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

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Terinngathor regiment Hexaelgathor regiment

List of numbers of the regiment Edit

Name of number Cascading-E notation (definition) Fast-growing hierarchy (approximation)
pentaelgathor E100#^#^#####100 \(f_{\omega^{\omega^{\omega^5}}}(100)\)
grand pentaelgathor E100(#^#^#^5)100#2 \(f_{\omega^{\omega^{\omega^5}}}^2(100)\)
grangol-carta-pentaelgathor E100(#^#^#^5)100#100 \(f_{\omega^{\omega^{\omega^5}}+1}(100)\)
pentaeltrigathor E100(#^#^#^5)100(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^5}}2}(100)\)
pentaeltergathor E100(#^#^#^5)100(#^#^#^5)100(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^5}}3}(100)\)
pentaelgathor-by-hyperion E100(#^#^#^5)*#100 \(f_{\omega^{\omega^{\omega^5}+1}}(100)\)
pentaelgathor-by-godgahlah E100(#^#^#^5)*#^#100 \(f_{\omega^{\omega^{\omega^5}+\omega}}(100)\)
pentaelgathor-by-godgathor E100(#^#^#^5)*#^#^#100 \(f_{\omega^{\omega^{\omega^5}+\omega^\omega}}(100)\)
pentaelgathor-by-gralgathor E100(#^#^#^5)*#^#^##100 \(f_{\omega^{\omega^{\omega^5}+\omega^{\omega^2}}}(100)\)
pentaelgathor-by-thraelgathor E100(#^#^#^5)*#^#^###100 \(f_{\omega^{\omega^{\omega^5}+\omega^{\omega^3}}}(100)\)
pentaelgathor-by-terinngathor E100(#^#^#^5)*#^#^####100 \(f_{\omega^{\omega^{\omega^5}+\omega^{\omega^4}}}(100)\)
deutero-pentaelgathor E100(#^#^#^5)*(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^5}2}}(100)\)
trito-pentaelgathor E100(#^#^#^5)*(#^#^#^5)*(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^5}3}}(100)\)
teterto-pentaelgathor E100(#^#^#^5)*(#^#^#^5)*(#^#^#^5)*(#^#^#^5)100 \(f_{\omega^{\omega^{\omega^5}4}}(100)\)
pepto-pentaelgathor E100#^(#^#^5*#)5 \(f_{\omega^{\omega^{\omega^5}5}}(100)\)
exto-pentaelgathor E100#^(#^#^5*#)6 \(f_{\omega^{\omega^{\omega^5}6}}(100)\)
epto-pentaelgathor E100#^(#^#^5*#)7 \(f_{\omega^{\omega^{\omega^5}7}}(100)\)
ogdo-pentaelgathor E100#^(#^#^5*#)8 \(f_{\omega^{\omega^{\omega^5}8}}(100)\)
ento-pentaelgathor E100#^(#^#^5*#)9 \(f_{\omega^{\omega^{\omega^5}9}}(100)\)
dekato-pentaelgathor E100#^(#^#^5*#)10 \(f_{\omega^{\omega^{\omega^5}10}}(100)\)
hecato-pentaelgathor E100#^(#^#^5*#)100 \(f_{\omega^{\omega^{\omega^5+1}}}(100)\)
pentaelgridgathor E100#^(#^#^5*##)100 \(f_{\omega^{\omega^{\omega^5+2}}}(100)\)
pentaelkubikgathor E100#^(#^#^5*###)100 \(f_{\omega^{\omega^{\omega^5+3}}}(100)\)
pentaelquarticgathor E100#^(#^#^5*####)100 \(f_{\omega^{\omega^{\omega^5+4}}}(100)\)
pentaelgodgathgathor E100#^(#^#^5*#^#)100 \(f_{\omega^{\omega^{\omega^5+\omega}}}(100)\)
pentaelgralgathgathor E100#^(#^#^5*#^##)100 \(f_{\omega^{\omega^{\omega^5+\omega^2}}}(100)\)
pentaelthraelgathgathor E100#^(#^#^5*#^###)100 \(f_{\omega^{\omega^{\omega^5+\omega^3}}}(100)\)
pentaelterinngathgathor E100#^(#^#^5*#^####)100 \(f_{\omega^{\omega^{\omega^5+\omega^4}}}(100)\)
pentaelgathordeus E100#^(#^#^5*#^#^5)100 \(f_{\omega^{\omega^{\omega^52}}}(100)\)
pentaelgathortruce E100#^(#^#^5*#^#^5*#^#^5)100 \(f_{\omega^{\omega^{\omega^53}}}(100)\)
pentaelgathorquad E100#^(#^#^5*#^#^5*#^#^5*#^#^5)100 = E100(#^#^#^6)4 \(f_{\omega^{\omega^{\omega^54}}}(100)\)
pentaelgathorquid E100(#^#^#^6)5 \(f_{\omega^{\omega^{\omega^55}}}(100)\)
pentaelgathorsid E100(#^#^#^6)6 \(f_{\omega^{\omega^{\omega^56}}}(100)\)
pentaelgathorseptuce E100(#^#^#^6)7 \(f_{\omega^{\omega^{\omega^57}}}(100)\)
pentaelgathoroctuce E100(#^#^#^6)8 \(f_{\omega^{\omega^{\omega^58}}}(100)\)
pentaelgathornonice E100(#^#^#^6)9 \(f_{\omega^{\omega^{\omega^59}}}(100)\)
pentaelgathordecice E100(#^#^#^6)10 \(f_{\omega^{\omega^{\omega^510}}}(100)\)
pentaelgathorvigintice E100(#^#^#^6)20 \(f_{\omega^{\omega^{\omega^520}}}(100)\)
pentaelgathortrigintice E100(#^#^#^6)30 \(f_{\omega^{\omega^{\omega^530}}}(100)\)
pentaelgathorquadragintice E100(#^#^#^6)40 \(f_{\omega^{\omega^{\omega^540}}}(100)\)
pentaelgathorquinquagintice E100(#^#^#^6)50 \(f_{\omega^{\omega^{\omega^550}}}(100)\)
pentaelgathorsexagintice E100(#^#^#^6)60 \(f_{\omega^{\omega^{\omega^560}}}(100)\)
pentaelgathorseptuagintice E100(#^#^#^6)70 \(f_{\omega^{\omega^{\omega^570}}}(100)\)
pentaelgathoroctogintice E100(#^#^#^6)80 \(f_{\omega^{\omega^{\omega^580}}}(100)\)
pentaelgathornonagintice E100(#^#^#^6)90 \(f_{\omega^{\omega^{\omega^590}}}(100)\)

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