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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

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

  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
Beyond...: Blasphemorgulus regiment

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