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Difference between revisions of "Jonathan Bowers"

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Numbers higher than those in the Gaggol group are referred to by Jonathan Bowers as the infinity scrapers. Here's a list of the names of those numbers that are infinity scrapers:
 
Numbers higher than those in the Gaggol group are referred to by Jonathan Bowers as the infinity scrapers. Here's a list of the names of those numbers that are infinity scrapers:
  
−
{| border="1"
+
{| class=wikitable
 
! Name || Value
 
! Name || Value
 
|-
 
|-
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| Hexatri || {3,3,3,3,3,3}
 
| Hexatri || {3,3,3,3,3,3}
 
|-
 
|-
−
| Hexadecal || {10,10,10,10,10,10} ||
+
| Hexadecal || {10,10,10,10,10,10}
 
|-
 
|-
 
| Hexadecalplex || {10,10,10,10,10,hexadecal}  
 
| Hexadecalplex || {10,10,10,10,10,hexadecal}  
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|-
 
|-
 
| Iteralplex || {10,10,10,10,10,10,...........,10,10,10}  
 
| Iteralplex || {10,10,10,10,10,10,...........,10,10,10}  
 +
|}
 +
The following numbers requre an extended array notation to define. These are defined recursively, using rules such as:
 +
:<math>\left\langle\begin{matrix}a&b\\2&\end{matrix}\right\rangle=\{a,a,\ldots,a\}</math> with ''a'' repeated ''b'' times.
 +
:<math>\left\langle\begin{matrix}a&b\\k&\end{matrix}\right\rangle=\left\langle\begin{matrix}a&a&\ldots&a\\k-1\end{matrix}\right\rangle</math> with ''a'' repeated ''b'' times.
 +
 +
{| class=wikitable
 +
! Name || Value
 
|-
 
|-
−
| Emperal || /10,10\
+
|Emperal
−
\10     / || Emperal is so large that it requires entended array notation to define it.
+
|<math>\left\langle\begin{matrix}10&10\\10&\end{matrix}\right\rangle</math>
 
|-
 
|-
−
| Emperalplex || /10, 10   \
+
|Emperalplex
−
\emperal /  
+
|<math>\left\langle\begin{matrix}10&10\\emperal&\end{matrix}\right\rangle</math>
 
|-
 
|-
−
| Hyperal || /10,10\
+
|Hyperal  
−
\10,10/  
+
|<math>\left\langle\begin{matrix}10&10\\10&10\end{matrix}\right\rangle</math>
 
|-
 
|-
−
| Hyperalplex || /10,10       \
+
| Hyperalplex
−
\10,hyperal/
+
|<math>\left\langle\begin{matrix}10&10\\10&Hyperal\end{matrix}\right\rangle</math>
 
|-
 
|-
−
| Dutritri || /3,3,3\
+
| Dutritri  
−
|3,3,3 |
+
|<math>\left\langle\begin{matrix}3&3&3\\3&3&3\\3&3&3\end{matrix}\right\rangle</math>
−
\3,3,3/
+
 
|-
 
|-
−
| Dutridecal || /10,10,10\
+
| Dutridecal
−
|10,10,10 |
+
|<math>\left\langle\begin{matrix}10&10&10\\10&10&10\\10&10&10\end{matrix}\right\rangle</math>
−
\10,10,10/
+
 
|-
 
|-
−
| Xappol || /10,10,10,10,10,10,10,10,10,10\
+
| Xappol || 10 by 10 array of 10's
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
\10,10,10,10,10,10,10,10,10,10/
+
 
|-
 
|-
−
| Xappolplex || /10,10,10,10,10,10,10,10,10,10\
+
| Xappolplex || xappol by xappol array of 10's
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
|10,10,10,10,10,10,10,10,10,10 |
+
−
\10,10,10,10,10,10,10,10,10,10/
+
 
|-
 
|-
 
| Dimentri || 3 x 3 x 3 array of 3's
 
| Dimentri || 3 x 3 x 3 array of 3's

Revision as of 20:22, 6 March 2006

Jonathan Bowers, mathematician (November 27, 1969–)

Polychora

One of the participants in the Uniform Polychora Project, an attempt to name higher-dimensional polychora. He independently began his search for polychora in 1990. Circa 1993, he invented his short names for the uniform polychora, which have come to be known as the Bowers style acronyms (or pet name). In 1997, he contacted others who are also interested in the subject, such as Magnus Wenninger, Vincent Matsko, and George Olshevsky.

Very large numbers

Bowers has proposed a series of names (including giggol, gaggol, geegol, goggol, tridecal, tetratri, dutritri, xappol, dimendecal, gongulus, trimentri, goppatoth, golapulus, golapulusplex, golapulusplux, big boowa and guapamonga) for extremely Large numbers, which he terms infinity scrapers (a pun on skyscraper), many of which are so unspeakably and unprecedentedly large as to require special newly-devised extended mathematical notations in order to be expressed.infinity scrapers

He is also the inventor of the Array Notation as a means to represent very large numbers. This notion is very similar to the Conway chained arrow notation and relies on the tetration operator <math>{\ ^{b}a = \atop {\ }} {{\underbrace{a^{a^{\cdot^{\cdot^{a}}}}}} \atop b}</math>, and its higher order analogues: pentation, sexation, heptation. some examples of which are

  • <math>\{a,b,1\} = a \{1\} b = a+b\;</math>
  • <math>\{a,b,2\} = a \{2\} b = a*b\;</math>
  • <math>\{a,b,3\} = a \{3\} b = a^b\;</math>
  • <math>\{a,b,4\} = a \{4\} b = \ ^{b}a</math> a tetrated to b.
  • <math>\{a,b,5\} = a \{5\} b = \ ^{\ ^{\ ^{\ ^a\cdot}\cdot}a}a</math> - a pentated to b - a tetrated to itself b times.
  • <math>\{a,b,c,2\} = a \{\{c\}\}b\;</math>
  • <math>\{a,2,1,2\} = a \{\{1\}\}2 = a \{a\}a\;</math>
  • <math>\{a,3,1,2\} = a \{\{1\}\}3 = a \{a \{a\}a\}a\;</math>
  • <math>\{a,b,1,2\} = a \{\{1\}\}b = a \{a\ldots\{a\}\ldots a\}a\;</math> - a expanded to b.
  • <math>\{a,b,2,2\} = a \{\{2\}\}b\;</math> - a expanded to itself b times.
Group Name Value Array notation
Googol group Googol <math>10^{100}=10^{10^2}</math> {10,100,2} = 10 {2} 100
Googolplex <math>10^{10^{100}}=10^{10^{10^2}}</math> {10,{10,100,2},2} = 10 {2} 10 {2} 100
Googolduplex <math>10^{10^{10^{100}}}</math> {10,{10,{10,100,2},2},2} = 10 {2} 10 {2} 10 {2} 100
Giggol group <math>\ ^{10}10</math> {10,10,4} = 10 {4} 10
Giggol <math>\ ^{100}10</math> {10,100,4} = 10 {4} 10: 10 to the power of itself 100 times.
Giggolplex 10 {4} 10 {4} 10: 10 tetrated to a giggol
Giggolduplex 10 {4} 10 {4} 10 {4} 100.
Gaggol group Gaggol {10,100,5} = 10 {5} 100: 10 pentated to 100.
gaggolplex 10 {5} gaggol = 10 {5} 10 {5} 100: 10 tetrated to itself a gaggol times.
geegol {10,100,6}=10 {6} 100
geegolplex {10,geegol, 6}
gygol {10,100,7}
gygolplex {10,gygol,7}
goggol {10,100,8}
goggolplex {10,goggol,8}
gagol {10,100,9}
gagolplex {10,gagol,9}
Infinity Scrapers Tridecal {10,10,10} = 10 {10} 10 = 10 decated to 10
boogol {10,10,100} = 10 {100} 10

Bowers notation extends beyond even these numbers and includes the Corporal {10,100,1,2}, Grand Tridecal {10,10,10,2}, Tetratri = {3,3,3,3}, General = {10,10,10,10}, Pentadecal = {10,10,10,10,10}, Iteral = {10,10,10,10,10,10,10,10,10,10}. Still larger numbers require an extended array notation and include the Emperal Group, Hyperal Group, Dutritri and Dutridecal. The largest number mentioned is the Guapamongaplex which is still considerably less than infinity, but is much larger than even Graham's number.

Large numbers that extend the -illion family

Jonathan Bowers has also created a number of names for large numbers that extend the -illion family of much smaller numbers than those mentioned above. Here is a list of the names of large numbers on the extended short scale, long scale and Knuth's extended myriadic scale:

Value Extended Short scale
 Extended Long scale
(Modified Chuquet): (Pelletier) 		Extended Myriadic
(Knuth) 		Extended Myriadic
(Knuth-Pelletier) 		Example of Numbers
in this range
0 Zero Zero Zero Zero
<math>{10}^0</math> One One One One π, e
<math>{10}^3</math> Thousand Thousand Thousand Thousand
<math>{10}^4</math> Ten thousand Ten thousand Myriad Myriad
<math>{10}^6</math> Million Million Hundred myriad Hundred myriad
<math>{10}^8</math> Hundred million Hundred million Myllion Myllion
<math>{10}^9</math> Billion Milliard Ten myllion Ten myllion
<math>{10}^{12}</math> Trillion Billion Myriad myllion Myriad myllion
<math>{10}^{15}</math> Quadrillion Billiard Thousand myriad myllion Thousand myriad myllion Age of universe in seconds
<math>{10}^{16}</math> Ten quadrillion Ten billiard Byllion Mylliard
<math>{10}^{24}</math> Septillion Quadrillion Myllion byllion Myllion mylliard Size (cm) of the homogenous patch
<math>{10}^{32}</math> Hundred nonillion Hundred quintillion Tryllion Byllion Temperature of universe (K) in Planck time
<math>{10}^{33}</math> Decillion Quintilliard Ten tryllion Ten byllion
<math>{10}^{60}</math> Novemdecillion Decillion Myriad myllion byllion tryllion Myriad myllion mylliard byllion
<math>{10}^{63}</math> Vigintillion Decilliard Thousand myriad myllion byllion tryllion Thousand myriad myllion mylliard byllion
<math>{10}^{64}</math> Ten vigintillion Ten decilliard Quadryllion Bylliard Atoms in universe
<math>{10}^{100}</math> Googol  ? Myriad tryllion quadryllion Myriad byllion bylliard Shannon number
<math>{10}^{128}</math> Hundred unquadragintillion Hundred unvigintillion Quintyllion Tryllion
<math>{10}^{256}</math> Ten quattoroctogintillion Ten duoquadragintilliard Sextyllion Trylliard
<math>{10}^{303}</math> Centillion Quinquagintilliard Thousand myriad myllion tryllion sextyllion Thousand myriad myllion byllion trylliard
<math>{10}^{512}</math> Hundred Centinovemsexagintillion Hundred Quinoctogintillion Septyllion Quadryllion
<math>{10}^{600}</math> Centinovemnonagintillion Centillion Myllion byllion quadryllion septyllion Myllion mylliard trylliard quadryllion
<math>{10}^{603}</math> Ducentillion Centilliard Thousand myllion byllion quadryllion septyllion Thousand myllion mylliard trylliard quadryllion
<math>{10}^{1024}</math> Ten trecentiquadragintillion Ten Centiseptuagintillion Octyllion Quadrylliard
<math>{10}^{2048}</math> Hundred Sexincentiunoctogintillion Hundred Trecentiunquadragintillion Nonyllion Quintyllion
<math>{10}^{3003}</math> Millillion Quincentilliard? Thousand myllion byllion tryllion quintyllion sextyllion septyllion nonyllion Thousand myllion mylliard byllion tryllion trylliard quadryllion quintyllion
<math>{10}^{4096}</math> Ten Millitrecentiquattuorsexagintillion Ten Sexincentiduooctagintilliard Decyllion Quintylliard
<math>{10}^{6000}</math> platillion Millillion Byllion tryllion sextyllion septyllion octyllion decyllion Mylliard byllion trylliard quadryllion quadrylliard quintylliard
<math>{10}^{6003}</math> Dumillillion? Millilliard Thousand byllion tryllion sextyllion septyllion octyllion decyllion Thousand mylliard byllion trylliard quadryllion quadrylliard

quintylliard

<math>{10}^{8192}</math> Hundred Dumilliseptincentinovemvigintillion Hundred Millitrecentiquinsexagintillion Undecyllion Sextyllion
<math>{10}^{16384}</math> Ten Quinmilliquadrincentisexagintillion Ten Dumilliseptincentitrigintilliard Duodecyllion Sextylliard
<math>{10}^{30,003}</math> Myrillion Quinmillilliard? Thousand byllion tryllion sextyllion octyllion decyllion undecyllion duodecyllion Thousand mylliard byllion trylliard quadrylliard quintylliard sextyllion sextylliard
<math>{10}^{60,000}</math> Myrianonmillinoncentinovemnonagintillion Myrillion Tryllion quadryllion septyllion nonyllion undecyllion duodecyllion tredecyllion Byllion bylliard quadryllion quintyllion sextyllion sextylliard septyllion
<math>{10}^{60,003}</math> Dumyrillion? Myrilliard Thousand tryllion quadryllion septyllion nonyllion undecyllion duodecyllion tredecyllion Thousand byllion bylliard quadryllion quintyllion sextyllion sextylliard septyllion
<math>{10}^{300,003}</math> Decemyrillion Quinmyrilliard Thousand tryllion quadryllion quintyllion sextyllion septyllion decyllion tredecyllion sexdecyllion Thousand byllion bylliard tryllion trylliard quadryllion quintylliard septyllion octylliard
<math>{10}^{600,000}</math> Novemnonagintanoncentinonmillinovamyriadecemyrillion Decemyrillion Quadryllion quintyllion sextyllion septyllion octyllion undecyllion quattordecyllion septemdecyllion Bylliard tryllion trylliard quadryllion quadrylliard sextyllion septylliard nonyllion
<math>{10}^{600,003}</math> Dudecemyrillion Decemyrilliard Thousand quadryllion quintyllion sextyllion septyllion octyllion undecyllion quattordecyllion septemdecyllion Thousand bylliard tryllion trylliard quadryllion quadrylliard sextyllion septylliard nonyllion
<math>{10}^{2,097,152}</math> Ten Decemyrianoncentiunquadragintillion Ten Tredecemyriaquadrincentisexseptuagintillion Novemdecyllion Decyllion Number of books in the Library of Babel is 251,312,000?2×101,834,097.
<math>{10}^{3,000,003}</math> Micrillion  ?  ?  ?
<math>{10}^{4,194,304}</math>  ?  ? Vigintyllion Decylliard
<math>{10}^{6,000,000}</math>  ? Micrillion  ?  ?
<math>{10}^{8,388,608}</math>  ?  ? Unvigintyllion Undecylliard
<math>{10}^{2,147,483,648}</math>  ?  ? Novemvigintyllion Quindecyllion
<math>{10}^{3,000,000,003}</math> Nanillion  ?  ?  ?
<math>{10}^{4,294,967,296}</math>  ?  ? Trigintyllion Quindecylliard
<math>{10}^{6,000,000,000}</math>  ? Micrilliard  ?  ?
<math>{10}^{8,589,934,592}</math>  ?  ? Untrigintyllion Sexdecyllion
<math>{10}^{{3 * {{10}^{12}}} + 3}</math> Picillion  ?  ?  ?
<math>{10}^{6 * {{10}^{12}}}</math>  ? Nanillion  ?  ?
<math>{10}^{{3 * {{10}^{15}}} + 3}</math> Femtillion  ?  ?  ?
<math>{10}^{6 * {{10}^{15}}}</math>  ? Nanilliard  ?  ?
<math>{10}^{{3 * {{10}^{18}}} + 3}</math> Attillion  ?  ?  ?
<math>{10}^{6 * {{10}^{18}}}</math>  ? Picillion  ?  ?
<math>{10}^{{3 * {{10}^{21}}} + 3}</math> Zeptillion  ?  ?  ?
<math>{10}^{6 * {{10}^{21}}}</math>  ? Picilliard  ?  ?
<math>{10}^{{3 * {{10}^{24}}} + 3}</math> Yoctillion  ?  ?  ?
<math>{10}^{6 * {{10}^{24}}}</math>  ? Femtillion  ?  ?
<math>{10}^{{3 * {{10}^{27}}} + 3}</math> Xonillion  ?  ?  ?
<math>{10}^{6 * {{10}^{27}}}</math>  ? Femtilliard  ?  ?
<math>{10}^{{3 * {{10}^{30}}} + 3}</math> Dekillion
Vecillion
Contillion 		 ?  ?  ?
<math>{10}^{6 * {{10}^{30}}}</math>  ? Attillion  ?  ?
<math>{{10}^2}^{102}</math>  ?  ? Centyllion Quinquagintylliard
<math>{10}^{{3 * {{10}^{33}}} + 3}</math> Mecillion  ?  ?  ?
<math>{10}^{6 * {{10}^{33}}}</math>  ? Attilliard  ?  ?
<math>{10}^{{3 * {{10}^{36}}} + 3}</math> Duecillion  ?  ?  ?
<math>{10}^{6 * {{10}^{36}}}</math>  ? Zeptillion  ?  ?
<math>{10}^{{3 * {{10}^{39}}} + 3}</math> Trecillion  ?  ?  ?
<math>{10}^{6 * {{10}^{39}}}</math>  ? Zeptilliard  ?  ?
<math>{10}^{{3 * {{10}^{42}}} + 3}</math> Tetrecillion  ?  ?  ?
<math>{10}^{6 * {{10}^{42}}}</math>  ? Yoctillion  ?  ?
<math>{10}^{{3 * {{10}^{45}}} + 3}</math> Pentecillion  ?  ?  ?
<math>{10}^{6 * {{10}^{45}}}</math>  ? Yoctilliard  ?  ?
<math>{10}^{{3 * {{10}^{48}}} + 3}</math> Hexecillion  ?  ?  ?
<math>{10}^{6 * {{10}^{48}}}</math>  ? Xonillion  ?  ?
<math>{10}^{{3 * {{10}^{51}}} + 3}</math> Heptecillion  ?  ?  ?
<math>{10}^{6 * {{10}^{51}}}</math>  ? Xonilliard  ?  ?
<math>{10}^{{3 * {{10}^{54}}} + 3}</math> Octecillion  ?  ?  ?
<math>{10}^{6 * {{10}^{54}}}</math>  ? Wettillion  ?  ?
<math>{10}^{{3 * {{10}^{57}}} + 3}</math> Ennecillion  ?  ?  ?
<math>{10}^{6 * {{10}^{57}}}</math>  ? Wettilliard  ?  ?
<math>{10}^{{3 * {{10}^{60}}} + 3}</math> Icocillion
Ducontillion 		 ?  ?  ?
<math>{10}^{6 * {{10}^{60}}}</math>  ? Dekillion  ?  ?
<math>{10}^{6 * {{10}^{63}}}</math>  ? Dekilliard  ?  ?
<math>{{10}^2}^{201}</math>  ?  ?  ? Centyllion
<math>{{10}^2}^{202}</math>  ?  ? Ducentyllion? Centylliard
<math>{10}^{{3 * {{10}^{90}}} + 3}</math> Triacontillion  ?  ?  ?
<math>{{10}^{10}}^{100}</math> Googolplex  ?  ?  ?
<math>{10}^{{3 * {{10}^{120}}} + 3}</math> Tetracontillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{150}}} + 3}</math> Pentacontillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{180}}} + 3}</math> Hexacontillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{210}}} + 3}</math> Heptacontillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{240}}} + 3}</math> Octacontillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{270}}} + 3}</math> Ennacontillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{300}}} + 3}</math> Hectillion
Icocontillion 		 ?  ?  ?
<math>{{10}^2}^{1,002}</math>  ?  ? Millyllion  ?
<math>{10}^{6 * {{10}^{600}}}</math>  ? Hectillion  ?  ?
<math>{10}^{6 * {{10}^{603}}}</math>  ? Hectilliard  ?  ?
<math>{{10}^2}^{2,001}</math>  ?  ?  ? Millyllion
<math>{{10}^2}^{2,002}</math>  ?  ? Dumillyllion Millylliard
<math>{10}^{{3 * {{10}^{3,000}}} + 3}</math> Killillion
Onillion
Zerillion 		 ?  ?  ?
<math>{{10}^2}^{10,002}</math>  ?  ? Myryllion  ?
<math>{10}^{6 * {{10}^{6,000}}}</math>  ? Killillion  ?  ?
<math>{10}^{6 * {{10}^{6,003}}}</math>  ? Killilliard  ?  ?
<math>{{10}^2}^{20,001}</math>  ?  ?  ? Myryllion
<math>{{10}^2}^{20,002}</math>  ?  ? Dumyryllion Myrylliard
<math>{10}^{{3 * {{10}^{3,000,000}}} + 3}</math> Megillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6,000,000}}}</math>  ? Megillion
Zerillion 		 ?  ?
<math>{10}^{{3 * {{10}^{3,000,000,000}}} + 3}</math> Gigillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6,000,000,000}}}</math>  ? Megilliard  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{12}}}}} + 3}</math> Terillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{12}}}}}</math>  ? Gigillion  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{15}}}}} + 3}</math> Petillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{15}}}}}</math>  ? Gigilliard  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{18}}}}} + 3}</math> Exillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{18}}}}}</math>  ? Terillion  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{21}}}}} + 3}</math> Zettillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{21}}}}}</math>  ? Terilliard  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{24}}}}} + 3}</math> Yottillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{24}}}}}</math>  ? Petillion  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{27}}}}} + 3}</math> Xennillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{27}}}}}</math>  ? Petilliard  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{30}}}}} + 3}</math> Teenillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{30}}}}}</math>  ? Exillion  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{33}}}}} + 3}</math> Mekillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{33}}}}}</math>  ? Exilliard  ?  ? First Skewes' number eee79 ( approx. 10101034 )
<math>{10}^{{3 * {{10}^{3 * {{10}^{36}}}}} + 3}</math> Duekillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{36}}}}}</math>  ? Zettillion  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{39}}}}} + 3}</math> Trekillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{39}}}}}</math>  ? Zettilliard  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{42}}}}} + 3}</math> Tetrekillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{42}}}}}</math>  ? Yottillion  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{45}}}}} + 3}</math> Pentekillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{45}}}}}</math>  ? Yottilliard  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{48}}}}} + 3}</math> Hexekillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{48}}}}}</math>  ? Xennillion  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{51}}}}} + 3}</math> Heptekillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{51}}}}}</math>  ? Xennilliard  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{54}}}}} + 3}</math> Octekillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{54}}}}}</math>  ? Wottillion  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{57}}}}} + 3}</math> Ennekillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{57}}}}}</math>  ? Wottilliard  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{60}}}}} + 3}</math> Twentillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{60}}}}}</math>  ? Onillion?  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{90}}}}} + 3}</math> Thirtillion  ?  ?  ?
<math>{{{10}^{10}}^{10}}^{100}</math> Googolduplex
<math>{10}^{{3 * {{10}^{3 * {{10}^{120}}}}} + 3}</math> Fortillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{150}}}}} + 3}</math> Fiftillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{180}}}}} + 3}</math> Sixtillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{210}}}}} + 3}</math> Seventillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{240}}}}} + 3}</math> Eightillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{270}}}}} + 3}</math> Nintillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{300}}}}} + 3}</math> Hundrillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{600}}}}}</math>  ? Onilliard?  ?  ? Second Skewes' number (1010101000)
<math>{10}^{{3 * {{10}^{3 * {{10}^{3,000}}}}} + 3}</math> Thousillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6,000}}}}}</math>  ? Zerilliard  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{30,000}}}}} + 3}</math> Myriaillion
Manillion 		 ?  ?  ?
<math>{10}^{{3 * {{10}^{6 * {{10}^{60,000}}}}}}</math>  ? Quillion?  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{300,000}}}}} + 3}</math> Lakhillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{600,000}}}}} + 3}</math>  ? Quilliard?  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{3,000,000}}}}} + 3}</math>  ?  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6,000,000}}}}}</math>  ? Teenillion  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{30,000,000}}}}} + 3}</math> Crorillion  ?  ?  ?
<math>{10}^{{3 * {{10}^{3 * {{10}^{300,000,000}}}}} + 3}</math> Awkillion  ?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6,000,000,000}}}}}</math>  ? Teenilliard  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{12}}}}}}}</math>  ? Twentillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{15}}}}}}}</math>  ? Twentilliard  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{18}}}}}}}</math>  ? Thirtillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{21}}}}}}}</math>  ? Thirtilliard  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{24}}}}}}}</math>  ? Fortillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{27}}}}}}}</math>  ? Fortilliard  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{30}}}}}}}</math>  ? Fiftillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{33}}}}}}}</math>  ? Fiftilliard  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{36}}}}}}}</math>  ? Sixtillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{39}}}}}}}</math>  ? Sixtilliard  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{42}}}}}}}</math>  ? Seventillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{45}}}}}}}</math>  ? Seventilliard  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{48}}}}}}}</math>  ? Eightillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{51}}}}}}}</math>  ? Eightilliard  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{54}}}}}}}</math>  ? Nintillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{57}}}}}}}</math>  ? Nintilliard  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{60}}}}}}}</math>  ? Hundrillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{63}}}}}}}</math>  ? Hundrilliard  ?  ?
<math>{{{{{10}^{10}}^{10}}^{10}}^{100}}</math> Googoltriplex
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{600}}}}}}}</math>  ? Thousillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{603}}}}}}}</math>  ? Thousilliard  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6,000}}}}}}}</math>  ? Myriaillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6,003}}}}}}}</math>  ? Myriailliard  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{60,000}}}}}}}</math>  ? Manillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{60,003}}}}}}}</math>  ? Manilliard?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{600,000}}}}}}}</math>  ? Lakhillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{600,003}}}}}}}</math>  ? Lakhilliard?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6,000,000}}}}}}}</math>  ? Wanillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6,000,003}}}}}}}</math>  ? Wanilliard?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{60,000,000}}}}}}}</math>  ? Crorillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{60,000,003}}}}}}}</math>  ? Crorilliard?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{600,000,000}}}}}}}</math>  ? Awkillion  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{600,000,003}}}}}}}</math>  ? Awkilliard?  ?  ?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^9}}}}}}}}</math> Bentrizillion  ?  ?  ?
<math>{{{{{10}^{10}}^{10}}^{10}}^{10}}^{100}</math> Googolquadriplex  ?  ? ...
Googolduplex and (98 more plexes) Googolcentplex ... ... ...
Googolduplex and (998 more plexes) Googolmilleplex ... ... ...
Googolplex and (999,999 more plexes) Googolmegaplex ... ... ...
Googolplex and (999,999,999 more plexes) Googolgigaplex ... ... ...
Googolplex and (999,999,999,999 more plexes) Googolteraplex ... ... ...
Googolplex and (999,999,999,999,999 more plexes) Googolpetaplex ... ... ...
Googolplex to the power of a googolplex Fzgoogolplex ... ... ...
{10,100,5} = 10 {5} 100: 10 pentated to 100 Giggol ... ... ...
{10,100,5} = 10 {5} 100: 10 pentated to 100 Giggolplex ... ... ...
... Mega ... ... ...
{10,100,5} = 10 {5} 100: 10 pentated to 100 Gaggol ... ... ...
10 {5} gaggol = 10 {5} 10 {5} 100: 10 tetrated to itself a gaggol times Gaggolplex ... ... ...
... Megaston ... ... ...
{5,5,5} = 5 {5} 5 = 5 {4} 5 {4} 5 {4} 5 {4} 5 Tripent ... ... ...
{7,7,7} = 7 {7} 7 (7 heptated to 7) Trisept ... ... ...
{10,100,6}=10 {6} 100 Geegol ... ... ...
{10,geegol, 6} Geegolplex ... ... ...
{10,100,7} Gygol ... ... ...
{10,gygol,7} Gygolplex ... ... ...
{10,100,8} Goggol ... ... ...
{10,goggol,8} Goggolplex ... ... ...
{10,100,9} Gagol ... ... ...
{10,gagol,9} Gagolplex ... ... ... Graham's number is much bigger.

Infinity scrapers

Numbers higher than those in the Gaggol group are referred to by Jonathan Bowers as the infinity scrapers. Here's a list of the names of those numbers that are infinity scrapers:

Name Value
Tridecal {10,10,10} = 10 {10} 10 = 10 decated to 10
Boogol {10,10,100} = 10 {100} 10
Boogolplex {10,10,boogol}
Moser's number ...
Graham's number ...
Corporal {10,100,1,2}
Corporalplex {10,corporal,1,2}
Grand Tridecal {10,10,10,2}
Tetratri {3,3,3,3}
General {10,10,10,10}
Generalplex {10,10,10,general}
Pentatri {3,3,3,3,3}
Pentadecal {10,10,10,10,10}
Pentadecalplex {10,10,10,10,pentadecal}
Hexatri {3,3,3,3,3,3}
Hexadecal {10,10,10,10,10,10}
Hexadecalplex {10,10,10,10,10,hexadecal}
Iteral {10,10,10,10,10,10,10,10,10,10}
Ultatri {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
Iteralplex {10,10,10,10,10,10,...........,10,10,10}

The following numbers requre an extended array notation to define. These are defined recursively, using rules such as:

<math>\left\langle\begin{matrix}a&b\\2&\end{matrix}\right\rangle=\{a,a,\ldots,a\}</math> with a repeated b times.
<math>\left\langle\begin{matrix}a&b\\k&\end{matrix}\right\rangle=\left\langle\begin{matrix}a&a&\ldots&a\\k-1\end{matrix}\right\rangle</math> with a repeated b times.
Name Value
Emperal <math>\left\langle\begin{matrix}10&10\\10&\end{matrix}\right\rangle</math>
Emperalplex <math>\left\langle\begin{matrix}10&10\\emperal&\end{matrix}\right\rangle</math>
Hyperal <math>\left\langle\begin{matrix}10&10\\10&10\end{matrix}\right\rangle</math>
Hyperalplex <math>\left\langle\begin{matrix}10&10\\10&Hyperal\end{matrix}\right\rangle</math>
Dutritri <math>\left\langle\begin{matrix}3&3&3\\3&3&3\\3&3&3\end{matrix}\right\rangle</math>
Dutridecal <math>\left\langle\begin{matrix}10&10&10\\10&10&10\\10&10&10\end{matrix}\right\rangle</math>
Xappol 10 by 10 array of 10's
Xappolplex xappol by xappol array of 10's
Dimentri 3 x 3 x 3 array of 3's
Colossal 10 x 10 x 10 array of 10's
Colossalplex colossal x colossal x colossal array of 10's
Dimendecal 10x10x10x10x10x10x10x10x10x10 array of 10's
Gongulus 100 dimensional array of 10's (10^100 array that is)
Gongulusplex gongulus dimensional array of 10's (10^gongulus array)
Dulatri (3^3)^2 array of 3's
Trimentri 3^(3^3) array of 3's
Goppatoth 10 tetrated to 100 array of 10's
Goppatothplex {10,goppatoth,4} array of 10's
Tridecatrix {10,10,10} array of 10's
Gongulus a "10^100 array of 10's" array of 10's.
Golapulus a * "10^100 array of tens" array of tens* array of tens.
Big Boowa X3, {X3,dutritriX, 2} X
Great Big Boowa X3,3,3X
Wompogulus 10^10 "100th level" exploded array of 10's
Wompogulusplex 10^10 "wompogulusth level" exploded array of 10's!!
Guapamonga 10^100 array of B's within "# #"
Guapamongaplex 10^100 array of B's within guapamonga-level "# #"

See also

External links

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