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

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Gralgathor regiment Terinngathor regiment

List of numbers of the regiment

Name of number Cascading-E notation (definition) Fast-growing hierarchy (approximation)
Thraelgathor E100#^#^###100 \(f_{\omega^{\omega^{\omega^3}}}(100)\)
Grand thraelgathor E100#^#^###100#2 \(f_{\omega^{\omega^{\omega^3}}}^2(100)\)
Grangol-carta-thraelgathor E100#^#^###100#100 \(f_{\omega^{\omega^{\omega^3}}+1}(100)\)
Gugold-carta-thraelgathor E100#^#^###100##100 \(f_{\omega^{\omega^{\omega^3}}+\omega}(100)\)
Throogol-carta-thraelgathor E100#^#^###100###100 \(f_{\omega^{\omega^{\omega^3}}+\omega^2}(100)\)
Tetroogol-carta-thraelgathor E100#^#^###100####100 \(f_{\omega^{\omega^{\omega^3}}+\omega^3}(100)\)
Godgahlah-carta-thraelgathor E100#^#^###100#^#100 \(f_{\omega^{\omega^{\omega^3}}+\omega^\omega}(100)\)
Gridgahlah-carta-thraelgathor E100#^#^###100#^##100 \(f_{\omega^{\omega^{\omega^3}}+\omega^{\omega^2}}(100)\)
Kubikahlah-carta-thraelgathor E100#^#^###100#^###100 \(f_{\omega^{\omega^{\omega^3}}+\omega^{\omega^3}}(100)\)
Quarticahlah-carta-thraelgathor E100#^#^###100#^####100 \(f_{\omega^{\omega^{\omega^3}}+\omega^{\omega^4}}(100)\)
Godgathor-carta-thraelgathor E100#^#^###100#^#^#100 \(f_{\omega^{\omega^{\omega^3}}+\omega^{\omega^\omega}}(100)\)
Gralgathor-carta-thraelgathor E100#^#^###100#^#^##100 \(f_{\omega^{\omega^{\omega^3}}+\omega^{\omega^{\omega^2}}}(100)\)
Thraeltrigathor E100#^#^###100#^#^###100 \(f_{\omega^{\omega^{\omega^3}}2}(100)\)
Thraeltergathor E100#^#^###100#^#^###100#^#^###100 = E100#^#^###*#4 \(f_{\omega^{\omega^{\omega^3}}3}(100)\)
Thraelpeggathor E100#^#^###*#5 \(f_{\omega^{\omega^{\omega^3}}4}(100)\)
Thraelhexgathor E100#^#^###*#6 \(f_{\omega^{\omega^{\omega^3}}5}(100)\)
Thraelhepgathor E100#^#^###*#7 \(f_{\omega^{\omega^{\omega^3}}6}(100)\)
Thrael-ahtgathor E100#^#^###*#8 \(f_{\omega^{\omega^{\omega^3}}7}(100)\)
Thrael-enngathor E100#^#^###*#9 \(f_{\omega^{\omega^{\omega^3}}8}(100)\)
Thraeldekagathor E100#^#^###*#10 \(f_{\omega^{\omega^{\omega^3}}9}(100)\)
Deutero-thraelgathor E100#^#^###*#^#^###100 \(f_{\omega^{\omega^{\omega^3}2}}(100)\)
Trito-thraelgathor E100#^#^###*#^#^###*#^#^###100 \(f_{\omega^{\omega^{\omega^3}3}}(100)\)
Teterto-thraelgathor E100#^#^###*#^#^###*#^#^###*#^#^###100 = E100#^(#^###*#)4 \(f_{\omega^{\omega^{\omega^3}4}}(100)\)
Pepto-thraelgathor E100#^(#^###*#)5 \(f_{\omega^{\omega^{\omega^3}5}}(100)\)
Exto-thraelgathor E100#^(#^###*#)6 \(f_{\omega^{\omega^{\omega^3}6}}(100)\)
Epto-thraelgathor E100#^(#^###*#)7 \(f_{\omega^{\omega^{\omega^3}7}}(100)\)
Ogdo-thraelgathor E100#^(#^###*#)8 \(f_{\omega^{\omega^{\omega^3}8}}(100)\)
Ento-thraelgathor E100#^(#^###*#)9 \(f_{\omega^{\omega^{\omega^3}9}}(100)\)
Dekato-thraelgathor E100#^(#^###*#)10 \(f_{\omega^{\omega^{\omega^3}10}}(100)\)
Isosto-thraelgathor E100#^(#^###*#)20 \(f_{\omega^{\omega^{\omega^3}20}}(100)\)
Trianto-thraelgathor E100#^(#^###*#)30 \(f_{\omega^{\omega^{\omega^3}30}}(100)\)
Saranto-thraelgathor E100#^(#^###*#)40 \(f_{\omega^{\omega^{\omega^3}40}}(100)\)
Peninto-thraelgathor E100#^(#^###*#)50 \(f_{\omega^{\omega^{\omega^3}50}}(100)\)
Exinto-thraelgathor E100#^(#^###*#)60 \(f_{\omega^{\omega^{\omega^3}60}}(100)\)
Ebdominto-thraelgathor E100#^(#^###*#)70 \(f_{\omega^{\omega^{\omega^3}70}}(100)\)
Ogdonto-thraelgathor E100#^(#^###*#)80 \(f_{\omega^{\omega^{\omega^3}80}}(100)\)
Eneninto-thraelgathor E100#^(#^###*#)90 \(f_{\omega^{\omega^{\omega^3}90}}(100)\)
Hecato-thraelgathor E100#^(#^###*#)100 \(f_{\omega^{\omega^{\omega^3+1}}}(100)\)
Thraelgridgathor E100#^(#^###*##)100 \(f_{\omega^{\omega^{\omega^3+2}}}(100)\)
Thraelkubikgathor E100#^(#^###*###)100 \(f_{\omega^{\omega^{\omega^3+3}}}(100)\)
Thraelquarticgathor E100#^(#^###*####)100 \(f_{\omega^{\omega^{\omega^3+4}}}(100)\)
Thraelgodgathgathor E100#^(#^###*#^#)100 \(f_{\omega^{\omega^{\omega^3+\omega}}}(100)\)
Thraelgodgathordeusgathor E100#^(#^###*#^#*#^#)100 \(f_{\omega^{\omega^{\omega^3+\omega2}}}(100)\)
Thraelgodgathortrucegathor E100#^(#^###*#^#*#^#*#^#)100 \(f_{\omega^{\omega^{\omega^3+\omega3}}}(100)\)
Thraelgodgathorquadgathor E100#^(#^###*#^#*#^#*#^#*#^#)100 = E100#^(#^###*#^##)4 \(f_{\omega^{\omega^{\omega^3+\omega4}}}(100)\)
Thraelgodgathorquidgathor E100#^(#^###*#^##)5 \(f_{\omega^{\omega^{\omega^3+\omega5}}}(100)\)
Thraelgodgathorsidgathor E100#^(#^###*#^##)6 \(f_{\omega^{\omega^{\omega^3+\omega6}}}(100)\)
Thraelgodgathorseptucegathor E100#^(#^###*#^##)7 \(f_{\omega^{\omega^{\omega^3+\omega7}}}(100)\)
Thraelgodgathoroctucegathor E100#^(#^###*#^##)8 \(f_{\omega^{\omega^{\omega^3+\omega8}}}(100)\)
Thraelgodgathornonicegathor E100#^(#^###*#^##)9 \(f_{\omega^{\omega^{\omega^3+\omega9}}}(100)\)
Thraelgodgathordecicegathor E100#^(#^###*#^##)10 \(f_{\omega^{\omega^{\omega^3+\omega10}}}(100)\)
Thraelgodgathorviginticegathor E100#^(#^###*#^##)20 \(f_{\omega^{\omega^{\omega^3+\omega20}}}(100)\)
Thraelgodgathorquinquaginticegathor E100#^(#^###*#^##)50 \(f_{\omega^{\omega^{\omega^3+\omega50}}}(100)\)
Thraelgralgathgathor E100#^(#^###*#^##)100 \(f_{\omega^{\omega^{\omega^3+\omega^2}}}(100)\)
Thraelgralgodgathgathgathor E100#^(#^###*#^##*#^#)100 \(f_{\omega^{\omega^{\omega^3+\omega^2+\omega}}}(100)\)
Thraelgralgodgathordeusgathgathor E100#^(#^###*#^##*#^#*#^#)100 \(f_{\omega^{\omega^{\omega^3+\omega^2+\omega2}}}(100)\)
Thraelgralgathordeusgathor E100#^(#^###*#^##*#^##)100 \(f_{\omega^{\omega^{\omega^3+\omega^22}}}(100)\)
Thraelgralgathortrucegathor E100#^(#^###*#^##*#^##*#^##)100 \(f_{\omega^{\omega^{\omega^3+\omega^23}}}(100)\)
Thraelgralgathorquadgathor E100#^(#^###*#^##*#^##*#^##*#^##)100 = E100#^(#^###*#^###)4 \(f_{\omega^{\omega^{\omega^3+\omega^24}}}(100)\)
Thraelgralgathorquidgathor E100#^(#^###*#^###)5 \(f_{\omega^{\omega^{\omega^3+\omega^25}}}(100)\)
Thraelgralgathorsidgathor E100#^(#^###*#^###)6 \(f_{\omega^{\omega^{\omega^3+\omega^26}}}(100)\)
Thraelgralgathorseptucegathor E100#^(#^###*#^###)7 \(f_{\omega^{\omega^{\omega^3+\omega^27}}}(100)\)
Thraelgralgathoroctucegathor E100#^(#^###*#^###)8 \(f_{\omega^{\omega^{\omega^3+\omega^28}}}(100)\)
Thraelgralgathornonicegathor E100#^(#^###*#^###)9 \(f_{\omega^{\omega^{\omega^3+\omega^29}}}(100)\)
Thraelgralgathordecicegathor E100#^(#^###*#^###)10 \(f_{\omega^{\omega^{\omega^3+\omega^210}}}(100)\)
Thraelgralgathorviginticegathor E100#^(#^###*#^###)20 \(f_{\omega^{\omega^{\omega^3+\omega^220}}}(100)\)
Thraelgralgathorquinquaginticegathor E100#^(#^###*#^###)50 \(f_{\omega^{\omega^{\omega^3+\omega^250}}}(100)\)
Thraelgathordeus E100#^(#^###*#^###)100 \(f_{\omega^{\omega^{\omega^32}}}(100)\)
Thraelgodgathgathordeus E100#^(#^###*#^###*#^#)100 \(f_{\omega^{\omega^{\omega^32+\omega}}}(100)\)
Thraelgralgathgathordeus E100#^(#^###*#^###*#^##)100 \(f_{\omega^{\omega^{\omega^32+\omega^2}}}(100)\)
Thraelgathortruce E100#^(#^###*#^###*#^###)100 \(f_{\omega^{\omega^{\omega^33}}}(100)\)
Thraelgathorquad E100#^(#^###*#^###*#^###*#^###)100 = E100#^#^####4 \(f_{\omega^{\omega^{\omega^34}}}(100)\)
Thraelgathorquid E100#^#^####5 \(f_{\omega^{\omega^{\omega^35}}}(100)\)
Thraelgathorsid E100#^#^####6 \(f_{\omega^{\omega^{\omega^36}}}(100)\)
Thraelgathorseptuce E100#^#^####7 \(f_{\omega^{\omega^{\omega^37}}}(100)\)
Thraelgathoroctuce E100#^#^####8 \(f_{\omega^{\omega^{\omega^38}}}(100)\)
Thraelgathornonice E100#^#^####9 \(f_{\omega^{\omega^{\omega^39}}}(100)\)
Thraelgathordecice E100#^#^####10 \(f_{\omega^{\omega^{\omega^310}}}(100)\)
Thraelgathorvigintice E100#^#^####20 \(f_{\omega^{\omega^{\omega^320}}}(100)\)
Thraelgathortrigintice E100#^#^####30 \(f_{\omega^{\omega^{\omega^330}}}(100)\)
Thraelgathorquadragintice E100#^#^####40 \(f_{\omega^{\omega^{\omega^340}}}(100)\)
Thraelgathorquinquagintice E100#^#^####50 \(f_{\omega^{\omega^{\omega^350}}}(100)\)
Thraelgathorsexagintice E100#^#^####60 \(f_{\omega^{\omega^{\omega^360}}}(100)\)
Thraelgathorseptuagintice E100#^#^####70 \(f_{\omega^{\omega^{\omega^370}}}(100)\)
Thraelgathoroctogintice E100#^#^####80 \(f_{\omega^{\omega^{\omega^380}}}(100)\)
Thraelgathornonagintice E100#^#^####90 \(f_{\omega^{\omega^{\omega^390}}}(100)\)

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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