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The dekaelgathor regiment is a series of numbers from E100(#^#^#^10)100 to E100(#^#^#^90)100 defined using Cascading-E notation (i.e. beginning from dekaelgathor and up to enenintaelgathor).[1] The numbers were coined by Sbiis Saibian.

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Ennaelgathor regiment Godtothol regiment

List of numbers of the regiment

Name of number Cascading-E notation (definition) Fast-growing hierarchy (approximation)
dekaelgathor E100(#^#^#^10)100 \(f_{\omega^{\omega^{\omega^{10}}}}(100)\)
grand dekaelgathor E100(#^#^#^10)100#2 \(f_{\omega^{\omega^{\omega^{10}}}}^2(100)\)
grangol-carta-dekaelgathor E100(#^#^#^10)100#100 \(f_{\omega^{\omega^{\omega^{10}}}+1}(100)\)
godgahlah-carta-dekaelgathor E100(#^#^#^10)100#^#100 \(f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega}}(100)\)
godgathor-carta-dekaelgathor E100(#^#^#^10)100#^#^#100 \(f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega}}}(100)\)
gralgathor-carta-dekaelgathor E100(#^#^#^10)100#^#^##100 \(f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^2}}}(100)\)
thraelgathor-carta-dekaelgathor E100(#^#^#^10)100#^#^###100 \(f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^3}}}(100)\)
terinngathor-carta-dekaelgathor E100(#^#^#^10)100#^#^####100 \(f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^4}}}(100)\)
pentaelgathor-carta-dekaelgathor E100(#^#^#^10)100(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^5}}}(100)\)
hexaelgathor-carta-dekaelgathor E100(#^#^#^10)100(#^#^#^6)100 \(f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^6}}}(100)\)
heptaelgathor-carta-dekaelgathor E100(#^#^#^10)100(#^#^#^7)100 \(f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^7}}}(100)\)
octaelgathor-carta-dekaelgathor E100(#^#^#^10)100(#^#^#^8)100 \(f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^8}}}(100)\)
ennaelgathor-carta-dekaelgathor E100(#^#^#^10)100(#^#^#^9)100 \(f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^9}}}(100)\)
dekaeltrigathor E100(#^#^#^10)100(#^#^#^10)100 \(f_{\omega^{\omega^{\omega^{10}}}2}(100)\)
dekaeltergathor E100(#^#^#^10)*#4 \(f_{\omega^{\omega^{\omega^{10}}}3}(100)\)
dekaelpeggathor E100(#^#^#^10)*#5 \(f_{\omega^{\omega^{\omega^{10}}}4}(100)\)
dekaelhexgathor E100(#^#^#^10)*#6 \(f_{\omega^{\omega^{\omega^{10}}}5}(100)\)
dekaelhepgathor E100(#^#^#^10)*#7 \(f_{\omega^{\omega^{\omega^{10}}}6}(100)\)
dekael-ahtgathor E100(#^#^#^10)*#8 \(f_{\omega^{\omega^{\omega^{10}}}7}(100)\)
dekael-enngathor E100(#^#^#^10)*#9 \(f_{\omega^{\omega^{\omega^{10}}}8}(100)\)
dekaeldekagathor E100(#^#^#^10)*#10 \(f_{\omega^{\omega^{\omega^{10}}}9}(100)\)
dekaelgathor-by-hyperion E100(#^#^#^10)*#100 \(f_{\omega^{\omega^{\omega^{10}}+1}}(100)\)
dekaelgathor-by-godgahlah E100(#^#^#^10)*#^#100 \(f_{\omega^{\omega^{\omega^{10}}+\omega}}(100)\)
dekaelgathor-by-godgathor E100(#^#^#^10)*#^#^#100 \(f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega}}}(100)\)
dekaelgathor-by-gralgathor E100(#^#^#^10)*#^#^##10 \(f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^2}}}(100)\)
dekaelgathor-by-thraelgathor E100(#^#^#^10)*#^#^###100 \(f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^3}}}(100)\)
dekaelgathor-by-terinngathor E100(#^#^#^10)*#^#^####100 \(f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^4}}}(100)\)
dekaelgathor-by-pentaelgathor E100(#^#^#^10)*(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^5}}}(100)\)
dekaelgathor-by-hexaelgathor E100(#^#^#^10)*(#^#^#^6)100 \(f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^6}}}(100)\)
dekaelgathor-by-heptaelgathor E100(#^#^#^10)*(#^#^#^7)100 \(f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^7}}}(100)\)
dekaelgathor-by-octaelgathor E100(#^#^#^10)*(#^#^#^8)100 \(f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^8}}}(100)\)
dekaelgathor-by-ennaelgathor E100(#^#^#^10)*(#^#^#^9)100 \(f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^9}}}(100)\)
deutero-dekaelgathor E100(#^#^#^10)*(#^#^#^10)100 \(f_{\omega^{\omega^{\omega^{10}}2}}(100)\)
trito-dekaelgathor E100(#^#^#^10)*(#^#^#^10)*(#^#^#^10)100 \(f_{\omega^{\omega^{\omega^{10}}3}}(100)\)
teterto-dekaelgathor E100#^(#^#^10*#)4 \(f_{\omega^{\omega^{\omega^{10}}4}}(100)\)
pepto-dekaelgathor E100#^(#^#^10*#)5 \(f_{\omega^{\omega^{\omega^{10}}5}}(100)\)
exto-dekaelgathor E100#^(#^#^10*#)6 \(f_{\omega^{\omega^{\omega^{10}}6}}(100)\)
epto-dekaelgathor E100#^(#^#^10*#)7 \(f_{\omega^{\omega^{\omega^{10}}7}}(100)\)
ogdo-dekaelgathor E100#^(#^#^10*#)8 \(f_{\omega^{\omega^{\omega^{10}}8}}(100)\)
ento-dekaelgathor E100#^(#^#^10*#)9 \(f_{\omega^{\omega^{\omega^{10}}9}}(100)\)
dekato-dekaelgathor E100#^(#^#^10*#)10 \(f_{\omega^{\omega^{\omega^{10}}10}}(100)\)
isosto-dekaelgathor E100#^(#^#^10*#)20 \(f_{\omega^{\omega^{\omega^{10}}20}}(100)\)
trianto-dekaelgathor E100#^(#^#^10*#)30 \(f_{\omega^{\omega^{\omega^{10}}30}}(100)\)
saranto-dekaelgathor E100#^(#^#^10*#)40 \(f_{\omega^{\omega^{\omega^{10}}40}}(100)\)
peninto-dekaelgathor E100#^(#^#^10*#)50 \(f_{\omega^{\omega^{\omega^{10}}50}}(100)\)
exinto-dekaelgathor E100#^(#^#^10*#)60 \(f_{\omega^{\omega^{\omega^{10}}60}}(100)\)
ebdominto-dekaelgathor E100#^(#^#^10*#)70 \(f_{\omega^{\omega^{\omega^{10}}70}}(100)\)
ogdonto-dekaelgathor E100#^(#^#^10*#)80 \(f_{\omega^{\omega^{\omega^{10}}80}}(100)\)
eneninto-dekaelgathor E100#^(#^#^10*#)90 \(f_{\omega^{\omega^{\omega^{10}}90}}(100)\)
hecato-dekaelgathor E100#^(#^#^10*#)100 \(f_{\omega^{\omega^{\omega^{10}+1}}}(100)\)
dekaelgridgathor E100#^(#^#^10*##)100 \(f_{\omega^{\omega^{\omega^{10}+2}}}(100)\)
dekaelkubikgathor E100#^(#^#^10*###)100 \(f_{\omega^{\omega^{\omega^{10}+3}}}(100)\)
dekaelquarticgathor E100#^(#^#^10*####)100 \(f_{\omega^{\omega^{\omega^{10}+4}}}(100)\)
dekaelgodgathgathor E100#^(#^#^10*#^#)100 \(f_{\omega^{\omega^{\omega^{10}+\omega}}}(100)\)
dekaelgralgathgathor E100#^(#^#^10*#^##)100 \(f_{\omega^{\omega^{\omega^{10}+\omega^2}}}(100)\)
dekaelthraelgathgathor E100#^(#^#^10*#^###)100 \(f_{\omega^{\omega^{\omega^{10}+\omega^3}}}(100)\)
dekaelterinngathgathor E100#^(#^#^10*#^####)100 \(f_{\omega^{\omega^{\omega^{10}+\omega^4}}}(100)\)
dekaelpentaelgathgathor E100#^(#^#^10*#^#^5)100 \(f_{\omega^{\omega^{\omega^{10}+\omega^5}}}(100)\)
dekaelhexaelgathgathor E100#^(#^#^10*#^#^6)100 \(f_{\omega^{\omega^{\omega^{10}+\omega^6}}}(100)\)
dekaelheptaelgathgathor E100#^(#^#^10*#^#^7)100 \(f_{\omega^{\omega^{\omega^{10}+\omega^7}}}(100)\)
dekaeloctaelgathgathor E100#^(#^#^10*#^#^8)100 \(f_{\omega^{\omega^{\omega^{10}+\omega^8}}}(100)\)
dekaelennaelgathgathor E100#^(#^#^10*#^#^9)100 \(f_{\omega^{\omega^{\omega^{10}+\omega^9}}}(100)\)
dekaelgathordeus E100#^(#^#^10*#^#^10)100 \(f_{\omega^{\omega^{\omega^{10}2}}}(100)\)
dekaelgathortruce E100#^(#^#^10*#^#^10*#^#^10)100 \(f_{\omega^{\omega^{\omega^{10}3}}}(100)\)
dekaelgathorquad E100(#^#^#^11)4 \(f_{\omega^{\omega^{\omega^{10}4}}}(100)\)
dekaelgathorquid E100(#^#^#^11)5 \(f_{\omega^{\omega^{\omega^{10}5}}}(100)\)
dekaelgathorsid E100(#^#^#^11)6 \(f_{\omega^{\omega^{\omega^{10}6}}}(100)\)
dekaelgathorseptuce E100(#^#^#^11)7 \(f_{\omega^{\omega^{\omega^{10}7}}}(100)\)
dekaelgathoroctuce E100(#^#^#^11)8 \(f_{\omega^{\omega^{\omega^{10}8}}}(100)\)
dekaelgathornonice E100(#^#^#^11)9 \(f_{\omega^{\omega^{\omega^{10}9}}}(100)\)
dekaelgathordecice E100(#^#^#^11)10 \(f_{\omega^{\omega^{\omega^{10}10}}}(100)\)
dekaelgathorvigintice E100(#^#^#^11)20 \(f_{\omega^{\omega^{\omega^{10}20}}}(100)\)
dekaelgathortrigintice E100(#^#^#^11)30 \(f_{\omega^{\omega^{\omega^{10}30}}}(100)\)
dekaelgathorquadragintice E100(#^#^#^11)40 \(f_{\omega^{\omega^{\omega^{10}40}}}(100)\)
dekaelgathorquinquagintice E100(#^#^#^11)50 \(f_{\omega^{\omega^{\omega^{10}50}}}(100)\)
dekaelgathorsexagintice E100(#^#^#^11)60 \(f_{\omega^{\omega^{\omega^{10}60}}}(100)\)
dekaelgathorseptuagintice E100(#^#^#^11)70 \(f_{\omega^{\omega^{\omega^{10}70}}}(100)\)
dekaelgathoroctogintice E100(#^#^#^11)80 \(f_{\omega^{\omega^{\omega^{10}80}}}(100)\)
dekaelgathornonagintice E100(#^#^#^11)90 \(f_{\omega^{\omega^{\omega^{10}90}}}(100)\)
endekaelgathor E100(#^#^#^11)100 \(f_{\omega^{\omega^{\omega^{11}}}}(100)\)
dodekaelgathor E100(#^#^#^12)100 \(f_{\omega^{\omega^{\omega^{12}}}}(100)\)
triadekaelgathor E100(#^#^#^13)100 \(f_{\omega^{\omega^{\omega^{13}}}}(100)\)
tetradekaelgathor E100(#^#^#^14)100 \(f_{\omega^{\omega^{\omega^{14}}}}(100)\)
pentadekaelgathor E100(#^#^#^15)100 \(f_{\omega^{\omega^{\omega^{15}}}}(100)\)
hexadekaelgathor E100(#^#^#^16)100 \(f_{\omega^{\omega^{\omega^{16}}}}(100)\)
heptadekaelgathor E100(#^#^#^17)100 \(f_{\omega^{\omega^{\omega^{17}}}}(100)\)
octadekaelgathor E100(#^#^#^18)100 \(f_{\omega^{\omega^{\omega^{18}}}}(100)\)
ennadekaelgathor E100(#^#^#^19)100 \(f_{\omega^{\omega^{\omega^{19}}}}(100)\)
icosi-aelgathor E100(#^#^#^20)100 \(f_{\omega^{\omega^{\omega^{20}}}}(100)\)
triantaelgathor E100(#^#^#^30)100 \(f_{\omega^{\omega^{\omega^{30}}}}(100)\)
sarantaelgathor E100(#^#^#^40)100 \(f_{\omega^{\omega^{\omega^{40}}}}(100)\)
penintaelgathor E100(#^#^#^50)100 \(f_{\omega^{\omega^{\omega^{50}}}}(100)\)
exintaelgathor E100(#^#^#^60)100 \(f_{\omega^{\omega^{\omega^{60}}}}(100)\)
ebdomintaelgathor E100(#^#^#^70)100 \(f_{\omega^{\omega^{\omega^{70}}}}(100)\)
ogdontaelgathor E100(#^#^#^80)100 \(f_{\omega^{\omega^{\omega^{80}}}}(100)\)
enenintaelgathor E100(#^#^#^90)100 \(f_{\omega^{\omega^{\omega^{90}}}}(100)\)

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 · 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