Ominongulus regiment

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 .https://sites.google.com/view/rpillagergoogology/exeominongulus accessed Sep 24, 2023https://sites.google.com/view/rpillagergoogology/linearexe Accessed Dec 30, 2023 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 ==
== See also ==
Category:Numbers
Category:Ominongulus series
Category:Series
Category:Numbers by Redstonepillager
Category:Numbers by Sbiis Saibian
Category:Hyper-E numbers
Category:Cascading-E numbers
Category:Hyper-Extended Cascading-E numbers
Category:Hyper-Hyper-Extended Cascading-E numbers
Category:ExE numbers using higher BEAF structures
Category:Tetration level
Category:Polynomial omega level
Category:Bachmann's collapsing level
Category:Class disputed
Category:Unformalised