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The terinngathor regiment is a series of numbers from E100#^#^####100 to E100(#^#^#^5)90 defined using Cascading-E notation (i.e. beginning from terinngathor and up to terinngathornonagintice).[1] The numbers were coined by Sbiis Saibian.

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Thraelgathor regiment Pentaelgathor regiment

List of numbers of the regiment

Name of number Cascading-E notation (definition) Fast-growing hierarchy (approximation)
terinngathor E100#^#^####100 \(f_{\omega^{\omega^{\omega^4}}}(100)\)
grand terinngathor E100#^#^####100#2 \(f_{\omega^{\omega^{\omega^4}}}^2(100)\)
grangol-carta-terinngathor E100#^#^####100#100 \(f_{\omega^{\omega^{\omega^4}}+1}(100)\)
gugold-carta-terinngathor E100#^#^####100##100 \(f_{\omega^{\omega^{\omega^4}}+\omega}(100)\)
throogol-carta-terinngathor E100#^#^####100###100 \(f_{\omega^{\omega^{\omega^4}}+\omega^2}(100)\)
tetroogol-carta-terinngathor E100#^#^####100####100 \(f_{\omega^{\omega^{\omega^4}}+\omega^3}(100)\)
godgahlah-carta-terinngathor E100#^#^####100#^#100 \(f_{\omega^{\omega^{\omega^4}}+\omega^\omega}(100)\)
grigahlah-carta-terinngathor E100#^#^####100#^##100 \(f_{\omega^{\omega^{\omega^4}}+\omega^{\omega^2}}(100)\)
kubikahlah-carta-terinngathor E100#^#^####100#^###100 \(f_{\omega^{\omega^{\omega^4}}+\omega^{\omega^3}}(100)\)
quarticahlah-carta-terinngathor E100#^#^####100#^####100 \(f_{\omega^{\omega^{\omega^4}}+\omega^{\omega^4}}(100)\)
godgathor-carta-terinngathor E100#^#^####100#^#^#100 \(f_{\omega^{\omega^{\omega^4}}+\omega^{\omega^\omega}}(100)\)
gralgathor-carta-terinngathor E100#^#^####100#^#^##100 \(f_{\omega^{\omega^{\omega^4}}+\omega^{\omega^{\omega^2}}}(100)\)
thraelgathor-carta-terinngathor E100#^#^####100#^#^###100 \(f_{\omega^{\omega^{\omega^4}}+\omega^{\omega^{\omega^3}}}(100)\)
terinntrigathor E100#^#^####100#^#^####100 \(f_{\omega^{\omega^{\omega^4}}2}(100)\)
terinntergathor E100#^#^####100#^#^####100#^#^####100

= E100#^#^####*#4

\(f_{\omega^{\omega^{\omega^4}}3}(100)\)
terinnpeggathor E100#^#^####*#5 \(f_{\omega^{\omega^{\omega^4}}4}(100)\)
terinnhexgathor E100#^#^####*#6 \(f_{\omega^{\omega^{\omega^4}}5}(100)\)
terinnhepgathor E100#^#^####*#7 \(f_{\omega^{\omega^{\omega^4}}6}(100)\)
terinn-ahtgathor E100#^#^####*#8 \(f_{\omega^{\omega^{\omega^4}}7}(100)\)
terinn-enngathor E100#^#^####*#9 \(f_{\omega^{\omega^{\omega^4}}8}(100)\)
terinndekagathor E100#^#^####*#10 \(f_{\omega^{\omega^{\omega^4}}9}(100)\)
terinngathor-by-hyperion E100#^#^####*#100 \(f_{\omega^{\omega^{\omega^4}+1}}(100)\)
terinngathor-by-deutero-hyperion E100#^#^####*##100 \(f_{\omega^{\omega^{\omega^4}+2}}(100)\)
terinngathor-by-trito-hyperion E100#^#^####*###100 \(f_{\omega^{\omega^{\omega^4}+3}}(100)\)
terinngathor-by-teterto-hyperion E100#^#^####*####100 \(f_{\omega^{\omega^{\omega^4}+4}}(100)\)
terinngathor-by-godgahlah E100#^#^####*#^#100 \(f_{\omega^{\omega^{\omega^4}+\omega}}(100)\)
terinngathor-by-gridgahlah E100#^#^####*#^##100 \(f_{\omega^{\omega^{\omega^4}+\omega^2}}(100)\)
terinngathor-by-kubikahlah E100#^#^####*#^###100 \(f_{\omega^{\omega^{\omega^4}+\omega^3}}(100)\)
terinngathor-by-quarticahlah E100#^#^####*#^####100 \(f_{\omega^{\omega^{\omega^4}+\omega^4}}(100)\)
terinngathor-by-godgathor E100#^#^####*#^#^#100 \(f_{\omega^{\omega^{\omega^4}+\omega^\omega}}(100)\)
terinngathor-by-gralgathor E100#^#^####*#^#^##100 \(f_{\omega^{\omega^{\omega^4}+\omega^{\omega^2}}}(100)\)
terinngathor-by-thraelgathor E100#^#^####*#^#^###100 \(f_{\omega^{\omega^{\omega^4}+\omega^{\omega^3}}}(100)\)
deutero-terinngathor E100#^#^####*#^#^####100 \(f_{\omega^{\omega^{\omega^4}2}}(100)\)
deutero-terinngathor-by-hyperion E100#^#^####*#^#^####*#100 \(f_{\omega^{\omega^{\omega^4}2+1}}(100)\)
deutero-terinngathor-by-deutero-hyperion E100#^#^####*#^#^####*##100 \(f_{\omega^{\omega^{\omega^4}2+2}}(100)\)
deutero-terinngathor-by-trito-hyperion E100#^#^####*#^#^####*###100 \(f_{\omega^{\omega^{\omega^4}2+3}}(100)\)
deutero-terinngathor-by-teterto-hyperion E100#^#^####*#^#^####*####100 \(f_{\omega^{\omega^{\omega^4}2+4}}(100)\)
deutero-terinngathor-by-godgahlah E100#^#^####*#^#^####*#^#100 \(f_{\omega^{\omega^{\omega^4}2+\omega}}(100)\)
deutero-terinngathor-by-gridgahlah E100#^#^####*#^#^####*#^##100 \(f_{\omega^{\omega^{\omega^4}2+\omega^2}}(100)\)
deutero-terinngathor-by-kubikahlah E100#^#^####*#^#^####*#^###100 \(f_{\omega^{\omega^{\omega^4}2+\omega^3}}(100)\)
deutero-terinngathor-by-quarticahlah E100#^#^####*#^#^####*#^####100 \(f_{\omega^{\omega^{\omega^4}2+\omega^4}}(100)\)
deutero-terinngathor-by-godgathor E100#^#^####*#^#^####*#^#^#100 \(f_{\omega^{\omega^{\omega^4}2+\omega^\omega}}(100)\)
deutero-terinngathor-by-gralgathor E100#^#^####*#^#^####*#^#^##100 \(f_{\omega^{\omega^{\omega^4}2+\omega^{\omega^2}}}(100)\)
deutero-terinngathor-by-thraelgathor E100#^#^####*#^#^####*#^#^###100 \(f_{\omega^{\omega^{\omega^4}2+\omega^{\omega^3}}}(100)\)
trito-terinngathor E100#^#^####*#^#^####*#^#^####100 \(f_{\omega^{\omega^{\omega^4}3}}(100)\)
teterto-terinngathor E100#^#^####*#^#^####*#^#^####*#^#^####100

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

\(f_{\omega^{\omega^{\omega^4}4}}(100)\)
pepto-terinngathor E100#^(#^####*#)5 \(f_{\omega^{\omega^{\omega^4}5}}(100)\)
exto-terinngathor E100#^(#^####*#)6 \(f_{\omega^{\omega^{\omega^4}6}}(100)\)
epto-terinngathor E100#^(#^####*#)7 \(f_{\omega^{\omega^{\omega^4}7}}(100)\)
ogdo-terinngathor E100#^(#^####*#)8 \(f_{\omega^{\omega^{\omega^4}8}}(100)\)
ento-terinngathor E100#^(#^####*#)9 \(f_{\omega^{\omega^{\omega^4}9}}(100)\)
dekato-terinngathor E100#^(#^####*#)10 \(f_{\omega^{\omega^{\omega^4}10}}(100)\)
isosto-terinngathor E100#^(#^####*#)20 \(f_{\omega^{\omega^{\omega^4}20}}(100)\)
trianto-terinngathor E100#^(#^####*#)30 \(f_{\omega^{\omega^{\omega^4}30}}(100)\)
saranto-terinngathor E100#^(#^####*#)40 \(f_{\omega^{\omega^{\omega^4}40}}(100)\)
peninto-terinngathor E100#^(#^####*#)50 \(f_{\omega^{\omega^{\omega^4}50}}(100)\)
exinto-terinngathor E100#^(#^####*#)60 \(f_{\omega^{\omega^{\omega^4}60}}(100)\)
ebdominto-terinngathor E100#^(#^####*#)70 \(f_{\omega^{\omega^{\omega^4}70}}(100)\)
ogdonto-terinngathor E100#^(#^####*#)80 \(f_{\omega^{\omega^{\omega^4}80}}(100)\)
eneninto-terinngathor E100#^(#^####*#)90 \(f_{\omega^{\omega^{\omega^4}90}}(100)\)
hecato-terinngathor E100#^(#^####*#)100 \(f_{\omega^{\omega^{\omega^4+1}}}(100)\)
terinngridgathor E100#^(#^####*##)100 \(f_{\omega^{\omega^{\omega^4+2}}}(100)\)
terinnkubikgathor E100#^(#^####*###)100 \(f_{\omega^{\omega^{\omega^4+3}}}(100)\)
terinnquarticgathor E100#^(#^####*####)100 = E100#^(#^####*#^#)4 \(f_{\omega^{\omega^{\omega^4+4}}}(100)\)
terinnquinticgathor E100#^(#^####*#^#)5 \(f_{\omega^{\omega^{\omega^4+5}}}(100)\)
terinnsexticgathor E100#^(#^####*#^#)6 \(f_{\omega^{\omega^{\omega^4+6}}}(100)\)
terinnsepticgathor E100#^(#^####*#^#)7 \(f_{\omega^{\omega^{\omega^4+7}}}(100)\)
terinnocticgathor E100#^(#^####*#^#)8 \(f_{\omega^{\omega^{\omega^4+8}}}(100)\)
terinnonicgathor E100#^(#^####*#^#)9 \(f_{\omega^{\omega^{\omega^4+9}}}(100)\)
terinndecicgathor E100#^(#^####*#^#)10 \(f_{\omega^{\omega^{\omega^4+10}}}(100)\)
terinnviginticgathor E100#^(#^####*#^#)20 \(f_{\omega^{\omega^{\omega^4+20}}}(100)\)
terinnquinquaginticgathor E100#^(#^####*#^#)50 \(f_{\omega^{\omega^{\omega^4+50}}}(100)\)
terinngodgathgathor E100#^(#^####*#^#)100 \(f_{\omega^{\omega^{\omega^4+\omega}}}(100)\)
terinngodgathordeusgathor E100#^(#^####*#^#*#^#)100 \(f_{\omega^{\omega^{\omega^4+\omega2}}}(100)\)
terinngralgathgathor E100#^(#^####*#^##)100 \(f_{\omega^{\omega^{\omega^4+\omega^2}}}(100)\)
terinnthraelgathgathor E100#^(#^####*#^###)100 \(f_{\omega^{\omega^{\omega^4+\omega^3}}}(100)\)
terinngathordeus E100#^(#^####*#^####)100 \(f_{\omega^{\omega^{\omega^42}}}(100)\)
terinngodgathgathordeus E100#^(#^####*#^####*#^#)100 \(f_{\omega^{\omega^{\omega^42+\omega}}}(100)\)
terinngodgathordeusgathordeus E100#^(#^####*#^####*#^#*#^#)100 \(f_{\omega^{\omega^{\omega^42+\omega2}}}(100)\)
terinngralgathgathordeus E100#^(#^####*#^####*#^##)100 \(f_{\omega^{\omega^{\omega^42+\omega^2}}}(100)\)
terinnthraelgathgathordeus E100#^(#^####*#^####*#^###)100 \(f_{\omega^{\omega^{\omega^42+\omega^3}}}(100)\)
terinngathortruce E100#^(#^####*#^####*#^####)100 \(f_{\omega^{\omega^{\omega^43}}}(100)\)
terinngathorquad E100#^(#^####*#^####*#^####*#^####)100

= E100(#^#^#^5)4

\(f_{\omega^{\omega^{\omega^44}}}(100)\)
terinngathorquid E100(#^#^#^5)5 \(f_{\omega^{\omega^{\omega^45}}}(100)\)
terinngathorsid E100(#^#^#^5)6 \(f_{\omega^{\omega^{\omega^46}}}(100)\)
terinngathorseptuce E100(#^#^#^5)7 \(f_{\omega^{\omega^{\omega^47}}}(100)\)
terinngathoroctuce E100(#^#^#^5)8 \(f_{\omega^{\omega^{\omega^48}}}(100)\)
terinngathornonice E100(#^#^#^5)9 \(f_{\omega^{\omega^{\omega^49}}}(100)\)
terinngathordecice E100(#^#^#^5)10 \(f_{\omega^{\omega^{\omega^410}}}(100)\)
terinngathorvigintice E100(#^#^#^5)20 \(f_{\omega^{\omega^{\omega^420}}}(100)\)
terinngathortrigintice E100(#^#^#^5)30 \(f_{\omega^{\omega^{\omega^430}}}(100)\)
terinngathorquadragintice E100(#^#^#^5)40 \(f_{\omega^{\omega^{\omega^440}}}(100)\)
terinngathorquinquagintice E100(#^#^#^5)50 \(f_{\omega^{\omega^{\omega^450}}}(100)\)
terinngathorsexagintice E100(#^#^#^5)60 \(f_{\omega^{\omega^{\omega^460}}}(100)\)
terinngathorseptuagintice E100(#^#^#^5)70 \(f_{\omega^{\omega^{\omega^470}}}(100)\)
terinngathoroctogintice E100(#^#^#^5)80 \(f_{\omega^{\omega^{\omega^480}}}(100)\)
terinngathornonagintice E100(#^#^#^5)90 \(f_{\omega^{\omega^{\omega^490}}}(100)\)

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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