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Difference between revisions of "Jonathan Bowers"
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| {10,10,10,10,10,10,...........,10,10,10} || Iteralplex | | {10,10,10,10,10,10,...........,10,10,10} || Iteralplex | ||
| + | |- | ||
| + | | {10,10,10,10,10,10,...........,10,10,10} || Iteralplex | ||
| + | |- | ||
| + | | {10,10,10,10,10,10,...........,10,10,10} || Iteralplex | ||
| + | |- | ||
| + | | {10,10,10,10,10,10,...........,10,10,10} || Iteralplex | ||
| + | |- | ||
| + | | {10,10,10,10,10,10,...........,10,10,10} || Iteralplex | ||
| + | |- | ||
| + | | {10,10,10,10,10,10,...........,10,10,10} || Iteralplex | ||
| + | |- | ||
| + | | {10,10,10,10,10,10,...........,10,10,10} || Iteralplex | ||
| + | |- | ||
| + | | /10,10\ | ||
| + | \10 || Emperal | ||
| + | |- | ||
| + | | /10, 10 \ | ||
| + | \emperal / || Emperalplex | ||
| + | | /10,10\ | ||
| + | \10,10/ || Hyperal | ||
| + | | /10,10 \ | ||
| + | \10,hyperal/ || Hyperalplex | ||
| + | | /3,3,3\ | ||
| + | |3,3,3 | | ||
| + | \3,3,3/ || Dutritri | ||
| + | | /10,10,10\ | ||
| + | |10,10,10 | | ||
| + | \10,10,10/ || Dutridecal | ||
| + | /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 | | ||
| + | \10,10,10,10,10,10,10,10,10,10/ || Xappol | ||
| + | /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 | ||
|} | |} | ||
Revision as of 19:03, 5 March 2006
Jonathan Bowers, mathematician (November 27, 1969–)
Contents
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.
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> | Vekillion 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> | Icokillion 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:
| Value | Name | Example of Numbers 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 | |||||||||||||||||||
| {10,10,10,10,10,10,10,10,10,10} | Iteral | |||||||||||||||||||
| {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} | Ultatri | |||||||||||||||||||
| {10,10,10,10,10,10,...........,10,10,10} | Iteralplex | |||||||||||||||||||
| {10,10,10,10,10,10,...........,10,10,10} | Iteralplex | |||||||||||||||||||
| {10,10,10,10,10,10,...........,10,10,10} | Iteralplex | |||||||||||||||||||
| {10,10,10,10,10,10,...........,10,10,10} | Iteralplex | |||||||||||||||||||
| {10,10,10,10,10,10,...........,10,10,10} | Iteralplex | |||||||||||||||||||
| {10,10,10,10,10,10,...........,10,10,10} | Iteralplex | |||||||||||||||||||
| {10,10,10,10,10,10,...........,10,10,10} | Iteralplex | |||||||||||||||||||
| /10,10\
\10 || Emperal | ||||||||||||||||||||
| /10, 10 \
\emperal / || Emperalplex |
/10,10\
\10,10/ || Hyperal |
/10,10 \
\10,hyperal/ || Hyperalplex |
/3,3,3\ |
\3,3,3/ || Dutritri |
/10,10,10\ |
\10,10,10/ || Dutridecal /10,10,10,10,10,10,10,10,10,10\ |
\10,10,10,10,10,10,10,10,10,10/ || Xappol /10,10,10,10,..........,10\ |
\10,10,10,10,..........,10/ || Xappolplex |
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.
