)
exto-heptaelgathor E100#^(#^#^7*#)6 \(f_{\omega^{\omega^{\omega^7}6}}(100)\)
epto-heptaelgathor E100#^(#^#^7*#)7 \(f_{\omega^{\omega^{\omega^7}7}}(100)\)
ogdo-heptaelgathor E100#^(#^#^7*#)8 \(f_{\omega^{\omega^{\omega^7}8}}(100)\)
ento-heptaelgathor E100#^(#^#^7*#)9 \(f_{\omega^{\omega^{\omega^7}9}}(100)\)
dekato-heptaelgathor E100#^(#^#^7*#)10 \(f_{\omega^{\omega^{\omega^7}10}}(100)\)
isosto-heptaelgathor E100#^(#^#^7*#)20 \(f_{\omega^{\omega^{\omega^7}20}}(100)\)
trianto-heptaelgathor E100#^(#^#^7*#)30 \(f_{\omega^{\omega^{\omega^7}30}}(100)\)
saranto-heptaelgathor E100#^(#^#^7*#)40 \(f_{\omega^{\omega^{\omega^7}40}}(100)\)
peninto-heptaelgathor E100#^(#^#^7*#)50 \(f_{\omega^{\omega^{\omega^7}50}}(100)\)
exinto-heptaelgathor E100#^(#^#^7*#)60 \(f_{\omega^{\omega^{\omega^7}60}}(100)\)
ebdominto-heptaelgathor E100#^(#^#^7*#)70 \(f_{\omega^{\omega^{\omega^7}70}}(100)\)
ogdonto-heptaelgathor E100#^(#^#^7*#)80 \(f_{\omega^{\omega^{\omega^7}80}}(100)\)
eneninto-heptaelgathor E100#^(#^#^7*#)90 \(f_{\omega^{\omega^{\omega^7}90}}(100)\)
hecato-heptaelgathor E100#^(#^#^7*#)100 \(f_{\omega^{\omega^{\omega^7+1}}}(100)\)
heptaelgridgathor E100#^(#^#^7*##)100 \(f_{\omega^{\omega^{\omega^7+2}}}(100)\)
heptaelkubikgathor E100#^(#^#^7*###)100 \(f_{\omega^{\omega^{\omega^7+3}}}(100)\)
heptaelquarticgathor E100#^(#^#^7*####)100 \(f_{\omega^{\omega^{\omega^7+4}}}(100)\)
heptaelgodgathgathor E100#^(#^#^7*#^#)100 \(f_{\omega^{\omega^{\omega^7+\omega}}}(100)\)
heptaelgralgathgathor E100#^(#^#^7*#^##)100 \(f_{\omega^{\omega^{\omega^7+\omega^2}}}(100)\)
heptaelthraelgathgathor E100#^(#^#^7*#^###)100 \(f_{\omega^{\omega^{\omega^7+\omega^3}}}(100)\)
heptaelterinngathgathor E100#^(#^#^7*#^####)100 \(f_{\omega^{\omega^{\omega^7+\omega^4}}}(100)\)
heptaelpentaelgathgathor E100#^(#^#^7*#^#^5)100 \(f_{\omega^{\omega^{\omega^7+\omega^5}}}(100)\)
heptaelhexaelgathgathor E100#^(#^#^7*#^#^6)100 \(f_{\omega^{\omega^{\omega^7+\omega^6}}}(100)\)
heptaelgathordeus E100#^(#^#^7*#^#^7)100 \(f_{\omega^{\omega^{\omega^72}}}(100)\)
heptaelgathortruce E100#^(#^#^7*#^#^7*#^#^7)100 \(f_{\omega^{\omega^{\omega^73}}}(100)\)
heptaelgathorquad E100(#^#^#^8)4 \(f_{\omega^{\omega^{\omega^74}}}(100)\)
heptaelgathorquid E100(#^#^#^8)5 \(f_{\omega^{\omega^{\omega^75}}}(100)\)
heptaelgathorsid E100(#^#^#^8)6 \(f_{\omega^{\omega^{\omega^76}}}(100)\)
heptaelgathorseptuce E100(#^#^#^8)7 \(f_{\omega^{\omega^{\omega^77}}}(100)\)
heptaelgathoroctuce E100(#^#^#^8)8 \(f_{\omega^{\omega^{\omega^78}}}(100)\)
heptaelgathornonice E100(#^#^#^8)9 \(f_{\omega^{\omega^{\omega^79}}}(100)\)
heptaelgathordecice E100(#^#^#^8)10 \(f_{\omega^{\omega^{\omega^710}}}(100)\)
heptaelgathorvigintice E100(#^#^#^8)20 \(f_{\omega^{\omega^{\omega^720}}}(100)\)
heptaelgathortrigintice E100(#^#^#^8)30 \(f_{\omega^{\omega^{\omega^730}}}(100)\)
heptaelgathorquadragintice E100(#^#^#^8)40 \(f_{\omega^{\omega^{\omega^740}}}(100)\)
heptaelgathorquinquagintice E100(#^#^#^8)50 \(f_{\omega^{\omega^{\omega^750}}}(100)\)
heptaelgathorsexagintice E100(#^#^#^8)60 \(f_{\omega^{\omega^{\omega^760}}}(100)\)
heptaelgathorseptuagintice E100(#^#^#^8)70 \(f_{\omega^{\omega^{\omega^770}}}(100)\)
heptaelgathoroctogintice E100(#^#^#^8)80 \(f_{\omega^{\omega^{\omega^780}}}(100)\)
heptaelgathornonagintice E100(#^#^#^8)90 \(f_{\omega^{\omega^{\omega^790}}}(100)\)

Sources

  1. Saibian, Sbiis. Cascading-E Numbers. Retrieved 2017-10-13.
Saibian's regiments

Hyper-E regiments: Guppy regiment · Grangol regiment · Greagol regiment · Gigangol regiment · Gorgegol regiment · Gulgol regiment · Gaspgol regiment · Ginorgol regiment · Gargantuul regiment · Googondol regiment
Extended Hyper-E regiments: Gugold regiment · Graatagold regiment · Greegold regiment · Grinningold regiment · Golaagold regiment · Gruelohgold regiment · Gaspgold regiment · Ginorgold regiment · Gargantuuld regiment · Googondold regiment · Gugolthra regiment · Throogol regiment · Tetroogol regiment · Pentoogol regiment · Hexoogol regiment · Heptoogol regiment · Ogdoogol regiment · Entoogol regiment · Dektoogol regiment
Cascading-E regiments: Godgahlah regiment · Gridgahlah regiment · Kubikahlah regiment · Quarticahlah regiment · Quinticahlah regiment · Sexticahlah regiment · Septicahlah regiment · Octicahlah regiment · Nonicahlah regiment · Decicahlah regiment · Godgathor regiment · Gralgathor regiment · Thraelgathor regiment · Terinngathor regiment · Pentaelgathor regiment · Hexaelgathor regiment · Heptaelgathor regiment · Octaelgathor regiment · Ennaelgathor regiment · Dekaelgathor regiment · Godtothol regiment · Godtertol regiment · Godtopol regiment · Godhathor regiment · Godheptol regiment · Godoctol regiment · Godentol regiment · Goddekathol regiment
Extended Cascading-E regiments: Tethrathoth regiment · Monster-Giant regiment · Tethriterator regiment · Tethracross regiment · Tethracubor regiment · Tethrateron regiment · Tethrapeton regiment · Tethrahexon regiment · Tethrahepton regiment · Tethra-ogdon regiment · Tethrennon regiment · Tethradekon regiment · Tethratope regiment · Pentacthulhum regiment · Pentacthulcross regiment · Pentacthulcubor regiment · Pentacthulteron regiment · Pentacthulpeton regiment · Pentacthulhexon regiment · Pentacthulhepton regiment · Pentacthul-ogdon regiment · Pentacthulennon regiment · Pentacthuldekon regiment · Pentacthultope regiment · Hexacthulhum super regiment · Heptacthulhum super regiment · Ogdacthulhum super regiment · Ennacthulhum super regiment · Dekacthulhum super regiment

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