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The greagol regiment is a series of numbers from E100#100#100 to E1#1#1#10,000 defined using Hyper-E Notation (i.e. beginning from greagol and up to myria-petaxis).[1] The numbers were coined by Sbiis Saibian.

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Grangol regiment Gigangol regiment

List of numbers of the regiment Edit

Name of number Hyper-E Notation (definition) Scientific notation (exact value) Pronunciation
greagol E100#100#100 
\left.
\begin{matrix}
\underbrace{10^{...^{10^{100}}}} \\
\underbrace{\quad\;\; \vdots \quad\;\;} \\
\underbrace{10^{...^{10^{100}}}} \\
100\quad 10's
\end{matrix}
\right \} \text{100 lower braces}
Greagol(1)
grangolthrex E100#100#1#2 = E100#100#grangol \left. \begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \}  \underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}
P-Grangolthrex(1)
grangoldexithrex E100#100#2#2 = E100#100#grangoldex \left. \begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \}  \underbrace{10^{10^{...{^{10^{100}}}}}}_{\underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}}
P-Grangoldexithrex
grangoldudexithrex E100#100#3#2 = E100#100#grangoldudex \left. \left.\begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \}  \begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\& & 100\quad 10's \end{matrix}  \right \} \text {3 lower braces}
P-Grangoldudexithrex
greagolthrex E100#100#100#2 = E100#100#(E100#100#100) = E100#100#greagol \left. \left.\begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \}  \begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \} \text {100 lower braces}
P-Greagolthrex
grangolduthrex E100#100#1#3 = E100#100#grangol#2 \left. \left.\begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \} \begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \} \underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}
P-Grangolduthrex
grangoldexiduthrex E100#100#2#3 = E100#100#grangoldex#2 \left. \left.\begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \} \begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \} \underbrace{10^{10^{...{^{10^{100}}}}}}_{\underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}}
P-Grangoldexiduthrex
grangoldudexiduthrex E100#100#3#3 = E100#100#grangoldudex#2 \left. \left.\left.\begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \} \begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \} \begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}} \\&&\underbrace{10^{10^{...{^{10^{100}}}}}} \\&&\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \} \text {3 lower braces}
P-Grangoldudexiduthrex
greagolduthrex E100#100#100#3 = E100#100#(E100#100#100#2) = E100#100#greagolthrex \left. \left.\left.\begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \} \begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \}  \begin{matrix}  &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\  & & \underbrace{\quad \;\; \vdots \quad\;\;}\\  & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix}  \right \} \text {100 lower braces}
P-Greagolduthrex
Name of number Hyper-E Notation (definition) Arrow notation (approximation) Pronunciation
grangoltrithrex E100#100#1#4 = E100#100#grangol#3 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101))))\)
P-Grangoltrithrex
grangoldexitrithrex E100#100#2#4 = E100#100#grangoldex#3 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3)))\)
P-Grangoldexitrithrex
grangoldudexitrithrex E100#100#3#4 = E100#100#grangoldudex#3 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4)))\)
Grangoldudexitrithrex
greagoltrithrex E100#100#100#4 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101)))\)
P-Greagoltrithrex
grangolquadrithrex E100#100#1#5 = E100#100#grangol#4 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101)))))\)
P-Grangolquadrithrex
grangoldexiquadrithrex E100#100#2#5 = E100#100#grangoldex#4 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3))))\)
P-Grangoldexiquadrithrex
grangoldudexiquadrithrex E100#100#3#5 = E100#100#grangoldudex#4 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4))))\)
P-Grangoldudexiquadrithrex
greagolquadrithrex E100#100#100#5 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101))))\)
P-Greagolquadrithrex
grangolquintithrex E100#100#1#6 = E100#100#grangol#5 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101))))))\)
P-Grangolquintithrex
grangoldexiquintithrex E100#100#2#6 = E100#100#grangoldex#5 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3)))))\)
P-Grangoldexiquintithrex
grangoldudexiquintithrex E100#100#3#6 = E100#100#grangoldudex#5 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4)))))\)
P-Grangoldudexiquintithrex
greagolquintithrex E100#100#100#6 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101)))))\)
P-Greagolquintithrex
greagolsextithrex E100#100#100#7 \(10\uparrow^4 8\)
P-Greagolsextithrex
greagolseptithrex E100#100#100#8 \(10\uparrow^4 9\)
P-Greagolseptithrex
greagoloctithrex E100#100#100#9 \(10\uparrow^4 10\)
P-Greagoloctithrex
greagolnonithrex E100#100#100#10 \(10\uparrow^4 11\)
P-Greagolnonithrex
greagoldecithrex E100#100#100#11 \(10\uparrow^4 12\)
P-Greagoldecithrex
greagolthrexichime E1000#1000#1000#2 \(10\uparrow^3 (10\uparrow^3 (1001))\)
P-Greagolthrexichime
greagolduthrexichime E1000#1000#1000#3 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001)))\)
P-Greagolduthrexichime
greagoltrithrexichime E1000#1000#1000#4 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001))))\)
P-Greagoltrithrexichime
greagolquadrithrexichime E1000#1000#1000#5 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001)))))\)
P-Greagolquadrithrexichime
greagolquintithrexichime E1000#1000#1000#6 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001))))))\)
P-Greagolquintithrexichime
greagoltoll E10,000#10,000#10,000 \(10\uparrow^3 (10^4)\)
P-Greagoltoll
greagolthrexitoll E10,000#10,000#10,000#2 \(10\uparrow^3 (10\uparrow^3 (10^4))\)
P-Greagolthrexitoll
greagolduthrexitoll E10,000#10,000#10,000#3 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))\)
P-Greagolduthrexitoll
greagoltrithrexitoll E10,000#10,000#10,000#4 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))\)
P-Greagoltrithrexitoll
greagolquadrithrexitoll E10,000#10,000#10,000#5 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4))))\)
P-Greagolquadrithrexitoll
greagolquintithrexitoll E10,000#10,000#10,000#6 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))))\)
P-Greagolquintithrexitoll
greagolgong E100,000#100,000#100,000 \(10\uparrow^3 (10^5)\)
P-Greagolgong
greagolthrexigong E100,000#100,000#100,000#2 \(10\uparrow^3 (10\uparrow^3 (10^5))\)
P-Greagolthrexigong
greagolduthrexigong E100,000#100,000#100,000#3 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5)))\)
P-Greagolduthrexigong
greagoltrithrexigong E100,000#100,000#100,000#4 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5))))\)
P-Greagoltrithrexigong
greagolquadrithrexigong E100,000#100,000#100,000#5 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5)))))\)
P-Greagolquadrithrexigong
greagolquintithrexigong E100,000#100,000#100,000#6 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5))))))\)
P-Greagolquintithrexigong
greagolbong E100,000,000#100,000,000#100,000,000 \(10\uparrow^3 (10^8)\)
P-Greagolbong
greagolthrexibong E100,000,000#100,000,000#100,000,000#2 \(10\uparrow^3 (10\uparrow^3 (10^8))\)
P-Greagolthrexibong
greagolduthrexibong E100,000,000#100,000,000#100,000,000#3 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^8)))\)
P-Greagolduthrexibong
greagolthrong E100,000,000,000#100,000,000,000#100,000,000,000 \(10\uparrow^3 (10^{11})\)
P-Greagolthrong
greagolthrexithrong E100,000,000,000#100,000,000,000#100,000,000,000#2 \(10\uparrow^3 (10\uparrow^3 (10^{11}))\)
P-Greagolthrexithrong
greagolduthrexithrong E100,000,000,000#100,000,000,000#100,000,000,000#3 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{11})))\)
P-Greagolduthrexithrong
gaggolchime E1#1#1000 \(10\uparrow^3 1000\)
P-Gaggolchime
gaggoltoll E1#1#10,000 \(10\uparrow^3 10000\)
P-Gaggoltoll
gaggolgong E1#1#100,000 \(10\uparrow^3 100000\)
P-Gaggolgong
gaggolbong E1#1#100,000,000 \(10\uparrow^3 10^8\)
P-Gaggolbong
gaggolthrong E1#1#100,000,000,000 \(10\uparrow^3 10^{11}\)
P-Gaggolthrong
googolthrex E100#1#1#2 = E100#1#googol \(10\uparrow^3 10^{100}\)
P-Googolthrex
googolplexithrex E100#2#1#2 = E100#2#googolplex \(10\uparrow^3 10^{10^{10^{100}}}\)
P-Googolplexithrex
googoldexithrex E100#1#2#2 = E100#1#(E100#1#2) \(10\uparrow^3 (10\uparrow^2 (10^{100}))\)
P-Googoldexithrex
greagolplex E(E100#100#100) \(10\uparrow (10\uparrow^3 (101))\)
P-Greagolplex
greagoldex E100#(E100#100#100) = E100#100#101 \(10\uparrow^2 (10\uparrow^3 (101))\)
P-Greagoldex
ecetonthrex E303#1#1#2 = E303#1#(E303) = E303#1#centillion \(10\uparrow^3 (10^{303})\)
P-Ecetonthrex
ecetonduthrex E303#1#1#3 = E303#1#ecetonthrex \(10\uparrow^3 (10\uparrow^3 (10^{303}))\)
P-Ecetonduthrex
ecetontrithrex E303#1#1#4 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303})))\)
P-Ecetontrithrex
ecetonquadrithrex E303#1#1#5 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303}))))\)
P-Ecetonquadrithrex
ecetonquintithrex E303#1#1#6 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303})))))\)
P-Ecetonquintithrex
tria-petaxis E1#1#1#3 = E1#1#deka-taxis \(10\uparrow^4 3\)
P-Tria-petaxis
tetra-petaxis E1#1#1#4 = E1#1#tria-petaxis \(10\uparrow^4 4\)
P-Tetra-petaxis
penta-petaxis E1#1#1#5 = E1#1#tetra-petaxis \(10\uparrow^4 5\)
P-Penta-petaxis
hexa-petaxis E1#1#1#6 = E1#1#penta-petaxis \(10\uparrow^4 6\)
P-Hexa-petaxis
hepta-petaxis E1#1#1#7 = E1#1#hexa-petaxis \(10\uparrow^4 7\)
P-Hepta-petaxis
octa-petaxis E1#1#1#8 = E1#1#hepta-petaxis \(10\uparrow^4 8\)
P-Octa-petaxis
enna-petaxis E1#1#1#9 = E1#1#octa-petaxis \(10\uparrow^4 9\)
P-Enna-petaxis
deka-petaxis E1#1#1#10 = E1#1#enna-petaxis \(10\uparrow^4 10\)
P-Deka-petaxis
hecta-petaxis E1#1#1#100 \(10\uparrow^4 100\)
P-Hecta-petaxis
chilia-petaxis E1#1#1#1000 \(10\uparrow^4 1000\)
P-Chilia-petaxis
myria-petaxis E1#1#1#10,000 \(10\uparrow^4 10000\)
P-Myria-petaxis

Etymology Edit

Parts of names Meaning Pronunciation
tria 3
P-Tria
tetra 4
P-Tetra
penta 5
P-Penta
hexa 6
P-Hexa
hepta 7
P-Hepta
octa 8
P-Octa
enna 9
P-Enna
deka 10
P-Deka
hecta 100
P-Hecta
chilia 1000
P-Chilia
myria 10000
P-Myria
ding multiply the base value by 5
P-Ding
chime multiply the base value by 10
P-Chime
bell multiply the base value by 50
P-Bell
toll multiply the base value by 100
P-Toll
gong multiply the base value by 1000
P-Gong
bong multiply the base value by \(10^6\)
P-Bong
throng multiply the base value by \(10^9\)
P-Throng
gandingan multiply the base value by \(10^{12}\)
P-Gandingan

Sources Edit

  1. Sbiis Saibian, 4.3.2 - Hyper-E Numbers
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 · Tethraennon 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