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The hexaelgathor regiment is a series of numbers from E100(#^#^#^6)100 to E100(#^#^#^7)90 defined using Cascading-E notation (i.e. beginning from hexaelgathor and up to hexaelgathornonagintice).[1] The numbers were coined by Sbiis Saibian.

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Pentaelgathor regiment Heptaelgathor regiment

List of numbers of the regiment

Name of number Cascading-E notation (definition) Fast-growing hierarchy (approximation)
hexaelgathor E100#^#^######100

= E100(#^#^#^6)100

\(f_{\omega^{\omega^{\omega^6}}}(100)\)
grand hexaelgathor E100(#^#^#^6)hexaelgathor \(f_{\omega^{\omega^{\omega^6}}}^2(100)\)
grangol-carta-hexaelgathor E100(#^#^#^6)100#100 \(f_{\omega^{\omega^{\omega^6}}+1}(100)\)
godgahlah-carta-hexaelgathor E100(#^#^#^6)100#^#100 \(f_{\omega^{\omega^{\omega^6}}+\omega^\omega}(100)\)
godgathor-carta-hexaelgathor E100(#^#^#^6)100#^#^#100 \(f_{\omega^{\omega^{\omega^6}}+\omega^{\omega^\omega}}(100)\)
gralgathor-carta-hexaelgathor E100(#^#^#^6)100#^#^##100 \(f_{\omega^{\omega^{\omega^6}}+\omega^{\omega^{\omega^2}}}(100)\)
thraelgathor-carta-hexaelgathor E100(#^#^#^6)100#^#^###100 \(f_{\omega^{\omega^{\omega^6}}+\omega^{\omega^{\omega^3}}}(100)\)
terinngathor-carta-hexaelgathor E100(#^#^#^6)100#^#^####100 \(f_{\omega^{\omega^{\omega^6}}+\omega^{\omega^{\omega^4}}}(100)\)
pentaelgathor-carta-hexaelgathor E100(#^#^#^6)100(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^6}}+\omega^{\omega^{\omega^5}}}(100)\)
hexaeltrigathor E100(#^#^#^6)100(#^#^#^6)100 \(f_{\omega^{\omega^{\omega^6}}2}(100)\)
hexaeltergathor E100(#^#^#^6)100(#^#^#^6)100(#^#^#^6)100

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

\(f_{\omega^{\omega^{\omega^6}}3}(100)\)
hexaelpeggathor E100(#^#^#^6)*#5 \(f_{\omega^{\omega^{\omega^6}}4}(100)\)
hexaelhexgathor E100(#^#^#^6)*#6 \(f_{\omega^{\omega^{\omega^6}}5}(100)\)
hexaelhepgathor E100(#^#^#^6)*#7 \(f_{\omega^{\omega^{\omega^6}}6}(100)\)
hexael-ahtgathor E100(#^#^#^6)*#8 \(f_{\omega^{\omega^{\omega^6}}7}(100)\)
hexael-enngathor E100(#^#^#^6)*#9 \(f_{\omega^{\omega^{\omega^6}}8}(100)\)
hexaeldekagathor E100(#^#^#^6)*#10 \(f_{\omega^{\omega^{\omega^6}}9}(100)\)
hexaelgathor-by-hyperion E100(#^#^#^6)*#100 \(f_{\omega^{\omega^{\omega^6}+1}}(100)\)
hexaelgathor-by-godgahlah E100(#^#^#^6)*#^#100 \(f_{\omega^{\omega^{\omega^6}+\omega}}(100)\)
hexaelgathor-by-godgathor E100(#^#^#^6)*#^#^#100 \(f_{\omega^{\omega^{\omega^6}+\omega^\omega}}(100)\)
hexaelgathor-by-gralgathor E100(#^#^#^6)*#^#^##100 \(f_{\omega^{\omega^{\omega^6}+\omega^{\omega^2}}}(100)\)
hexaelgathor-by-thraelgathor E100(#^#^#^6)*#^#^###100 \(f_{\omega^{\omega^{\omega^6}+\omega^{\omega^3}}}(100)\)
hexaelgathor-by-terinngathor E100(#^#^#^6)*#^#^####100 \(f_{\omega^{\omega^{\omega^6}+\omega^{\omega^4}}}(100)\)
hexaelgathor-by-pentaelgathor E100(#^#^#^6)*(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^6}+\omega^{\omega^5}}}(100)\)
deutero-hexaelgathor E100(#^#^#^6)*(#^#^#^6)100 \(f_{\omega^{\omega^{\omega^6}2}}(100)\)
trito-hexaelgathor E100(#^#^#^6)*(#^#^#^6)*(#^#^#^6)100 \(f_{\omega^{\omega^{\omega^6}3}}(100)\)
teterto-hexaelgathor E100(#^#^#^6)*(#^#^#^6)*(#^#^#^6)*(#^#^#^6)100

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

\(f_{\omega^{\omega^{\omega^6}4}}(100)\)
pepto-hexaelgathor E100#^(#^#^6*#)5 \(f_{\omega^{\omega^{\omega^6}5}}(100)\)
exto-hexaelgathor E100#^(#^#^6*#)6 \(f_{\omega^{\omega^{\omega^6}6}}(100)\)
epto-hexaelgathor E100#^(#^#^6*#)7 \(f_{\omega^{\omega^{\omega^6}7}}(100)\)
ogdo-hexaelgathor E100#^(#^#^6*#)8 \(f_{\omega^{\omega^{\omega^6}8}}(100)\)
ento-hexaelgathor E100#^(#^#^6*#)9 \(f_{\omega^{\omega^{\omega^6}9}}(100)\)
dekato-hexaelgathor E100#^(#^#^6*#)10 \(f_{\omega^{\omega^{\omega^6}10}}(100)\)
isosto-hexaelgathor E100#^(#^#^6*#)20 \(f_{\omega^{\omega^{\omega^6}20}}(100)\)
trianto-hexaelgathor E100#^(#^#^6*#)30 \(f_{\omega^{\omega^{\omega^6}30}}(100)\)
saranto-hexaelgathor E100#^(#^#^6*#)40 \(f_{\omega^{\omega^{\omega^6}40}}(100)\)
peninto-hexaelgathor E100#^(#^#^6*#)50 \(f_{\omega^{\omega^{\omega^6}50}}(100)\)
exinto-hexaelgathor E100#^(#^#^6*#)60 \(f_{\omega^{\omega^{\omega^6}60}}(100)\)
ebdominto-hexaelgathor E100#^(#^#^6*#)70 \(f_{\omega^{\omega^{\omega^6}70}}(100)\)
ogdonto-hexaelgathor E100#^(#^#^6*#)80 \(f_{\omega^{\omega^{\omega^6}80}}(100)\)
eneninto-hexaelgathor E100#^(#^#^6*#)90 \(f_{\omega^{\omega^{\omega^6}90}}(100)\)
hecato-hexaelgathor E100#^(#^#^6*#)100 \(f_{\omega^{\omega^{\omega^6+1}}}(100)\)
hexaelgridgathor E100#^(#^#^6*##)100 \(f_{\omega^{\omega^{\omega^6+2}}}(100)\)
hexaelkubikgathor E100#^(#^#^6*###)100 \(f_{\omega^{\omega^{\omega^6+3}}}(100)\)
hexaelquarticgathor E100#^(#^#^6*####)100 \(f_{\omega^{\omega^{\omega^6+4}}}(100)\)
hexaelgodgathgathor E100#^(#^#^6*#^#)100 \(f_{\omega^{\omega^{\omega^6+\omega}}}(100)\)
hexaelgralgathgathor E100#^(#^#^6*#^##)100 \(f_{\omega^{\omega^{\omega^6+\omega^2}}}(100)\)
hexaelthraelgathgathor E100#^(#^#^6*#^###)100 \(f_{\omega^{\omega^{\omega^6+\omega^3}}}(100)\)
hexaelterinngathgathor E100#^(#^#^6*#^####)100 \(f_{\omega^{\omega^{\omega^6+\omega^4}}}(100)\)
hexaelpentaelgathgathor E100#^(#^#^6*#^#^5)100 \(f_{\omega^{\omega^{\omega^6+\omega^5}}}(100)\)
hexaelgathordeus E100#^(#^#^6*#^#^6)100 \(f_{\omega^{\omega^{\omega^62}}}(100)\)
hexaelgathortruce E100#^(#^#^6*#^#^6*#^#^6)100 \(f_{\omega^{\omega^{\omega^63}}}(100)\)
hexaelgathorquad E100#^(#^#^6*#^#^6*#^#^6*#^#^6)100 = E100(#^#^#^7)4 \(f_{\omega^{\omega^{\omega^64}}}(100)\)
hexaelgathorquid E100(#^#^#^7)5 \(f_{\omega^{\omega^{\omega^65}}}(100)\)
hexaelgathorsid E100(#^#^#^7)6 \(f_{\omega^{\omega^{\omega^66}}}(100)\)
hexaelgathorseptuce E100(#^#^#^7)7 \(f_{\omega^{\omega^{\omega^67}}}(100)\)
hexaelgathoroctuce E100(#^#^#^7)8 \(f_{\omega^{\omega^{\omega^68}}}(100)\)
hexaelgathornonice E100(#^#^#^7)9 \(f_{\omega^{\omega^{\omega^69}}}(100)\)
hexaelgathordecice E100(#^#^#^7)10 \(f_{\omega^{\omega^{\omega^610}}}(100)\)
hexaelgathorvigintice E100(#^#^#^7)20 \(f_{\omega^{\omega^{\omega^620}}}(100)\)
hexaelgathortrigintice E100(#^#^#^7)30 \(f_{\omega^{\omega^{\omega^630}}}(100)\)
hexaelgathorquadragintice E100(#^#^#^7)40 \(f_{\omega^{\omega^{\omega^640}}}(100)\)
hexaelgathorquinquagintice E100(#^#^#^7)50 \(f_{\omega^{\omega^{\omega^650}}}(100)\)
hexaelgathorsexagintice E100(#^#^#^7)60 \(f_{\omega^{\omega^{\omega^660}}}(100)\)
hexaelgathorseptuagintice E100(#^#^#^7)70 \(f_{\omega^{\omega^{\omega^670}}}(100)\)
hexaelgathoroctogintice E100(#^#^#^7)80 \(f_{\omega^{\omega^{\omega^680}}}(100)\)
hexaelgathornonagintice E100(#^#^#^7)90 \(f_{\omega^{\omega^{\omega^690}}}(100)\)

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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