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Difference between revisions of "Jonathan Bowers"

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* <math>\{a,b,2,2\} = a \{\{2\}\}b\;</math> - ''a'' expanded to itself ''b'' times.
 
* <math>\{a,b,2,2\} = a \{\{2\}\}b\;</math> - ''a'' expanded to itself ''b'' times.
  
−
{| border="1"
+
{| class="wikitable"
 
!Group
 
!Group
 
!Name
 
!Name
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|[[Googol]]
 
|[[Googol]]
 
|<math>10^{100}=10^{10^2}</math>
 
|<math>10^{100}=10^{10^2}</math>
−
|{10,100,2} = 10 {2} 100
+
|{10,100,3} = 10 {3} 100
 
|-
 
|-
 
|[[Googolplex]]
 
|[[Googolplex]]
 
|<math>10^{10^{100}}=10^{10^{10^2}}</math>
 
|<math>10^{10^{100}}=10^{10^{10^2}}</math>
−
|{10,{10,100,2},2} = 10 {2} 10 {2} 100
+
|{10,{10,100,3},3} = 10 {3} 10 {3} 100
 
|-
 
|-
−
|Googolduplex
+
|Googolplexian
 
|<math>10^{10^{10^{100}}}</math>
 
|<math>10^{10^{10^{100}}}</math>
−
|{10,{10,{10,100,2},2},2} = 10 {2} 10 {2} 10 {2} 100
+
|{10,{10,{10,100,3},3},3} = 10 {3} 10 {3} 10 {3} 100
 
|-
 
|-
 
|rowspan=4|Giggol group
 
|rowspan=4|Giggol group
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|}
 
|}
  
−
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.
+
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==
+
==Illion group==
−
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:
+
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 -illion numbers on the short scale.
  
−
{| border="1"
+
{| class=wikitable
−
! Value || Extended [[long and short scales|Short scale]]<br/>  || Extended [[long and short scales|Long scale]]<br/> (Modified&nbsp;[[Nicolas Chuquet|Chuquet]]): ([[Jacques Pelletier du Mans|Pelletier]]) || Extended Myriadic <br/> ([[Knuth]]) || Extended Myriadic <br/> ([[Knuth-Pelletier]]) || Example of Numbers <br/> in this range
+
! Name || Short scale value
 
|-
 
|-
−
|0 || [[0 (number)|Zero]] || [[0 (number)|Zero]] || [[0 (number)|Zero]] || [[0 (number)|Zero]]
+
| [[Million]] || <math>{10}^6</math>
 
|-
 
|-
−
|<math>{10}^0</math> || [[1 (number)|One]] || [[1 (number)|One]] || [[1 (number)|One]] || [[1 (number)|One]] || [[Pi|&pi;]], [[E (number)|e]]
+
| [[Billion]] || <math>{10}^9</math>
 
|-
 
|-
−
|<math>{10}^3</math> || [[1000 (number)|Thousand]] || [[1000 (number)|Thousand]] || [[1000 (number)|Thousand]] || [[1000 (number)|Thousand]]
+
| [[Trillion]] || <math>{10}^{12}</math>
 
|-
 
|-
−
|<math>{10}^4</math> || [[Ten thousand]] || Ten thousand || [[Myriad]] || [[Myriad]]
+
| [[Quadrillion]] || <math>{10}^{15}</math>
 
|-
 
|-
−
|<math>{10}^6</math> || [[Million]] || [[Million]] || Hundred myriad || Hundred myriad
+
| [[Quintillion]] || <math>{10}^{18}</math>
 
|-
 
|-
−
|<math>{10}^8</math> || [[Hundred million]] || Hundred million || Myllion || Myllion
+
| [[Sextillion]] || <math>{10}^{21}</math>
 
|-
 
|-
−
|<math>{10}^9</math> || [[Billion]] || [[Milliard]] || Ten myllion || Ten myllion
+
| [[Septillion]] || <math>{10}^{24}</math>
 
|-
 
|-
−
|<math>{10}^{12}</math> || [[Trillion]] || [[Billion]] || Myriad myllion || Myriad myllion
+
| [[Octillion]] || <math>{10}^{27}</math>
 
|-
 
|-
−
|<math>{10}^{15}</math> || [[Quadrillion]] || [[Billiard]] || Thousand myriad myllion || Thousand myriad myllion || Age of universe in seconds
+
| [[Nonillion]] || <math>{10}^{30}</math>
 
|-
 
|-
−
|<math>{10}^{16}</math> || [[Ten quadrillion]] || [[Ten billiard]] || Byllion || Mylliard
+
| [[Decillion]] || <math>{10}^{33}</math>
 
|-
 
|-
−
|<math>{10}^{24}</math> || [[Septillion]] || [[Quadrillion]] || Myllion byllion || Myllion mylliard ||Size (cm) of the [[homogenous patch]]
+
| [[Undecillion]] || <math>{10}^{33}</math>
 
|-
 
|-
−
|<math>{10}^{32}</math> || [[Hundred nonillion]] || [[Hundred quintillion]] || Tryllion || Byllion ||Temperature of universe (K) in [[Planck time]]
+
| [[Duodecillion]] || 10<sup>39</sup>
 
|-
 
|-
−
|<math>{10}^{33}</math> || [[Decillion]] || [[Quintilliard]] || Ten tryllion || Ten byllion
+
| [[Tredecillion]] || 10<sup>42</sup>
 
|-
 
|-
−
|<math>{10}^{60}</math> || [[Novemdecillion]] || [[Decillion]] || Myriad myllion byllion tryllion || Myriad myllion mylliard byllion
+
| [[Quattuordecillion]] || 10<sup>45</sup>
 
|-
 
|-
−
|<math>{10}^{63}</math> || [[Vigintillion]] || [[Decilliard]] || Thousand myriad myllion byllion tryllion || Thousand myriad myllion mylliard byllion
+
| [[Quindecillion]] || 10<sup>48</sup>
 
|-
 
|-
−
|<math>{10}^{64}</math> || [[Ten vigintillion]]|| [[Ten decilliard]] || Quadryllion || Bylliard || Atoms in universe
+
| [[Sexdecillion]] || 10<sup>51</sup>
 
|-
 
|-
−
|<math>{10}^{100}</math> || [[Googol]] || ? || Myriad tryllion quadryllion|| Myriad byllion bylliard||[[Shannon number]]
+
| [[Septendecillion]] || 10<sup>54</sup>
 
|-
 
|-
−
|<math>{10}^{128}</math> || Hundred [[unquadragintillion]] || Hundred [[unvigintillion]] || Quintyllion || Tryllion
+
| [[Octodecillion]] || 10<sup>57</sup>
 
|-
 
|-
−
|<math>{10}^{256}</math> || Ten [[quattoroctogintillion]] || Ten [[duoquadragintilliard]] || Sextyllion || Trylliard
+
| [[Novemdecillion]] || 10<sup>60</sup>
 
|-
 
|-
−
|<math>{10}^{303}</math> || [[Centillion]] || [[Quinquagintilliard]] || Thousand myriad myllion tryllion sextyllion || Thousand myriad myllion byllion trylliard
+
| [[Vigintillion]] || 10<sup>63</sup>
 
|-
 
|-
−
|<math>{10}^{512}</math> || Hundred [[Centinovemsexagintillion]]
+
| [[Trigintillion]] || 10<sup>93</sup>
−
|| 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
+
| [[Googol]] <br> (Ten Duotrigintillion) || 10<sup>100</sup>
 
|-
 
|-
−
|<math>{10}^{1024}</math> || Ten [[trecentiquadragintillion]] || Ten Centiseptuagintillion || Octyllion || Quadrylliard
+
| [[Quadragintillion]] || 10<sup>123</sup>
 
|-
 
|-
−
|<math>{10}^{2048}</math> || Hundred [[Sexincentiunoctogintillion]] || Hundred [[Trecentiunquadragintillion]] || Nonyllion || Quintyllion
+
| [[Quinquagintillion]] || 10<sup>153</sup>
 
|-
 
|-
−
|<math>{10}^{3003}</math> || [[Millillion]] || Quincentilliard? || Thousand myllion byllion tryllion quintyllion sextyllion septyllion nonyllion || Thousand myllion mylliard byllion  tryllion trylliard quadryllion quintyllion
+
| [[Sexagintillion]] || 10<sup>183</sup>
 +
|-   
 +
| [[Septuagintillion]] || 10<sup>213</sup>
 
|-
 
|-
−
|<math>{10}^{4096}</math> || Ten [[Millitrecentiquattuorsexagintillion]] || Ten Sexincentiduooctagintilliard  || Decyllion || Quintylliard
+
| [[Octogintillion]] || 10<sup>243</sup>
 +
|- 
 +
| [[Nonagintillion]] || 10<sup>273</sup>
 
|-
 
|-
−
|<math>{10}^{6000}</math> || platillion
+
| [[Centillion]] || 10<sup>300</sup>
−
!|| [[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
+
| [[Platillion]] || <math>{10}^{6000}</math>
−
quintylliard
+
 
|-
 
|-
−
|<math>{10}^{8192}</math> || Hundred [[Dumilliseptincentinovemvigintillion]] || Hundred [[Millitrecentiquinsexagintillion]] || Undecyllion || Sextyllion ||
+
| [[Myrillion]] || <math>{10}^{6000}</math>
 
|-
 
|-
−
|<math>{10}^{16384}</math> || Ten [[Quinmilliquadrincentisexagintillion]] || Ten [[Dumilliseptincentitrigintilliard]] || Duodecyllion || Sextylliard
+
| Micrillion ||  10^ 3000003
 
|-
 
|-
−
|<math>{10}^{30,003}</math> || [[Myrillion]] || Quinmillilliard? || Thousand byllion tryllion sextyllion octyllion decyllion undecyllion duodecyllion || Thousand mylliard byllion trylliard quadrylliard quintylliard sextyllion sextylliard
+
| Nanillion ||  10^ 3billion3
 
|-
 
|-
−
|<math>{10}^{60,000}</math> || [[Myrianonmillinoncentinovemnonagintillion]] || [[Myrillion]] || Tryllion quadryllion septyllion nonyllion undecyllion duodecyllion tredecyllion || Byllion bylliard quadryllion quintyllion sextyllion sextylliard septyllion
+
| Picillion || 10^ 3trillion3
 
|-
 
|-
−
|<math>{10}^{60,003}</math> || [[Dumyrillion]]? || [[Myrilliard]] || Thousand tryllion quadryllion septyllion nonyllion undecyllion duodecyllion tredecyllion || Thousand byllion bylliard quadryllion quintyllion sextyllion sextylliard septyllion
+
| Femtillion || 10^ 3quadrillion3
 
|-
 
|-
−
|<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
+
| Attillion || 10^ 3 quintillion3
 
|-
 
|-
−
|<math>{10}^{600,000}</math> || [[Novemnonagintanoncentinonmillinovamyriadecemyrillion]]|| [[Decemyrillion]] || Quadryllion quintyllion sextyllion septyllion octyllion undecyllion quattordecyllion septemdecyllion || Bylliard tryllion trylliard quadryllion quadrylliard sextyllion septylliard nonyllion
+
| Zeptillion || 10^ 3sextillion3
 
|-
 
|-
−
|<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
+
| Yoctillion || 10^ 3septillion3
 
|-
 
|-
−
|<math>{10}^{2,097,152}</math> || Ten [[Decemyrianoncentiunquadragintillion]] || Ten [[Tredecemyriaquadrincentisexseptuagintillion]] || Novemdecyllion || Decyllion || Number of books in ''[[the Library of Babel]]'' is 25<sup>1,312,000</sup>?2&times;10<sup>1,834,097</sup>.
+
| Xonillion || 10^ 3octillion3
 
|-
 
|-
−
|<math>{10}^{3,000,003}</math> || [[Micrillion]] || ? || ? || ?
+
| Vecillion || 10^ 3nonillion3
 
|-
 
|-
−
|<math>{10}^{4,194,304}</math> || ? || ? || Vigintyllion || Decylliard
+
| Mecillion || 10^ 3decillion3
 
|-
 
|-
−
|<math>{10}^{6,000,000}</math> || ? || Micrillion || ? || ?
+
| Duecillion || 10^ 3undecillion3
 
|-
 
|-
−
|<math>{10}^{8,388,608}</math> || ? || ? || Unvigintyllion || Undecylliard
+
| Trecillion || 10^ 3doedecillion3
 
|-
 
|-
−
|<math>{10}^{2,147,483,648}</math> || ? || ? || Novemvigintyllion || Quindecyllion
+
| Tetrecillion || 10^ 3tridecillion3
 
|-
 
|-
−
|<math>{10}^{3,000,000,003}</math> || [[Nanillion]] || ? || ? || ?
+
| Pentecillion || 10^ 3quattuordecillion3
 
|-
 
|-
−
|<math>{10}^{4,294,967,296}</math> || ? || ? || Trigintyllion || Quindecylliard
+
| Hexecillion || 10^ 3quindecillion3
 
|-
 
|-
−
|<math>{10}^{6,000,000,000}</math> || ? || [[Micrilliard]] || ? || ?
+
| Heptecillion || 10^ 3sexdecillion3
 
|-
 
|-
−
|<math>{10}^{8,589,934,592}</math> || ? || ? || Untrigintyllion || Sexdecyllion
+
| Octecillion || 10^ 3septendecillion3
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{12}}} + 3}</math> || [[Picillion]] || ? || ? || ?
+
|Ennecillion || 10^ 3octodecillion3
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{12}}}</math> || ? || Nanillion || ? || ?
+
| Icosillion || 10^ 3novemdecillion3
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{15}}} + 3}</math> || [[Femtillion]] || ? || ? || ?
+
| Triacontillion || 10^ (3x10^90+3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{15}}}</math> || ? || Nanilliard || ? || ?
+
| [[Googolplex]] || 10^10^100
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{18}}} + 3}</math> || [[Attillion]] || ? || ? || ?
+
| Tetracontillion || 10^ (3x10^120+3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{18}}}</math> || ? || Picillion || ? || ?
+
| Pentacontillion || 10^ (3x10^150+3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{21}}} + 3}</math> || [[Zeptillion]] || ? || ? || ?
+
| Hexacontillion || 10^ (3x10^180+3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{21}}}</math> || ? || [[Picilliard]] || ? || ?
+
| Heptacontillion || 10^ (3x10^210+3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{24}}} + 3}</math> || [[Yoctillion]] || ? || ? || ?
+
| Octacontillion || 10^ (3x10^240+3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{24}}}</math> || ? || Femtillion || ? || ?
+
| Ennacontillion || 10^ (3x10^270+3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{27}}} + 3}</math> || [[Xonillion]] || ? || ? || ?
+
| Hectillion || 10^ (3x10^300+3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{27}}}</math> || ? || [[Femtilliard]] || ? || ?
+
| Killillion || 10^ (3x10^3000+3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{30}}} + 3}</math> || Dekillion<br/>Vecillion<br/>Contillion || ? || ? || ?
+
| Megillion || 10^ (3x10^3million +3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{30}}}</math> || ? || [[Attillion]] || ? || ?
+
| Gigillion || 10^ (3x10^3billion +3)
 
|-
 
|-
−
|<math>{{10}^2}^{102}</math> || ? || ? || Centyllion || Quinquagintylliard
+
| Terillion || 10^ (3x10^3trillion +3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{33}}} + 3}</math> || [[Mecillion]] || ? || ? || ?
+
| Petillion || 10^ (3x10^3quadrillion +3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{33}}}</math> || ? || [[Attilliard]] || ? || ?
+
| Exillion || 10^ (3x10^3quintillion +3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{36}}} + 3}</math> || [[Duecillion]] || ? || ? || ?
+
| Zettillion || 10^ (3x10^3sextillion +3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{36}}}</math> || ? || Zeptillion || ? || ?
+
| Yottillion || 10^ (3x10^3septillion +3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{39}}} + 3}</math> || [[Trecillion]] || ? || ? || ?
+
| Xennillion || 10^ (3x10^3octillion +3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{39}}}</math> || ? || [[Zeptilliard]] || ? || ?
+
| Vekillion || 10^ (3x10^3nonillion +3) 
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{42}}} + 3}</math> || [[Tetrecillion]] || ? || ? || ?
+
| Mekillion || 10^ (3x10^3decillion +3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{42}}}</math> || ? || [[Yoctillion]] || ? || ?
+
| Duekillion || 10^ (3x10^3undecillion +3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{45}}} + 3}</math> || [[Pentecillion]] || ? || ? || ?
+
| Trekillion || 10^ (3x10^3doedecillion +3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{45}}}</math> || ? || Yoctilliard || ? || ?
+
| Tetrekillion || 10^ (3x10^3tridecillion +3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{48}}} + 3}</math> || [[Hexecillion]] || ? || ? || ?
+
| Pentekillion || 10^ (3x10^3quattuordecillion +3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{48}}}</math> || ? || Xonillion || ? || ?
+
| Hexekillion || 10^ (3x10^3quindecillion +3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{51}}} + 3}</math> || [[Heptecillion]] || ? || ? || ?
+
| Heptekillion || 10^ (3x10^3sexdecillion +3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{51}}}</math> || ? || [[Xonilliard]] || ? || ?
+
| Octekillion || 10^ (3x10^3septendecillion +3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{54}}} + 3}</math> || [[Octecillion]] || ? || ? || ?
+
| Ennekillion || 10^ (3x10^3octodecillion +3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{54}}}</math> || ? || Wettillion || ? || ?
+
| Twentillion || 10^ (3x10^(3x10^60) +3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{57}}} + 3}</math> || [[Ennecillion]] || ? || ? || ?
+
| Triatwentillion || 10^ (3x10^(3x10^69) +3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{57}}}</math> || ? || [[Wettilliard]] || ? || ?
+
| Thirtillion || 10^ (3x10^(3x10^90)+3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{60}}} + 3}</math> || [[Icocillion]]<br/>Ducontillion || ? || ? || ?
+
| Googolplexian || 10^10^10^100
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{60}}}</math> || ? || [[Dekillion]] || ? || ?
+
| Fortillion || 10^ (3x10^(3x10^120)+3)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{63}}}</math> || ? || [[Dekilliard]] || ? || ?
+
| Fiftillion || 10^ (3x10^(3x10^150)+3)
 
|-
 
|-
−
|<math>{{10}^2}^{201}</math> || ? || ? || ? || Centyllion
+
| Sixtillion || 10^ (3x10^(3x10^180)+3)
 
|-
 
|-
−
|<math>{{10}^2}^{202}</math> || ? || ? || Ducentyllion? || Centylliard
+
| Seventillion || 10^ (3x10^(3x10^210)+3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{90}}} + 3}</math> || [[Triacontillion]] || ? || ? || ?
+
| Eightillion || 10^ (3x10^(3x10^240)+3)
 
|-
 
|-
−
|<math>{{10}^{10}}^{100}</math> || [[Googolplex]] || ? || ? || ?
+
| Nintillion || 10^ (3x10^(3x10^270)+3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{120}}} + 3}</math> || [[Tetracontillion]] || ? || ? || ?
+
| Hundrillion || 10^ (3x10^(3x10^300)+3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{150}}} + 3}</math> || [[Pentacontillion]] || ? || ? || ?
+
| Thousillion || 10^ (3x10^(3x10^3000)+3)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{180}}} + 3}</math> || [[Hexacontillion]] || ? || ? || ?
+
| Manillion || <math>{10}^{{3 * {{10}^{3 * {{10}^{30,000}}}}} + 3}</math>
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{210}}} + 3}</math> || [[Heptacontillion]] || ? || ? || ?
+
| Lakhillion || <math>{10}^{{3 * {{10}^{3 * {{10}^{300,000}}}}} + 3}</math>
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{240}}} + 3}</math> || [[Octacontillion]] || ? || ? || ?
+
| Crorillion || <math>{10}^{{3 * {{10}^{3 * {{10}^{30,000,000}}}}} + 3}</math>  
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{270}}} + 3}</math> || [[Ennacontillion]] || ? || ? || ?
+
| Awkillion || <math>{10}^{{3 * {{10}^{3 * {{10}^{300,000,000}}}}} + 3}</math>
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{300}}} + 3}</math> || [[Hectillion]]<br/>[[Icocontillion]] || ? || ? || ?
+
| Bentrizillion || <math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^9}}}}}}}}</math>
 +
|}
 +
 
 +
==Googol, giggol and gaggol groups==
 +
Jonathan Bowers defines the googol, giggol, and gaggol groups as being lower than the infinity scrapers. Here's a list of the names of numbers in these groups:
 +
 
 +
{| class=wikitable
 +
! Name || Value
 
|-
 
|-
−
|<math>{{10}^2}^{1,002}</math> || ? || ? || Millyllion || ?
+
| Googol || 10^100
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{600}}}</math> || ? || [[Hectillion]] || ? || ?
+
| Googolplex || 10^10^100
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{603}}}</math> || ? || [[Hectilliard]] || ? || ?
+
| Googolplexian || 10^10^10^100
 
|-
 
|-
−
|<math>{{10}^2}^{2,001}</math> || ? || ? || ? || Millyllion
+
| Googoltriplex || 10^10^10^10^100
 
|-
 
|-
−
|<math>{{10}^2}^{2,002}</math> || ? || ? || Dumillyllion || Millylliard
+
| Googolquadriplex || 10^10^10^10^10^100
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3,000}}} + 3}</math> || Killillion<br/>Onillion<br/>Zerillion || ? || ? || ?
+
| Googolquinplex ||10^10^10^10^10^10^100
 
|-
 
|-
−
|<math>{{10}^2}^{10,002}</math> || ? || ? || Myryllion || ?
+
| Googolcentplex || Googolplexian and (98 more plexes)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6,000}}}</math> || ? || [[Killillion]] || ? || ?
+
| Googolmilleplex || Googolplexian and (998 more plexes)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6,003}}}</math> || ? || Killilliard || ? || ?
+
| Googolmegaplex || Googolplex and (999,999 more plexes)
 
|-
 
|-
−
|<math>{{10}^2}^{20,001}</math> || ? || ? || ? || Myryllion
+
| Googolgigaplex || Googolplex and (999,999,999 more plexes)
 
|-
 
|-
−
|<math>{{10}^2}^{20,002}</math> || ? || ? || Dumyryllion || Myrylliard
+
| Googolteraplex || Googolplex and (999,999,999,999 more plexes)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3,000,000}}} + 3}</math> || Megillion || ? || ? || ?
+
| Googolpetaplex || Googolplex and (999,999,999,999,999 more plexes)
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6,000,000}}}</math> || ? || Megillion<br/>Zerillion || ? || ?
+
| Fzgoogolplex || Googolplex to the power of a googolplex
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3,000,000,000}}} + 3}</math> || Gigillion || ? || ? || ?
+
| Giggol || {10,100,4} = 10 {4} 100: 10 tetrated to 100
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6,000,000,000}}}</math> || ? || Megilliard || ? || ?
+
| Giggolplex || {10,Giggol,4} = 10 {4} Giggol: 10 tetrated to Giggol 
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{12}}}}} + 3}</math> || Terillion || ? || ? || ?
+
| Mega || ...
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{12}}}}}</math> || ? || Gigillion || ? || ?
+
| Gaggol || {10,100,5} = 10 {5} 100: 10 pentated to 100
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{15}}}}} + 3}</math> || Petillion || ? || ? || ?
+
| Gaggolplex || 10 {5} gaggol = 10 {5} 10 {5} 100: 10 tetrated to itself a gaggol times
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{15}}}}}</math>|| ? || Gigilliard || ? || ?
+
| Megaston || ...
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{18}}}}} + 3}</math> || Exillion || ? || ? || ?
+
| Tripent || {5,5,5} = 5 {5} 5 = 5 {4} 5 {4} 5 {4} 5 {4} 5
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{18}}}}}</math> || ? || Terillion || ? || ?
+
| Trisept || {7,7,7} = 7 {7} 7 (7 heptated to 7)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{21}}}}} + 3}</math> || Zettillion || ? || ? || ?
+
| Geegol || {10,100,6}=10 {6} 100
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{21}}}}}</math> || ? || Terilliard || ? || ?
+
| Geegolplex || {10,geegol, 6}  
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{24}}}}} + 3}</math> || Yottillion || ? || ? || ?
+
| Gygol || {10,100,7}  
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{24}}}}}</math> || ? || Petillion || ? || ?
+
| Gygolplex || {10,gygol,7}  
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{27}}}}} + 3}</math> || Xennillion || ? || ? || ?
+
| Goggol || {10,100,8}  
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{27}}}}}</math> || ? || Petilliard || ? || ?
+
| Goggolplex || {10,goggol,8}  
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{30}}}}} + 3}</math> || Vekillion<br/>Teenillion || ? || ? || ?
+
| Gagol || {10,100,9}  
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{30}}}}}</math> || ? || Exillion || ? || ?
+
| Gagolplex || {10,gagol,9}
 +
|}
 +
 
 +
==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:
 +
 
 +
{| class=wikitable
 +
! Name || Value
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{33}}}}} + 3}</math> || Mekillion || ? || ? || ?
+
| Tridecal || {10,10,10} = 10 {10} 10 = 10 decated to 10
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{33}}}}}</math> || ? || Exilliard || ? || ? || First [[Skewes' number]] e<sup>e<sup>e<sup>79</sup></sup></sup> ( approx. 10<sup>10<sup>10<sup>34</sup></sup></sup> )
+
| Boogol || {10,10,100} = 10 {100} 10
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{36}}}}} + 3}</math> || Duekillion || ? || ? || ?
+
| Boogolplex || {10,10,boogol}
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{36}}}}}</math> || ? || Zettillion || ? || ?
+
| Moser's number || ...
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{39}}}}} + 3}</math> || Trekillion || ? || ? || ?
+
| [[Graham's number]] || ...
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{39}}}}}</math> || ? || Zettilliard || ? || ?
+
| Corporal || {10,100,1,2}  
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{42}}}}} + 3}</math> || Tetrekillion || ? || ? || ?
+
| Corporalplex || {10,corporal,1,2}  
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{42}}}}}</math> || ? || Yottillion || ? || ?
+
| Grand Tridecal || {10,10,10,2}
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{45}}}}} + 3}</math> || Pentekillion || ? || ? || ?
+
| Tetratri || {3,3,3,3}
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{45}}}}}</math> || ? || Yottilliard || ? || ?
+
| General || {10,10,10,10}  
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{48}}}}} + 3}</math> || Hexekillion || ? || ? || ?
+
| Generalplex || {10,10,10,general}  
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{48}}}}}</math> || ? || Xennillion || ? || ?
+
| Pentatri || {3,3,3,3,3}  
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{51}}}}} + 3}</math> || Heptekillion || ? || ? || ?
+
| Pentadecal  || {10,10,10,10,10}
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{51}}}}}</math> || ? || Xennilliard || ? || ?
+
| Pentadecalplex || {10,10,10,10,pentadecal}
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{54}}}}} + 3}</math> || Octekillion || ? || ? || ?
+
| Hexatri || {3,3,3,3,3,3}
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{54}}}}}</math> || ? || Wottillion || ? || ?
+
| Hexadecal || {10,10,10,10,10,10}
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{57}}}}} + 3}</math> || Ennekillion || ? || ? || ?
+
| Hexadecalplex || {10,10,10,10,10,hexadecal}  
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{57}}}}}</math> || ? || Wottilliard || ? || ?
+
| Iteral || {10,10,10,10,10,10,10,10,10,10}  
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{60}}}}} + 3}</math> || Icokillion<br/>Twentillion || ? || ? || ?
+
| 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}
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{60}}}}}</math> || ? || Onillion? || ? || ?
+
| 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
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{90}}}}} + 3}</math> || Thirtillion || ? || ? || ?
+
|Emperal
 +
|<math>\left\langle\begin{matrix}10&10\\10&\end{matrix}\right\rangle</math>
 
|-
 
|-
−
|<math>{{{10}^{10}}^{10}}^{100}</math> || Googolduplex
+
|Emperalplex
 +
|<math>\left\langle\begin{matrix}10&10\\emperal&\end{matrix}\right\rangle</math>
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{120}}}}} + 3}</math> || Fortillion || ? || ? || ?
+
|Hyperal
 +
|<math>\left\langle\begin{matrix}10&10\\10&10\end{matrix}\right\rangle</math>
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{150}}}}} + 3}</math> || Fiftillion || ? || ? || ?
+
| Hyperalplex
 +
|<math>\left\langle\begin{matrix}10&10\\10&Hyperal\end{matrix}\right\rangle</math>
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{180}}}}} + 3}</math> || Sixtillion || ? || ? || ?
+
| Dutritri
 +
|<math>\left\langle\begin{matrix}3&3&3\\3&3&3\\3&3&3\end{matrix}\right\rangle</math>
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{210}}}}} + 3}</math> || Seventillion || ? || ? || ?
+
| Dutridecal
 +
|<math>\left\langle\begin{matrix}10&10&10\\10&10&10\\10&10&10\end{matrix}\right\rangle</math>
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{240}}}}} + 3}</math> || Eightillion || ? || ? || ?
+
| Xappol || 10 by 10 array of 10's
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{270}}}}} + 3}</math> || Nintillion || ? || ? || ?
+
| Xappolplex || xappol by xappol array of 10's
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{300}}}}} + 3}</math> || Hundrillion || ? || ? || ?
+
| Dimentri || 3 x 3 x 3 array of 3's
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{600}}}}}</math> || ? || Onilliard? || ? || ? || Second [[Skewes' number]] (10<sup>10<sup>10<sup>1000</sup></sup></sup>)
+
| Colossal || 10 x 10 x 10 array of 10's
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{3,000}}}}} + 3}</math> || Thousillion || ? || ? || ?
+
| Colossalplex || colossal x colossal x colossal array of 10's
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{6,000}}}}}</math> || ? || Zerilliard || ? || ?
+
| Dimendecal || 10x10x10x10x10x10x10x10x10x10 array of 10's
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{30,000}}}}} + 3}</math> || Myriaillion<br/>Manillion || ? || ? || ?
+
| Gongulus || 100 dimensional array of 10's  (10^100 array that is)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{6 * {{10}^{60,000}}}}}}</math> || ? || Quillion? || ? || ?
+
| Gongulusplex || gongulus dimensional array of 10's (10^gongulus array)
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{300,000}}}}} + 3}</math> || Lakhillion || ? || ? || ?
+
| Dulatri || (3^3)^2 array of 3's
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{600,000}}}}} + 3}</math> || ? || Quilliard? || ? || ?
+
| Trimentri || 3^(3^3) array of 3's
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{3,000,000}}}}} + 3}</math> || ? || ? || ? || ?
+
| Goppatoth || 10 tetrated to 100 array of 10's
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{6,000,000}}}}}</math> || ? || Teenillion || ? || ?
+
| Goppatothplex || {10,goppatoth,4} array of 10's
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{30,000,000}}}}} + 3}</math> || Crorillion || ? || ? || ?
+
| Tridecatrix || {10,10,10} array of 10's
 
|-
 
|-
−
|<math>{10}^{{3 * {{10}^{3 * {{10}^{300,000,000}}}}} + 3}</math> || Awkillion || ? || ? || ?
+
| Gongulus || a "10^100 array of 10's" array of 10's.
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{6,000,000,000}}}}}</math> || ? || Teenilliard || ? || ?
+
| Golapulus || a * "10^100 array of tens" array of tens* array of tens.
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{12}}}}}}}</math> || ? || Twentillion || ? || ?
+
| Big Boowa || X3, {X3,dutritriX, 2} X
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{15}}}}}}}</math> || ? || Twentilliard || ? || ?
+
| Great Big Boowa || X3,3,3X
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{18}}}}}}}</math> || ? || Thirtillion || ? || ?
+
| Wompogulus || 10^10 "100th level" exploded array of 10's
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{21}}}}}}}</math> || ? || Thirtilliard || ? || ?
+
| Wompogulusplex || 10^10 "wompogulusth level" exploded array of 10's!!
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{24}}}}}}}</math> || ? || Fortillion || ? || ?
+
| Guapamonga || 10^100 array of B's within "# #"
 
|-
 
|-
−
|<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{27}}}}}}}</math> || ? || Fortilliard || ? || ?
+
| Guapamongaplex || 10^100 array of B's within guapamonga-level "# #"
−
|-
+
−
|<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:
 
−
 
−
{| border="1"
 
−
! Value || Name || Example of Numbers <br/> in this range
 
−
|-
 
−
| {10,10,10} = 10 {10} 10 = 10 decated to 10 || Tridecal
 
−
|-
 
−
| {10,10,100} = 10 {100} 10 || Boogol
 
−
|-
 
−
| {10,10,boogol} || Boogolplex 
 
−
|-
 
−
| ... || Moser's number 
 
−
|-
 
−
| ... || [[Graham's number]] || A corporal is much larger.
 
−
|-
 
−
| {10,100,1,2} || Corporal 
 
−
|-
 
−
| {10,corporal,1,2} || Corporalplex
 
−
|-
 
−
| {10,10,10,2} || Grand Tridecal
 
−
|-
 
−
| {3,3,3,3} || Tetratri
 
−
|-
 
−
| {10,10,10,10} || General
 
−
|-
 
−
| {10,10,10,general}  || Generalplex
 
−
|-
 
−
| {3,3,3,3,3} || Pentatri
 
−
|-
 
−
| {10,10,10,10,10} || Pentadecal
 
−
|-
 
−
| {10,10,10,10,pentadecal} || Pentadecalplex
 
−
|-
 
−
| {3,3,3,3,3,3} || Hexatri
 
−
|-
 
−
| {10,10,10,10,10,10} || Hexadecal
 
−
|-
 
−
| {10,10,10,10,10,hexadecal} || Hexadecalplex
 
−
|}
 
−
 
−
==Googillion==
 
−
A googillion began as an astronomer's "largest number" synonym for everyday real-world objects that are unknown and unknowable numbers. Example: from [[string theory]], how many strings are there in the universe? The answer is a googillion. In theory, there is a real finite number of strings in the universe at any given point in time. The number is both an unknown and unknowable largest number. So a googillion is a general term for all extremely large numbers. Since any largest number can become larger simply by adding the number one, all the strings in the universe plus one is also a googillion. A googillion does not represent a specific number. It is a flexible term that represents any and many numbers that are too large to be proved.
 
  
 
==See also==
 
==See also==
Line 615: Line 493:
 
* [http://members.cox.net/hedrondude/home.htm Jonathan's home page]
 
* [http://members.cox.net/hedrondude/home.htm Jonathan's home page]
  
−
{{Mathbiostub}}
 
 
[[Category:Living people|Bowers, Jonathan]]
 
[[Category:Living people|Bowers, Jonathan]]
 
[[Category:Large numbers]]
 
[[Category:Large numbers]]
 +
[[Category:Mathematicians|Bowers, Jonathan]]

Latest revision as of 14:51, 4 January 2016

Jonathan Bowers, mathematician (November 27, 1969–)

Polychora[edit]

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[edit]

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> {10,100,3} = 10 {3} 100
Googolplex <math>10^{10^{100}}=10^{10^{10^2}}</math> {10,{10,100,3},3} = 10 {3} 10 {3} 100
Googolplexian <math>10^{10^{10^{100}}}</math> {10,{10,{10,100,3},3},3} = 10 {3} 10 {3} 10 {3} 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.

Illion group[edit]

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 -illion numbers on the short scale.

Name Short scale value
Million <math>{10}^6</math>
Billion <math>{10}^9</math>
Trillion <math>{10}^{12}</math>
Quadrillion <math>{10}^{15}</math>
Quintillion <math>{10}^{18}</math>
Sextillion <math>{10}^{21}</math>
Septillion <math>{10}^{24}</math>
Octillion <math>{10}^{27}</math>
Nonillion <math>{10}^{30}</math>
Decillion <math>{10}^{33}</math>
Undecillion <math>{10}^{33}</math>
Duodecillion 1039
Tredecillion 1042
Quattuordecillion 1045
Quindecillion 1048
Sexdecillion 1051
Septendecillion 1054
Octodecillion 1057
Novemdecillion 1060
Vigintillion 1063
Trigintillion 1093
Googol
(Ten Duotrigintillion) 		10100
Quadragintillion 10123
Quinquagintillion 10153
Sexagintillion 10183
Septuagintillion 10213
Octogintillion 10243
Nonagintillion 10273
Centillion 10300
Platillion <math>{10}^{6000}</math>
Myrillion <math>{10}^{6000}</math>
Micrillion 10^ 3000003
Nanillion 10^ 3billion3
Picillion 10^ 3trillion3
Femtillion 10^ 3quadrillion3
Attillion 10^ 3 quintillion3
Zeptillion 10^ 3sextillion3
Yoctillion 10^ 3septillion3
Xonillion 10^ 3octillion3
Vecillion 10^ 3nonillion3
Mecillion 10^ 3decillion3
Duecillion 10^ 3undecillion3
Trecillion 10^ 3doedecillion3
Tetrecillion 10^ 3tridecillion3
Pentecillion 10^ 3quattuordecillion3
Hexecillion 10^ 3quindecillion3
Heptecillion 10^ 3sexdecillion3
Octecillion 10^ 3septendecillion3
Ennecillion 10^ 3octodecillion3
Icosillion 10^ 3novemdecillion3
Triacontillion 10^ (3x10^90+3)
Googolplex 10^10^100
Tetracontillion 10^ (3x10^120+3)
Pentacontillion 10^ (3x10^150+3)
Hexacontillion 10^ (3x10^180+3)
Heptacontillion 10^ (3x10^210+3)
Octacontillion 10^ (3x10^240+3)
Ennacontillion 10^ (3x10^270+3)
Hectillion 10^ (3x10^300+3)
Killillion 10^ (3x10^3000+3)
Megillion 10^ (3x10^3million +3)
Gigillion 10^ (3x10^3billion +3)
Terillion 10^ (3x10^3trillion +3)
Petillion 10^ (3x10^3quadrillion +3)
Exillion 10^ (3x10^3quintillion +3)
Zettillion 10^ (3x10^3sextillion +3)
Yottillion 10^ (3x10^3septillion +3)
Xennillion 10^ (3x10^3octillion +3)
Vekillion 10^ (3x10^3nonillion +3)
Mekillion 10^ (3x10^3decillion +3)
Duekillion 10^ (3x10^3undecillion +3)
Trekillion 10^ (3x10^3doedecillion +3)
Tetrekillion 10^ (3x10^3tridecillion +3)
Pentekillion 10^ (3x10^3quattuordecillion +3)
Hexekillion 10^ (3x10^3quindecillion +3)
Heptekillion 10^ (3x10^3sexdecillion +3)
Octekillion 10^ (3x10^3septendecillion +3)
Ennekillion 10^ (3x10^3octodecillion +3)
Twentillion 10^ (3x10^(3x10^60) +3)
Triatwentillion 10^ (3x10^(3x10^69) +3)
Thirtillion 10^ (3x10^(3x10^90)+3)
Googolplexian 10^10^10^100
Fortillion 10^ (3x10^(3x10^120)+3)
Fiftillion 10^ (3x10^(3x10^150)+3)
Sixtillion 10^ (3x10^(3x10^180)+3)
Seventillion 10^ (3x10^(3x10^210)+3)
Eightillion 10^ (3x10^(3x10^240)+3)
Nintillion 10^ (3x10^(3x10^270)+3)
Hundrillion 10^ (3x10^(3x10^300)+3)
Thousillion 10^ (3x10^(3x10^3000)+3)
Manillion <math>{10}^{{3 * {{10}^{3 * {{10}^{30,000}}}}} + 3}</math>
Lakhillion <math>{10}^{{3 * {{10}^{3 * {{10}^{300,000}}}}} + 3}</math>
Crorillion <math>{10}^{{3 * {{10}^{3 * {{10}^{30,000,000}}}}} + 3}</math>
Awkillion <math>{10}^{{3 * {{10}^{3 * {{10}^{300,000,000}}}}} + 3}</math>
Bentrizillion <math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^9}}}}}}}}</math>

Googol, giggol and gaggol groups[edit]

Jonathan Bowers defines the googol, giggol, and gaggol groups as being lower than the infinity scrapers. Here's a list of the names of numbers in these groups:

Name Value
Googol 10^100
Googolplex 10^10^100
Googolplexian 10^10^10^100
Googoltriplex 10^10^10^10^100
Googolquadriplex 10^10^10^10^10^100
Googolquinplex 10^10^10^10^10^10^100
Googolcentplex Googolplexian and (98 more plexes)
Googolmilleplex Googolplexian and (998 more plexes)
Googolmegaplex Googolplex and (999,999 more plexes)
Googolgigaplex Googolplex and (999,999,999 more plexes)
Googolteraplex Googolplex and (999,999,999,999 more plexes)
Googolpetaplex Googolplex and (999,999,999,999,999 more plexes)
Fzgoogolplex Googolplex to the power of a googolplex
Giggol {10,100,4} = 10 {4} 100: 10 tetrated to 100
Giggolplex {10,Giggol,4} = 10 {4} Giggol: 10 tetrated to Giggol
Mega ...
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
Megaston ...
Tripent {5,5,5} = 5 {5} 5 = 5 {4} 5 {4} 5 {4} 5 {4} 5
Trisept {7,7,7} = 7 {7} 7 (7 heptated to 7)
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[edit]

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[edit]

External links[edit]

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