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The octaelgathor regiment is a series of numbers from E100(#^#^#^8)100 to E100(#^#^#^9)90 defined using Cascading-E notation (i.e. beginning from octaelgathor and up to octaelgathornonagintice).[1] The numbers were coined by Sbiis Saibian.

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Heptaelgathor regiment Ennaelgathor regiment

List of numbers of the regiment Edit

Name of number Cascading-E notation (definition) Fast-growing hierarchy (approximation)
octaelgathor E100(#^#^#^8)100 \(f_{\omega^{\omega^{\omega^8}}}(100)\)
grand octaelgathor E100(#^#^#^8)100#2 \(f_{\omega^{\omega^{\omega^8}}}^2(100)\)
grangol-carta-octaelgathor E100(#^#^#^8)100#100 \(f_{\omega^{\omega^{\omega^8}}+1}(100)\)
godgahlah-carta-octaelgathor E100(#^#^#^8)100#^#100 \(f_{\omega^{\omega^{\omega^8}}+\omega^{\omega}}(100)\)
godgathor-carta-octaelgathor E100(#^#^#^8)100#^#^#100 \(f_{\omega^{\omega^{\omega^8}}+\omega^{\omega^\omega}}(100)\)
gralgathor-carta-octaelgathor E100(#^#^#^8)100#^#^##100 \(f_{\omega^{\omega^{\omega^8}}+\omega^{\omega^{\omega^2}}}(100)\)
thraelgathor-carta-octaelgathor E100(#^#^#^8)100#^#^###100 \(f_{\omega^{\omega^{\omega^8}}+\omega^{\omega^{\omega^3}}}(100)\)
terinngathor-carta-octaelgathor E100(#^#^#^8)100#^#^####100 \(f_{\omega^{\omega^{\omega^8}}+\omega^{\omega^{\omega^4}}}(100)\)
pentaelgathor-carta-octaelgathor E100(#^#^#^8)100(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^8}}+\omega^{\omega^{\omega^5}}}(100)\)
hexaelgathor-carta-octaelgathor E100(#^#^#^8)100(#^#^#^6)100 \(f_{\omega^{\omega^{\omega^8}}+\omega^{\omega^{\omega^6}}}(100)\)
heptaelgathor-carta-octaelgathor E100(#^#^#^8)100(#^#^#^7)100 \(f_{\omega^{\omega^{\omega^8}}+\omega^{\omega^{\omega^7}}}(100)\)
octaeltrigathor E100(#^#^#^8)100(#^#^#^8)100 \(f_{\omega^{\omega^{\omega^8}}2}(100)\)
octaeltergathor E100(#^#^#^8)*#4 \(f_{\omega^{\omega^{\omega^8}}3}(100)\)
octaelpeggathor E100(#^#^#^8)*#5 \(f_{\omega^{\omega^{\omega^8}}4}(100)\)
octaelhexgathor E100(#^#^#^8)*#6 \(f_{\omega^{\omega^{\omega^8}}5}(100)\)
octaelhepgathor E100(#^#^#^8)*#7 \(f_{\omega^{\omega^{\omega^8}}6}(100)\)
octael-ahtgathor E100(#^#^#^8)*#8 \(f_{\omega^{\omega^{\omega^8}}7}(100)\)
octael-enngathor E100(#^#^#^8)*#9 \(f_{\omega^{\omega^{\omega^8}}8}(100)\)
octaeldekagathor E100(#^#^#^8)*#10 \(f_{\omega^{\omega^{\omega^8}}9}(100)\)
octaelgathor-by-hyperion E100(#^#^#^8)*#100 \(f_{\omega^{\omega^{\omega^8}+1}}(100)\)
octaelgathor-by-godgahlah E100(#^#^#^8)*#^#100 \(f_{\omega^{\omega^{\omega^8}+\omega}}(100)\)
octaelgathor-by-godgathor E100(#^#^#^8)*#^#^#100 \(f_{\omega^{\omega^{\omega^8}+\omega^{\omega}}}(100)\)
octaelgathor-by-gralgathor E100(#^#^#^8)*#^#^##10 \(f_{\omega^{\omega^{\omega^8}+\omega^{\omega^2}}}(100)\)
octaelgathor-by-thraelgathor E100(#^#^#^8)*#^#^###100 \(f_{\omega^{\omega^{\omega^8}+\omega^{\omega^3}}}(100)\)
octaelgathor-by-terinngathor E100(#^#^#^8)*#^#^####100 \(f_{\omega^{\omega^{\omega^8}+\omega^{\omega^4}}}(100)\)
octaelgathor-by-pentaelgathor E100(#^#^#^8)*(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^8}+\omega^{\omega^5}}}(100)\)
octaelgathor-by-hexaelgathor E100(#^#^#^8)*(#^#^#^6)100 \(f_{\omega^{\omega^{\omega^8}+\omega^{\omega^6}}}(100)\)
octaelgathor-by-heptaelgathor E100(#^#^#^8)*(#^#^#^7)100 \(f_{\omega^{\omega^{\omega^8}+\omega^{\omega^7}}}(100)\)
deutero-octaelgathor E100(#^#^#^8)*(#^#^#^8)100 \(f_{\omega^{\omega^{\omega^8}2}}(100)\)
trito-octaelgathor E100(#^#^#^8)*(#^#^#^8)*(#^#^#^8)100 \(f_{\omega^{\omega^{\omega^8}3}}(100)\)
teterto-octaelgathor E100#^(#^#^8*#)4 \(f_{\omega^{\omega^{\omega^8}4}}(100)\)
pepto-octaelgathor E100#^(#^#^8*#)5 \(f_{\omega^{\omega^{\omega^8}5}}(100)\)
exto-octaelgathor E100#^(#^#^8*#)6 \(f_{\omega^{\omega^{\omega^8}6}}(100)\)
epto-octaelgathor E100#^(#^#^8*#)7 \(f_{\omega^{\omega^{\omega^8}7}}(100)\)
ogdo-octaelgathor E100#^(#^#^8*#)8 \(f_{\omega^{\omega^{\omega^8}8}}(100)\)
ento-octaelgathor E100#^(#^#^8*#)9 \(f_{\omega^{\omega^{\omega^8}9}}(100)\)
dekato-octaelgathor E100#^(#^#^8*#)10 \(f_{\omega^{\omega^{\omega^8}10}}(100)\)
isosto-octaelgathor E100#^(#^#^8*#)20 \(f_{\omega^{\omega^{\omega^8}20}}(100)\)
trianto-octaelgathor E100#^(#^#^8*#)30 \(f_{\omega^{\omega^{\omega^8}30}}(100)\)
saranto-octaelgathor E100#^(#^#^8*#)40 \(f_{\omega^{\omega^{\omega^8}40}}(100)\)
peninto-octaelgathor E100#^(#^#^8*#)50 \(f_{\omega^{\omega^{\omega^8}50}}(100)\)
exinto-octaelgathor E100#^(#^#^8*#)60 \(f_{\omega^{\omega^{\omega^8}60}}(100)\)
ebdominto-octaelgathor E100#^(#^#^8*#)70 \(f_{\omega^{\omega^{\omega^8}70}}(100)\)
ogdonto-octaelgathor E100#^(#^#^8*#)80 \(f_{\omega^{\omega^{\omega^8}80}}(100)\)
eneninto-octaelgathor E100#^(#^#^8*#)90 \(f_{\omega^{\omega^{\omega^8}90}}(100)\)
hecato-octaelgathor E100#^(#^#^8*#)100 \(f_{\omega^{\omega^{\omega^8+1}}}(100)\)
octaelgridgathor E100#^(#^#^8*##)100 \(f_{\omega^{\omega^{\omega^8+2}}}(100)\)
octaelkubikgathor E100#^(#^#^8*###)100 \(f_{\omega^{\omega^{\omega^8+3}}}(100)\)
octaelquarticgathor E100#^(#^#^8*####)100 \(f_{\omega^{\omega^{\omega^8+4}}}(100)\)
octaelgodgathgathor E100#^(#^#^8*#^#)100 \(f_{\omega^{\omega^{\omega^8+\omega}}}(100)\)
octaelgralgathgathor E100#^(#^#^8*#^##)100 \(f_{\omega^{\omega^{\omega^8+\omega^2}}}(100)\)
octaelthraelgathgathor E100#^(#^#^8*#^###)100 \(f_{\omega^{\omega^{\omega^8+\omega^3}}}(100)\)
octaelterinngathgathor E100#^(#^#^8*#^####)100 \(f_{\omega^{\omega^{\omega^8+\omega^4}}}(100)\)
octaelpentaelgathgathor E100#^(#^#^8*#^#^5)100 \(f_{\omega^{\omega^{\omega^8+\omega^5}}}(100)\)
octaelhexaelgathgathor E100#^(#^#^8*#^#^6)100 \(f_{\omega^{\omega^{\omega^8+\omega^6}}}(100)\)
octaelheptaelgathgathor E100#^(#^#^8*#^#^7)100 \(f_{\omega^{\omega^{\omega^8+\omega^7}}}(100)\)
octaelgathordeus E100#^(#^#^8*#^#^8)100 \(f_{\omega^{\omega^{\omega^82}}}(100)\)
octaelgathortruce E100#^(#^#^8*#^#^8*#^#^8)100 \(f_{\omega^{\omega^{\omega^83}}}(100)\)
octaelgathorquad E100(#^#^#^9)4 \(f_{\omega^{\omega^{\omega^84}}}(100)\)
octaelgathorquid E100(#^#^#^9)5 \(f_{\omega^{\omega^{\omega^85}}}(100)\)
octaelgathorsid E100(#^#^#^9)6 \(f_{\omega^{\omega^{\omega^86}}}(100)\)
octaelgathorseptuce E100(#^#^#^9)7 \(f_{\omega^{\omega^{\omega^87}}}(100)\)
octaelgathoroctuce E100(#^#^#^9)8 \(f_{\omega^{\omega^{\omega^88}}}(100)\)
octaelgathornonice E100(#^#^#^9)9 \(f_{\omega^{\omega^{\omega^89}}}(100)\)
octaelgathordecice E100(#^#^#^9)10 \(f_{\omega^{\omega^{\omega^810}}}(100)\)
octaelgathorvigintice E100(#^#^#^9)20 \(f_{\omega^{\omega^{\omega^820}}}(100)\)
octaelgathortrigintice E100(#^#^#^9)30 \(f_{\omega^{\omega^{\omega^830}}}(100)\)
octaelgathorquadragintice E100(#^#^#^9)40 \(f_{\omega^{\omega^{\omega^840}}}(100)\)
octaelgathorquinquagintice E100(#^#^#^9)50 \(f_{\omega^{\omega^{\omega^850}}}(100)\)
octaelgathorsexagintice E100(#^#^#^9)60 \(f_{\omega^{\omega^{\omega^860}}}(100)\)
octaelgathorseptuagintice E100(#^#^#^9)70 \(f_{\omega^{\omega^{\omega^870}}}(100)\)
octaelgathoroctogintice E100(#^#^#^9)80 \(f_{\omega^{\omega^{\omega^880}}}(100)\)
octaelgathornonagintice E100(#^#^#^9)90 \(f_{\omega^{\omega^{\omega^890}}}(100)\)

Sources Edit

  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 · Tethraennon 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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