The ominongulus regiment is an incomplete series of numbers from \(E100\#100\) up to ???? defined using a climbing method of Hyper-Hyper-Extended Cascading-E Notation. The numbers were coined by Sbiis Saibian, YouTuber Douglas Shamlin Jr and wiki user Redstonepillager.[1][2] As the Extensible-E System is not formalised at this level, the numbers here are currently ill-defined; thus, the Fast-growing hierarchy approximations are representative of an intended value of the googolisms, assuming them to be well-defined.
According to the creator, this regiment will be forever incomplete.
List of numbers in the regiment[]
| Name of number | Definition | FGH approximation (intended) (using Buchholz's function) |
|---|---|---|
| henodgulus (grangol) | E100{#,1(1)2}100 = E100#100 | \(f_3(100)\) |
| duodgulus (godgahlah) | E100{#,2(1)2}100 = E100#^#100 | \(f_{\omega^{\omega}}(100)\) |
| triodgulus (godsgodgulus) | E100{#,3(1)2}100 = E100#{#}#100 | \(f_{\varphi(\omega,0,0)}(100)\) |
| terodgulus (general gogulus) | E100{#,4(1)2}100 = E100{#,#,#,#}100 | \(f_{\varphi(\omega,\omega,0,0)}(100)\) |
| penodgulus | E100{#,5(1)2}100 = E100{#,#,#,#,#}100 | \(f_{\varphi(\omega,\omega,\omega,0,0)}(100)\) |
| exodgulus | E100{#,6(1)2}100 = E100{#,#,#,#,#,#}100 | \(f_{\varphi(\omega,\omega,\omega,\omega,0,0)}(100)\) |
| eptodgulus | E100{#,7(1)2}100 = E100{#,#,#,#,#,#,#}100 | \(f_{\varphi(\omega,\omega,\omega,\omega,\omega,0,0)}(100)\) |
| ogdodgulus | E100{#,8(1)2}100 = E100{#,#,#,#,#,#,#,#}100 | \(f_{\varphi(\omega,\omega,\omega,\omega,\omega,\omega,0,0)}(100)\) |
| entodgulus | E100{#,9(1)2}100 = E100{#,#,#,#,#,#,#,#,#}100 | \(f_{\varphi(\omega,\omega,\omega,\omega,\omega,\omega,\omega,0,0)}(100)\) |
| dektodgulus (demagogue) | E100{#,10(1)2}100 = E100{#,#,#,#,#,#,#,#,#,#}100 | \(f_{\varphi(\omega,\omega,\omega,\omega,\omega,\omega,\omega,\omega,0,0)}(100)\) |
| hendektodgulus | E100{#,11(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{9},0,0)}(100)\) |
| dodektodgulus | E100{#,12(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{10},0,0)}(100)\) |
| trisdektodgulus | E100{#,13(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{11},0,0)}(100)\) |
| terdektodgulus | E100{#,14(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{12},0,0)}(100)\) |
| pendektodgulus | E100{#,15(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{13},0,0)}(100)\) |
| exdektodgulus | E100{#,16(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{14},0,0)}(100)\) |
| eptdektodgulus | E100{#,17(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{15},0,0)}(100)\) |
| ogddektodgulus | E100{#,18(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{16},0,0)}(100)\) |
| entdektodgulus | E100{#,19(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{17},0,0)}(100)\) |
| icosodgulus | E100{#,20(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{18},0,0)}(100)\) |
| triantodgulus | E100{#,30(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{28},0,0)}(100)\) |
| sarantodgulus | E100{#,40(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{38},0,0)}(100)\) |
| penintodgulus | E100{#,50(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{48},0,0)}(100)\) |
| exintodgulus | E100{#,60(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{58},0,0)}(100)\) |
| ebdomintodgulus | E100{#,70(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{68},0,0)}(100)\) |
| ogdondodgulus | E100{#,80(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{78},0,0)}(100)\) |
| eninodgulus | E100{#,90(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{88},0,0)}(100)\) |
| ominongulus | E100{#,100(1)2}100 = E100{#,#(1)2}100 | \(f_{\varphi(\underbrace{\omega,\omega,\ldots,\omega}_{98},0,0)}(100)\) \(\approx\) \(f\)\(_{\psi_{0}(\Omega^{\Omega^{\omega}})}\)\((100)\) |
| gigasodgulus | E100{#,#(1)2}500 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(500)\) |
| chiliasodgulus | E100{#,#(1)2}1,000 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(1000)\) |
| myriasodgulus | E100{#,#(1)2}10,000 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(10,000)\) |
| hotalodgulus | E100{#,#(1)2}100,000 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(100,000)\) |
| pseudomonarchia daemonum | E100{#,#(1)2}44,435,622 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(44,435,622)\) |
| octadodgulus | E100{#,#(1)2}100,000,000 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(100,000,000)\) |
| sedeniadodgulus | E100{#,#(1)2}1016 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(10^{16})\) |
| googlodgulus | E100{#,#(1)2}10100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(10^{100})\) |
| granglodgulus | E100{#,#(1)2}(E100#100) | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(f_3(100))\) |
| godgahlodgulus | E100{#,#(1)2}(E100#^#100) | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(f_{\omega^{\omega}}(100))\) |
| godsgodgulodgulus | E100{#,#(1)2}(E100#{#}#100) | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(f_{\varphi(\omega,0,0)}(100))\) |
| terodgodgulus | E100{#,#(1)2}(E100{#,#,#,#}100) | \(f_{\psi_0(\Omega^{\Omega^{\omega}})}(f_{\varphi(\omega,\omega,0,0)}(100))\) |
| grand ominongulus | E100{#,#(1)2}100#2 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})} ^2 (100)\) |
| grand pseudomonarchia daemonum | E100{#,#(1)2}44,435,622#2 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})} ^2 (44,435,622)\) |
| grand grand ominongulus | E100{#,#(1)2}100#3 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})} ^3 (100)\) |
| grand grand grand ominongulus | E100{#,#(1)2}100#4 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})} ^4 (100)\) |
| grangol-carta-ominongulus | E100{#,#(1)2}100#100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+1}(100)\) |
| greagol-carta-ominongulus | E100{#,#(1)2}100#100#100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+2}(100)\) |
| gigangol-carta-ominongulus | E100{#,#(1)2}100#100#100#100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+3}(100)\) |
| gugolda-carta-ominongulus | E100{#,#(1)2}100##100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+\omega}(100)\) |
| throogol-carta-ominongulus | E100{#,#(1)2}100###100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+\omega^2}(100)\) |
| godgahlah-carta-ominongulus | E100{#,#(1)2}100#^#100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+\omega^{\omega}}(100)\) |
| godsgodgulus-carta-ominongulus | E100{#,#(1)2}100#{#}#100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+\varphi(\omega,0,0)}(100)\) |
| blasphemorgulus-carta-ominongulus | E100{#,#(1)2}100#{{1}}#100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+\varphi(1,0,0,0)}(100)\) |
| pentemorgulus-carta-ominongulus | E100{#,#(1)2}100{#,#,1,1,2}100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+\varphi(1,0,0,0,0)}(100)\) |
| hexemorgulus-carta-ominongulus | E100{#,#(1)2}100{#,#,1,1,1,2}100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+\varphi(1,0,0,0,0,0)}(100)\) |
| heptemorgulus-carta-ominongulus | E100{#,#(1)2}100{#,#,1,1,1,1,2}100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+\varphi(1,0,0,0,0,0,0)}(100)\) |
| ottemorgulus-carta-ominongulus | E100{#,#(1)2}100{#,#,1,1,1,1,1,2}100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+\varphi(1,0,0,0,0,0,0,0)}(100)\) |
| entemorgulus-carta-ominongulus | E100{#,#(1)2}100{#,#,1,1,1,1,1,1,2}100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+\varphi(1,0,0,0,0,0,0,0,0)}(100)\) |
| deckemorgulus-carta-ominongulus | E100{#,#(1)2}100{#,#,1,1,1,1,1,1,1,2}100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})+\varphi(1,0,0,0,0,0,0,0,0,0)}(100)\) |
| ominongulus-by-deuteron | E100{#,#(1)2}100{#,#(1)2}100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})2}(100)\) |
| ominongulus-by-triton | E100{#,#(1)2}100{#,#(1)2}100{#,#(1)2}100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})3}(100)\) |
| ominongulus-by-teterton | E100{#,#(1)2}100{#,#(1)2}100{#,#(1)2}100{#,#(1)2}100 | \(f_{\psi_0(\Omega^{\Omega^{\omega}})4}(100)\) |
History of sources[]
The page was initially referenced in https://sites.google.com/view/rpillagergoogology/exeominongulus but the site creator has since moved the URL of said page to https://sites.google.com/view/rpillagergoogology/linearexe.
Sources[]
- ↑ https://sites.google.com/view/rpillagergoogology/exeominongulus[dead link] accessed Sep 24, 2023
- ↑ https://sites.google.com/view/rpillagergoogology/linearexe Accessed Dec 30, 2023
See also[]
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