The heptaelgathor regiment is a series of numbers from E100(#^#^#^7)100 to E100(#^#^#^8)90 defined using Cascading-E notation (i.e. beginning from heptaelgathor and up to heptaelgathornonagintice).[1] The numbers were coined by Sbiis Saibian.
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Hexaelgathor regiment | Octaelgathor regiment |
List of numbers of the regiment[]
Name of number | Cascading-E notation (definition) | Fast-growing hierarchy (approximation) |
Heptaelgathor | E100#^#^#######100 = E100(#^#^#^7)100 | \(f_{\omega^{\omega^{\omega^7}}}(100)\) |
Grand heptaelgathor | E100(#^#^#^7)100#2 | \(f_{\omega^{\omega^{\omega^7}}}^2(100)\) |
Grangol-carta-heptaelgathor | E100(#^#^#^7)100#100 | \(f_{\omega^{\omega^{\omega^7}}+1}(100)\) |
Godgahlah-carta-heptaelgathor | E100(#^#^#^7)100#^#100 | \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega}}(100)\) |
Godgathor-carta-heptaelgathor | E100(#^#^#^7)100#^#^#100 | \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^\omega}}(100)\) |
Gralgathor-carta-heptaelgathor | E100(#^#^#^7)100#^#^##100 | \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^{\omega^2}}}(100)\) |
Thraelgathor-carta-heptaelgathor | E100(#^#^#^7)100#^#^###100 | \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^{\omega^3}}}(100)\) |
Terinngathor-carta-heptaelgathor | E100(#^#^#^7)100#^#^####100 | \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^{\omega^4}}}(100)\) |
Pentaelgathor-carta-heptaelgathor | E100(#^#^#^7)100(#^#^#^5)100 | \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^{\omega^5}}}(100)\) |
Hexaelgathor-carta-heptaelgathor | E100(#^#^#^7)100(#^#^#^6)100 | \(f_{\omega^{\omega^{\omega^7}}+\omega^{\omega^{\omega^6}}}(100)\) |
Heptaeltrigathor | E100(#^#^#^7)100(#^#^#^7)100 | \(f_{\omega^{\omega^{\omega^7}}2}(100)\) |
Heptaeltergathor | E100(#^#^#^7)*#4 | \(f_{\omega^{\omega^{\omega^7}}3}(100)\) |
Heptaelpeggathor | E100(#^#^#^7)*#5 | \(f_{\omega^{\omega^{\omega^7}}4}(100)\) |
Heptaelhexgathor | E100(#^#^#^7)*#6 | \(f_{\omega^{\omega^{\omega^7}}5}(100)\) |
Heptaelhepgathor | E100(#^#^#^7)*#7 | \(f_{\omega^{\omega^{\omega^7}}6}(100)\) |
Heptael-ahtgathor | E100(#^#^#^7)*#8 | \(f_{\omega^{\omega^{\omega^7}}7}(100)\) |
Heptael-enngathor | E100(#^#^#^7)*#9 | \(f_{\omega^{\omega^{\omega^7}}8}(100)\) |
Heptaeldekagathor | E100(#^#^#^7)*#10 | \(f_{\omega^{\omega^{\omega^7}}9}(100)\) |
Heptaelgathor-by-hyperion | E100(#^#^#^7)*#100 | \(f_{\omega^{\omega^{\omega^7}+1}}(100)\) |
Heptaelgathor-by-godgahlah | E100(#^#^#^7)*#^#100 | \(f_{\omega^{\omega^{\omega^7}+\omega}}(100)\) |
Heptaelgathor-by-godgathor | E100(#^#^#^7)*#^#^#100 | \(f_{\omega^{\omega^{\omega^7}+\omega^\omega}}(100)\) |
Heptaelgathor-by-gralgathor | E100(#^#^#^7)*#^#^##100 | \(f_{\omega^{\omega^{\omega^7}+\omega^{\omega^2}}}(100)\) |
Heptaelgathor-by-thraelgathor | E100(#^#^#^7)*#^#^###100 | \(f_{\omega^{\omega^{\omega^7}+\omega^{\omega^3}}}(100)\) |
Heptaelgathor-by-terinngathor | E100(#^#^#^7)*#^#^####100 | \(f_{\omega^{\omega^{\omega^7}+\omega^{\omega^4}}}(100)\) |
Heptaelgathor-by-pentaelgathor | E100(#^#^#^7)*(#^#^#^5)100 | \(f_{\omega^{\omega^{\omega^7}+\omega^{\omega^5}}}(100)\) |
Heptaelgathor-by-hexaelgathor | E100(#^#^#^7)*(#^#^#^6)100 | \(f_{\omega^{\omega^{\omega^7}+\omega^{\omega^6}}}(100)\) |
Deutero-heptaelgathor | E100(#^#^#^7)*(#^#^#^7)100 | \(f_{\omega^{\omega^{\omega^7}2}}(100)\) |
Trito-heptaelgathor | E100(#^#^#^7)*(#^#^#^7)*(#^#^#^7)100 | \(f_{\omega^{\omega^{\omega^7}3}}(100)\) |
Teterto-heptaelgathor | E100#^(#^#^7*#)4 | \(f_{\omega^{\omega^{\omega^7}4}}(100)\) |
Pepto-heptaelgathor | E100#^(#^#^7*#)5 | \(f_{\omega^{\omega^{\omega^7}5}}(100)\) |
Exto-heptaelgathor | E100#^(#^#^7*#)6 | \(f_{\omega^{\omega^{\omega^7}6}}(100)\) |
Epto-heptaelgathor | E100#^(#^#^7*#)7 | \(f_{\omega^{\omega^{\omega^7}7}}(100)\) |
Ogdo-heptaelgathor | E100#^(#^#^7*#)8 | \(f_{\omega^{\omega^{\omega^7}8}}(100)\) |
Ento-heptaelgathor | E100#^(#^#^7*#)9 | \(f_{\omega^{\omega^{\omega^7}9}}(100)\) |
Dekato-heptaelgathor | E100#^(#^#^7*#)10 | \(f_{\omega^{\omega^{\omega^7}10}}(100)\) |
isosto-heptaelgathor | E100#^(#^#^7*#)20 | \(f_{\omega^{\omega^{\omega^7}20}}(100)\) |
trianto-heptaelgathor | E100#^(#^#^7*#)30 | \(f_{\omega^{\omega^{\omega^7}30}}(100)\) |
saranto-heptaelgathor | E100#^(#^#^7*#)40 | \(f_{\omega^{\omega^{\omega^7}40}}(100)\) |
peninto-heptaelgathor | E100#^(#^#^7*#)50 | \(f_{\omega^{\omega^{\omega^7}50}}(100)\) |
exinto-heptaelgathor | E100#^(#^#^7*#)60 | \(f_{\omega^{\omega^{\omega^7}60}}(100)\) |
ebdominto-heptaelgathor | E100#^(#^#^7*#)70 | \(f_{\omega^{\omega^{\omega^7}70}}(100)\) |
ogdonto-heptaelgathor | E100#^(#^#^7*#)80 | \(f_{\omega^{\omega^{\omega^7}80}}(100)\) |
eneninto-heptaelgathor | E100#^(#^#^7*#)90 | \(f_{\omega^{\omega^{\omega^7}90}}(100)\) |
hecato-heptaelgathor | E100#^(#^#^7*#)100 | \(f_{\omega^{\omega^{\omega^7+1}}}(100)\) |
heptaelgridgathor | E100#^(#^#^7*##)100 | \(f_{\omega^{\omega^{\omega^7+2}}}(100)\) |
heptaelkubikgathor | E100#^(#^#^7*###)100 | \(f_{\omega^{\omega^{\omega^7+3}}}(100)\) |
heptaelquarticgathor | E100#^(#^#^7*####)100 | \(f_{\omega^{\omega^{\omega^7+4}}}(100)\) |
heptaelgodgathgathor | E100#^(#^#^7*#^#)100 | \(f_{\omega^{\omega^{\omega^7+\omega}}}(100)\) |
heptaelgralgathgathor | E100#^(#^#^7*#^##)100 | \(f_{\omega^{\omega^{\omega^7+\omega^2}}}(100)\) |
heptaelthraelgathgathor | E100#^(#^#^7*#^###)100 | \(f_{\omega^{\omega^{\omega^7+\omega^3}}}(100)\) |
heptaelterinngathgathor | E100#^(#^#^7*#^####)100 | \(f_{\omega^{\omega^{\omega^7+\omega^4}}}(100)\) |
heptaelpentaelgathgathor | E100#^(#^#^7*#^#^5)100 | \(f_{\omega^{\omega^{\omega^7+\omega^5}}}(100)\) |
heptaelhexaelgathgathor | E100#^(#^#^7*#^#^6)100 | \(f_{\omega^{\omega^{\omega^7+\omega^6}}}(100)\) |
heptaelgathordeus | E100#^(#^#^7*#^#^7)100 | \(f_{\omega^{\omega^{\omega^72}}}(100)\) |
heptaelgathortruce | E100#^(#^#^7*#^#^7*#^#^7)100 | \(f_{\omega^{\omega^{\omega^73}}}(100)\) |
heptaelgathorquad | E100(#^#^#^8)4 | \(f_{\omega^{\omega^{\omega^74}}}(100)\) |
heptaelgathorquid | E100(#^#^#^8)5 | \(f_{\omega^{\omega^{\omega^75}}}(100)\) |
heptaelgathorsid | E100(#^#^#^8)6 | \(f_{\omega^{\omega^{\omega^76}}}(100)\) |
heptaelgathorseptuce | E100(#^#^#^8)7 | \(f_{\omega^{\omega^{\omega^77}}}(100)\) |
heptaelgathoroctuce | E100(#^#^#^8)8 | \(f_{\omega^{\omega^{\omega^78}}}(100)\) |
heptaelgathornonice | E100(#^#^#^8)9 | \(f_{\omega^{\omega^{\omega^79}}}(100)\) |
heptaelgathordecice | E100(#^#^#^8)10 | \(f_{\omega^{\omega^{\omega^710}}}(100)\) |
heptaelgathorvigintice | E100(#^#^#^8)20 | \(f_{\omega^{\omega^{\omega^720}}}(100)\) |
heptaelgathortrigintice | E100(#^#^#^8)30 | \(f_{\omega^{\omega^{\omega^730}}}(100)\) |
heptaelgathorquadragintice | E100(#^#^#^8)40 | \(f_{\omega^{\omega^{\omega^740}}}(100)\) |
heptaelgathorquinquagintice | E100(#^#^#^8)50 | \(f_{\omega^{\omega^{\omega^750}}}(100)\) |
heptaelgathorsexagintice | E100(#^#^#^8)60 | \(f_{\omega^{\omega^{\omega^760}}}(100)\) |
heptaelgathorseptuagintice | E100(#^#^#^8)70 | \(f_{\omega^{\omega^{\omega^770}}}(100)\) |
heptaelgathoroctogintice | E100(#^#^#^8)80 | \(f_{\omega^{\omega^{\omega^780}}}(100)\) |
heptaelgathornonagintice | E100(#^#^#^8)90 | \(f_{\omega^{\omega^{\omega^790}}}(100)\) |
Sources[]
- ↑ Saibian, Sbiis. Cascading-E Numbers. Retrieved 2017-10-13.
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
Redstonepillager's extensions: Extended Gridgahlah regiment · Tethratopothoth regiment · Godsgodgulus regiment · Blasphemorgulus regiment · Blasphemordeugulus regiment · Ominongulus regiment