Unknown95387 (talk | contribs) (added commas) Tag: Visual edit |
m (Undo revision 280924 by Matthewhanna10 (talk)) |
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− | <!-- |
+ | {{<!-- |
____ _ _ |
____ _ _ |
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|_| |___/ |
|_| |___/ |
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− | ( |
+ | (That also goes for this wiki in general. See the About page.) |
This is an important page in this wiki, pal. ^_^ |
This is an important page in this wiki, pal. ^_^ |
||
+ | -->ListNav}}This is a list of [[googology|googolisms]] in ascending order. |
||
− | --> |
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+ | |||
− | {{ListNav}} |
||
+ | This list contains ill-defined large numbers, e.g. [[:Category:BEAF|BEAF numbers beyond tetrational arrays]], [[BIG FOOT]], [[Little Bigeddon]], [[Sasquatch]], and large numbers whose well-definedness is not known, e.g. [[:Category:-tar|large numbers defined by Taranovsky's ordinal notation]] and [[Bashicu matrix system|Bashicu matrix number]] with respect to Bashicu matrix system version 2.3. |
||
− | This is a list of [[googology|googologisms]] in ascending order. |
||
+ | |||
+ | This page (the main list) lists the more notable googolisms on each class; click the "More..." link at the end of each section to see more googolisms in that class. |
||
==Class 0 (0 - 6)== |
==Class 0 (0 - 6)== |
||
Line 35: | Line 37: | ||
|[[Zero]] |
|[[Zero]] |
||
|0 |
|0 |
||
+ | |- |
||
+ | |[[Googolplexianminex]] |
||
+ | |\(10^{-(10^{10^{10^{100}}})}\) |
||
+ | |- |
||
+ | |[[Googolplexminex]] |
||
+ | |\(10^{-(10^{10^{100}})}\) |
||
|- |
|- |
||
|[[Googolminex]] |
|[[Googolminex]] |
||
− | |10 |
+ | |\(10^{-(10^{100})}\) or 1/[[googolplex]] |
|- |
|- |
||
|[[One]] |
|[[One]] |
||
Line 57: | Line 65: | ||
|6 |
|6 |
||
|} |
|} |
||
+ | '''[[List of googolisms/Class 0 and 1|More...]]''' |
||
==Class 1 (7 - 1,000,000)== |
==Class 1 (7 - 1,000,000)== |
||
Line 75: | Line 84: | ||
|[[Ten]] |
|[[Ten]] |
||
|10 |
|10 |
||
+ | |- |
||
+ | |[[12|Dozen]] |
||
+ | |12 |
||
|- |
|- |
||
|[[Hundred]] |
|[[Hundred]] |
||
Line 161: | Line 173: | ||
|- |
|- |
||
|[[Avogadro's number]] |
|[[Avogadro's number]] |
||
− | |6. |
+ | |6.02214076*10<sup>23</sup> |
|- |
|- |
||
|[[Septillion]](S) / [[Quadrillion]](L) |
|[[Septillion]](S) / [[Quadrillion]](L) |
||
Line 247: | Line 259: | ||
|10<sup>213</sup> |
|10<sup>213</sup> |
||
|- |
|- |
||
− | |[[ |
+ | |[[Hundertime]] |
|4.71193079990*10<sup>219</sup> |
|4.71193079990*10<sup>219</sup> |
||
|- |
|- |
||
Line 338: | Line 350: | ||
|- |
|- |
||
|[[Largest known prime]] |
|[[Largest known prime]] |
||
− | |2<sup> |
+ | |2<sup>82,589,933</sup>-1 ~ 1.488944*10<sup>24,862,047</sup> |
|- |
|- |
||
|[[Nanillion]] |
|[[Nanillion]] |
||
Line 426: | Line 438: | ||
|[[Dohectillion]] |
|[[Dohectillion]] |
||
|10<sup>3*10<sup>600</sup>+3</sup> |
|10<sup>3*10<sup>600</sup>+3</sup> |
||
+ | |- |
||
+ | |[[Googolplexichime]] |
||
+ | |10<sup>10<sup>1,000</sup></sup> |
||
|- |
|- |
||
|[[Killillion]] |
|[[Killillion]] |
||
− | |10<sup>3*10<sup> |
+ | |10<sup>3*10<sup>3,000</sup>+3</sup> |
|- |
|- |
||
|[[Googolplexigong]] |
|[[Googolplexigong]] |
||
Line 557: | Line 572: | ||
|- |
|- |
||
|[[Gijillion]] |
|[[Gijillion]] |
||
− | |10<sup>3*10<sup>3*10<sup> |
+ | |10<sup>3*10<sup>3*10<sup>300,000,0000</sup></sup>+3</sup> |
|- |
|- |
||
|[[Pentalogue]] |
|[[Pentalogue]] |
||
Line 581: | Line 596: | ||
|- |
|- |
||
|[[Ecetontriplex]] |
|[[Ecetontriplex]] |
||
− | |10<sup>10<sup>10<sup>303</sup></sup></sup> |
+ | |10<sup>10<sup>10<sup>10<sup>303</sup></sup></sup></sup> |
|- |
|- |
||
|[[Gigafaxul]] |
|[[Gigafaxul]] |
||
Line 668: | Line 683: | ||
|- |
|- |
||
|[[Chilialogue]] |
|[[Chilialogue]] |
||
− | + | |10↑↑1,000 |
|
|- |
|- |
||
|[[Grangolgong]] |
|[[Grangolgong]] |
||
Line 710: | Line 725: | ||
|- |
|- |
||
|[[Tria-teraksys]] |
|[[Tria-teraksys]] |
||
− | |E1#1#3 = |
+ | |E1#1#3 = 10↑↑↑3 = 10↑↑10↑↑10 |
|- |
|- |
||
|[http://googology.wikia.com/wiki/Equiduoxal Equiduoxal] |
|[http://googology.wikia.com/wiki/Equiduoxal Equiduoxal] |
||
Line 921: | Line 936: | ||
!Name |
!Name |
||
!Value |
!Value |
||
+ | |- |
||
+ | |[[Laver_table|\(q(6)\)]] (lower bound) |
||
+ | | |
||
|- |
|- |
||
|[[Moser]] |
|[[Moser]] |
||
Line 1,085: | Line 1,103: | ||
|- |
|- |
||
|[[Kaboodol]] |
|[[Kaboodol]] |
||
− | |\(\underbrace{10 \rightarrow\ldots\rightarrow 10}_{102} < kaboodol < \underbrace{10 \rightarrow\ldots\rightarrow 10}_{103}\) |
+ | |\(\underbrace{10 \rightarrow\ldots\rightarrow 10}_{102} < \text{kaboodol} < \underbrace{10 \rightarrow\ldots\rightarrow 10}_{103}\) |
|- |
|- |
||
|[[Throogol]] |
|[[Throogol]] |
||
Line 1,109: | Line 1,127: | ||
|- |
|- |
||
|[[Kaboodolplex]] |
|[[Kaboodolplex]] |
||
+ | |\(\underbrace{10 \rightarrow\ldots\rightarrow 10}_{\text{kaboodol}+2} < \text{kaboodolplex} < \underbrace{10 \rightarrow\ldots\rightarrow 10}_{\text{kaboodol}+3}\) |
||
− | | |
||
|- |
|- |
||
|[[Troogolplex]] |
|[[Troogolplex]] |
||
Line 1,710: | Line 1,728: | ||
|[[Pentaelgathor]] |
|[[Pentaelgathor]] |
||
|E100#^#^#####100 |
|E100#^#^#####100 |
||
+ | |- |
||
+ | |[[Quintongulus]] |
||
+ | |{10,100 (0,0,0,0,0,1) 2} |
||
+ | |- |
||
+ | |[[Sextongulus]] |
||
+ | |{10,100 (0,0,0,0,0,0,1) 2} |
||
+ | |- |
||
+ | |[[Septongulus]] |
||
+ | |{10,100 (0,0,0,0,0,0,0,1) 2} |
||
+ | |- |
||
+ | |[[Octongulus]] |
||
+ | |{10,100 (0,0,0,0,0,0,0,0,1) 2} |
||
|- |
|- |
||
|[[Goplexulus]] |
|[[Goplexulus]] |
||
Line 1,725: | Line 1,755: | ||
!Name |
!Name |
||
!Value |
!Value |
||
+ | |- |
||
+ | |[[Extendol]] |
||
+ | |s(3,3{1`2}2) |
||
|- |
|- |
||
|[[Graltothol]] |
|[[Graltothol]] |
||
Line 1,731: | Line 1,764: | ||
|[[Goduplexulus]] |
|[[Goduplexulus]] |
||
|{10,100 ((100)1) 2} |
|{10,100 ((100)1) 2} |
||
+ | |- |
||
+ | |[[Thraeltothol]] |
||
+ | |E100#^#^#^###100 |
||
+ | |- |
||
+ | |[[Terinntothol]] |
||
+ | |E100#^#^#^####100 |
||
+ | |- |
||
+ | |[[Pentaeltothol]] |
||
+ | |E100#^#^#^#####100 |
||
|- |
|- |
||
|[[Godtertol]] |
|[[Godtertol]] |
||
Line 1,746: | Line 1,788: | ||
!Name |
!Name |
||
!Value |
!Value |
||
+ | |- |
||
+ | |[[Graltertol]] |
||
+ | |E100#^#^#^#^##100 |
||
+ | |- |
||
+ | |[[Thraeltertol]] |
||
+ | |E100#^#^#^#^###100 |
||
|- |
|- |
||
|[[Godtopol]] |
|[[Godtopol]] |
||
|E100#^#^#^#^#^#100 |
|E100#^#^#^#^#^#100 |
||
+ | |- |
||
+ | |[[Graltopol]] |
||
+ | |E100#^#^#^#^#^##100 |
||
|- |
|- |
||
|[[Godhathor]] |
|[[Godhathor]] |
||
Line 1,758: | Line 1,809: | ||
|[[Godoctol]] |
|[[Godoctol]] |
||
|E100#^#^#^#^#^#^#^#^#100 |
|E100#^#^#^#^#^#^#^#^#100 |
||
+ | |- |
||
+ | |[[Godentol]] |
||
+ | |E100#^#^#^#^#^#^#^#^#^#100 |
||
+ | |- |
||
+ | |[[Goddekathol]] |
||
+ | |E100#^#^#^#^#^#^#^#^#^#^#100 |
||
|- |
|- |
||
|[[Tethrathoth]] |
|[[Tethrathoth]] |
||
Line 1,812: | Line 1,869: | ||
|[[Great and Terrible Tethrathoth]] |
|[[Great and Terrible Tethrathoth]] |
||
|E100#^^#>#100#2 |
|E100#^^#>#100#2 |
||
+ | |- |
||
+ | |[[Gippatoth]] |
||
+ | |100↑↑(2 × 100) & 10 |
||
+ | |- |
||
+ | |[[Gappatoth]] |
||
+ | |100↑↑(3 × 100) & 10 |
||
+ | |- |
||
+ | |[[Geepatoth]] |
||
+ | |100↑↑(4 × 100) & 10 |
||
+ | |- |
||
+ | |[[Grangol-carta-tethriterator]] |
||
+ | |E100#^^#>#100#100 |
||
+ | |- |
||
+ | |[[Tethriterhecate]] |
||
+ | |E100#^^#>#*#100 |
||
+ | |- |
||
+ | |[[Deutero-tethriterator]] |
||
+ | |E100#^^#>#*#^^#>#100 |
||
+ | |- |
||
+ | |[[Tethriterfact]] |
||
+ | |E100(#^^#>#)^#100 |
||
+ | |- |
||
+ | |[[Terrible tethriterator]] |
||
+ | |E100(#^^#>#)^^#100 |
||
+ | |- |
||
+ | |[[Tethriditerator]] |
||
+ | |E100#^^#>(#+#)100 |
||
+ | |- |
||
+ | |[[Tethrigriditerator]] |
||
+ | |E100#^^#>##100 |
||
+ | |- |
||
+ | |[[Tethrispatialator]] |
||
+ | |E100#^^#>#^#100 |
||
+ | |- |
||
+ | |[[Dustaculated-tethrathoth]] |
||
+ | |E100#^^#>#^^#100 |
||
+ | |- |
||
+ | |[[Tristaculated-tethrathoth]] |
||
+ | |E100#^^#>#^^#>#^^#100 |
||
+ | |- |
||
+ | |[[Tethracross]] |
||
+ | |E100#^^##100 |
||
+ | |- |
||
+ | |[[Boppatoth]] |
||
+ | |100↑↑(100<sup>2</sup>) & 10 |
||
|} |
|} |
||
Line 1,822: | Line 1,924: | ||
!Value |
!Value |
||
|- |
|- |
||
+ | |[[Terrible tethracross]] |
||
− | |[[Triakulus]] |
||
+ | |E100(#^^##)^^#100 |
||
− | |{3,3,3} & 3 |
||
|- |
|- |
||
+ | |[[Secundotethrated-tethracross]] |
||
− | |[[Kungulus]] |
||
+ | |E100(#^^##)^^##100 |
||
− | |{10,100,3} & 10 |
||
|- |
|- |
||
− | |[[ |
+ | |[[Tethritercross]] |
− | |E100#^^##100 |
+ | |E100#^^##>#100 |
|- |
|- |
||
+ | |[[Dustaculated-tethracross]] |
||
− | |[[Kungulusplex]] |
||
+ | |E100#^^##>#^^##100 |
||
− | |{10,kungulus,3} & 10 |
||
|- |
|- |
||
− | |[[ |
+ | |[[Tethracubor]] |
+ | |E100#^^###100 |
||
− | |{10,100,4} & 10 |
||
|- |
|- |
||
− | |[[ |
+ | |[[Troppatoth]] |
+ | |100↑↑(100<sup>3</sup>) & 10 |
||
− | |{10,10,10} & 10 |
||
|- |
|- |
||
+ | |[[Terrible tethracubor]] |
||
− | |[[Humongulus]] |
||
+ | |E100(#^^###)^^#100 |
||
− | |{10,10,100} & 10 |
||
+ | |- |
||
+ | |[[Tethraducubor]] |
||
+ | |E100(#^^###)^^###100 |
||
+ | |- |
||
+ | |[[Tethritercubor]] |
||
+ | |E100#^^###>#100 |
||
+ | |- |
||
+ | |[[Dustaculated-tethracubor]] |
||
+ | |E100#^^###>#^^###100 |
||
+ | |- |
||
+ | |[[Tethrateron]] |
||
+ | |E100#^^####100 |
||
+ | |- |
||
+ | |[[Quadroppatoth]] |
||
+ | |100↑↑(100<sup>4</sup>) & 10 |
||
+ | |- |
||
+ | |[[Terrible tethrateron]] |
||
+ | |E100(#^^####)^^#100 |
||
+ | |- |
||
+ | |[[Tethraduteron]] |
||
+ | |E100(#^^####)^^####100 |
||
+ | |- |
||
+ | |[[Tethra-hectateron]] |
||
+ | |E100#^^####>#100 |
||
+ | |- |
||
+ | |[[Dustaculated-tethrateron]] |
||
+ | |E100#^^####>#^^####100 |
||
+ | |- |
||
+ | |[[Tethrapeton]] |
||
+ | |E100#^^#^#5 |
||
+ | |- |
||
+ | |[[Tethrahexon]] |
||
+ | |E100#^^#^#6 |
||
+ | |- |
||
+ | |[[Tethrahepton]] |
||
+ | |E100#^^#^#7 |
||
+ | |- |
||
+ | |[[Tethra-ogdon]] |
||
+ | |E100#^^#^#8 |
||
+ | |- |
||
+ | |[[Tethrennon]] |
||
+ | |E100#^^#^#9 |
||
+ | |- |
||
+ | |[[Tethradekon]] |
||
+ | |E100#^^#^#10 |
||
+ | |- |
||
+ | |[[Tethrafact]] |
||
+ | |E100#^^#^#100 |
||
+ | |- |
||
+ | |[[Tethrato-tethrathoth]] |
||
+ | |E100#^^#^^#100 |
||
+ | |- |
||
+ | |[[Tethrarxitet]] |
||
+ | |E100#^^#^^#^^#100 |
||
|- |
|- |
||
|[[Pentacthulhum]] |
|[[Pentacthulhum]] |
||
Line 1,854: | Line 2,010: | ||
!Name |
!Name |
||
!Value |
!Value |
||
+ | |- |
||
+ | |[[Pentacthuldugon]] |
||
+ | |E100(#^^^#)^^^#100 |
||
+ | |- |
||
+ | |[[Pentacthuliterator]] |
||
+ | |E100#^^^#>#100 |
||
|- |
|- |
||
|[[Hugexul]] |
|[[Hugexul]] |
||
Line 1,860: | Line 2,022: | ||
|[[Superior Hugexul]] |
|[[Superior Hugexul]] |
||
|200![200(1)200,200] |
|200![200(1)200,200] |
||
+ | |- |
||
+ | |[[Dustaculated-pentacthulhum]] |
||
+ | |E100#^^^#>#^^^#100 |
||
+ | |- |
||
+ | |[[Pentacthulcross]] |
||
+ | |E100#^^^##100 |
||
+ | |- |
||
+ | |[[Bisuperior Hugexul]] |
||
+ | |200![200(1)200,200,200] |
||
+ | |- |
||
+ | |[[Pentacthulcubor]] |
||
+ | |E100#^^^###100 |
||
+ | |- |
||
+ | |[[Pentacthulteron]] |
||
+ | |E100#^^^####100 |
||
+ | |- |
||
+ | |[[Pentacthultope]] |
||
+ | |E100#^^^#^#100 |
||
+ | |- |
||
+ | |[[Pentacthularxitri]] |
||
+ | |E100#^^^#^^^#100 |
||
|- |
|- |
||
|[[Hexacthulhum]] |
|[[Hexacthulhum]] |
||
Line 1,866: | Line 2,049: | ||
|[[Hugebixul]] |
|[[Hugebixul]] |
||
|200![200(1)200(1)200] |
|200![200(1)200(1)200] |
||
+ | |- |
||
+ | |[[Hexacthuliterator]] |
||
+ | |E100#^^^^#>#100 |
||
+ | |- |
||
+ | |[[Superior Hugebixul]] |
||
+ | |200![200(1)200(1)200,200] |
||
+ | |- |
||
+ | |[[Hexacthulcross]] |
||
+ | |E100#^^^^##100 |
||
+ | |- |
||
+ | |[[Heptacthulhum]] |
||
+ | |E100#{5}#100 |
||
+ | |- |
||
+ | |[[Hugetrixul]] |
||
+ | |200![200(1)200(1)200(1)200] |
||
+ | |- |
||
+ | |[[Ogdacthulhum]] |
||
+ | |E100#{6}#100 |
||
+ | |- |
||
+ | |[[Hugequaxul]] |
||
+ | |200![200(1)200(1)200(1)200(1)200] |
||
+ | |- |
||
+ | |[[Ennacthulhum]] |
||
+ | |E100#{7}#100 |
||
+ | |- |
||
+ | |[[Dekacthulhum]] |
||
+ | |E100#{8}#100 |
||
+ | |- |
||
+ | |[[Goliath]] |
||
+ | |E100#{10}#100 |
||
+ | |- |
||
+ | |[[Godsgodgulus]] |
||
+ | |E100#{#}#100 |
||
+ | |- |
||
+ | |[[Godsgodgulcross]] |
||
+ | |E100#{#}##100 |
||
+ | |- |
||
+ | |[[Godsgodeus]] |
||
+ | |E100#{#+#}#100 |
||
+ | |- |
||
+ | |[[The centurion]] |
||
+ | |E100#{#^#}#100 |
||
+ | |- |
||
+ | |[[Ohmygosh-ohmygosh-ohmygooosh]] |
||
+ | |E100#{#{#}#}#100 |
||
+ | |- |
||
+ | |[[Blasphemorgulus]] |
||
+ | |E100{#,#,1,2}100 |
||
+ | |- |
||
+ | |[[Hundrelasphemorgue]] |
||
+ | |E100{#,#+1,1,2}100 |
||
|- |
|- |
||
|[[Enormaxul]] |
|[[Enormaxul]] |
||
Line 1,872: | Line 2,106: | ||
|[[Superior Enormaxul]] |
|[[Superior Enormaxul]] |
||
|200![200(2)200,200] |
|200![200(2)200,200] |
||
+ | |- |
||
+ | |[[Bisuperior Enormaxul]] |
||
+ | |200![200(2)200,200,200] |
||
|- |
|- |
||
|[[Enormabixul]] |
|[[Enormabixul]] |
||
|200![200(2)200(2)200] |
|200![200(2)200(2)200] |
||
+ | |- |
||
+ | |[[Enormatrixul]] |
||
+ | |200![200(2)200(2)200(2)200] |
||
+ | |- |
||
+ | |[[Enormaquaxul]] |
||
+ | |200![200(2)200(2)200(2)200(2)200] |
||
|- |
|- |
||
|[[Destruxul]] |
|[[Destruxul]] |
||
Line 1,881: | Line 2,124: | ||
|[[Great Destruxul]] |
|[[Great Destruxul]] |
||
|200![200(200)200(200)200] |
|200![200(200)200(200)200] |
||
+ | |- |
||
+ | |[[Bigreat Destruxul]] |
||
+ | |200![200(200)200(200)200(200)200] |
||
|- |
|- |
||
|[[Bird's number]] |
|[[Bird's number]] |
||
|\(f_{\vartheta(\Omega^{\omega})+2}(f_{\vartheta(\Omega^{\omega})+1}(f_{\vartheta(\Omega^{\omega})}(f_{\vartheta(\Omega^{\omega})}(7))))\) |
|\(f_{\vartheta(\Omega^{\omega})+2}(f_{\vartheta(\Omega^{\omega})+1}(f_{\vartheta(\Omega^{\omega})}(f_{\vartheta(\Omega^{\omega})}(7))))\) |
||
|- |
|- |
||
+ | |[[TREE(3)|<nowiki>TREE[3]</nowiki>]] (lower bound) |
||
− | |Lower bound for [[TREE(3)]] |
||
+ | | |
||
− | |\(\approx\{X,X (1) 2\}+1 \&\ 3[3]\) |
||
|- |
|- |
||
|[[Destrubixul]] |
|[[Destrubixul]] |
||
|200![200([200(200)200])200] |
|200![200([200(200)200])200] |
||
+ | |- |
||
+ | |[[Destrutrixul]] |
||
+ | |200![200([200([200(200)200])200])200] |
||
+ | |- |
||
+ | |[[Destruquaxul]] |
||
+ | |200![200([200([200([200(200)200])200])200])200] |
||
|- |
|- |
||
|[[Golapulus]] |
|[[Golapulus]] |
||
− | | |
+ | |10<sup>100</sup>&10&10 |
|- |
|- |
||
|[[Extremexul]] |
|[[Extremexul]] |
||
− | |200![<sub>2</sub>200,200,200,200] |
+ | |200![1(1)[<sub>2</sub>200,200,200,200]] |
|} |
|} |
||
Line 1,901: | Line 2,153: | ||
==Higher computable level== |
==Higher computable level== |
||
+ | |||
+ | Since the comparison (or even the well-definedness) of numbers of this level is unknown, the order of entries does not necessarily imply the order of the sizes. Also, several numbers are defined by an OCF, which is uncomputable, and are not known to be computable. |
||
{| |
{| |
||
Line 1,907: | Line 2,161: | ||
|- |
|- |
||
|[[Extremebixul]] |
|[[Extremebixul]] |
||
− | |200![<sub>2</sub>200,200,200,200,200] |
+ | |200![1(1)[<sub>2</sub>200,200,200,200,200]] |
+ | |- |
||
+ | |[[Extremetrixul]] |
||
+ | |200![1(1)[<sub>2</sub>200,200,200,200,200,200]] |
||
+ | |- |
||
+ | |[[Extremequaxul]] |
||
+ | |200![1(1)[<sub>2</sub>200,200,200,200,200,200,200]] |
||
|- |
|- |
||
|[[Gigantixul]] |
|[[Gigantixul]] |
||
− | |200![<sub>3</sub>200,200,200] |
+ | |200![1(1)[<sub>3</sub>200,200,200]] |
− | |- |
||
− | |[[Golapulusplex]] |
||
− | |{10,100} & 10 & 10 & 10 |
||
|- |
|- |
||
|[[Gigantibixul]] |
|[[Gigantibixul]] |
||
− | |200![<sub>3</sub>200,200,200,200] |
+ | |200![1(1)[<sub>3</sub>200,200,200,200]] |
+ | |- |
||
+ | |[[Gigantitrixul]] |
||
+ | |200!1(1)[<sub>3</sub>200,200,200,200,200]] |
||
+ | |- |
||
+ | |[[Gigantiquaxul]] |
||
+ | |200![1(1)[<sub>3</sub>200,200,200,200,200,200]] |
||
|- |
|- |
||
|[[Nucleaxul]] |
|[[Nucleaxul]] |
||
|200![<sub>200</sub>200] |
|200![<sub>200</sub>200] |
||
− | |- |
||
− | |[[Subcubic graph number|SCG(13)]] |
||
− | | |
||
− | |- |
||
− | |[[Big boowa]] |
||
− | |{3,3,3 / 2} |
||
− | |- |
||
− | |[[Great big boowa]] |
||
− | |{3,3,4 / 2} |
||
− | |- |
||
− | |[[Grand boowa]] |
||
− | |{3,3,big boowa / 2} |
||
− | |- |
||
− | |[[Super gongulus]] |
||
− | |{10,10 (100) 2 / 2} |
||
− | |- |
||
− | |[[Wompogulus]] |
||
− | |{10,10 (10) 2 / 100} |
||
− | |- |
||
− | |[[Guapamonga]] |
||
− | |10<sup>100</sup> && (10<sup>100</sup> & 10) |
||
− | |- |
||
− | |[[Guapamongaplex]] |
||
− | |10<sup>guapamonga</sup> && (10<sup>guapamonga</sup> & 10) |
||
|- |
|- |
||
|[[Nucleabixul]] |
|[[Nucleabixul]] |
||
|200![<sub>[<sub>200</sub>200]</sub>200] |
|200![<sub>[<sub>200</sub>200]</sub>200] |
||
|- |
|- |
||
+ | |[[Subcubic graph number|SCG(13)]] (lower bound) |
||
− | |[[Big hoss]] |
||
+ | | |
||
− | |{L,100}<sub>100,100</sub> = {100,100 ////...100 /'s...//// 2} = {100,100 (1)/ 2} |
||
|- |
|- |
||
− | |[[ |
+ | |[[Nucleatrixul]] |
+ | |200![<sub>[<sub>[<sub>200</sub>200]</sub>200]</sub>200] |
||
− | |{100,100 ////...100 /'s...//// 100} |
||
|- |
|- |
||
− | |[[ |
+ | |[[Nucleaquaxul]] |
+ | |200![<sub>[<sub>[<sub>[<sub>200</sub>200]</sub>200]</sub>200]</sub>200] |
||
− | |{big hoss, big hoss //////...big hoss /'s...////// 2} = {big hoss,big hoss (1)/ 2} |
||
− | |- |
||
− | |[[Bukuwaha]] |
||
− | |{L,100<sup>100</sup>}<sub>100,100</sub> |
||
|- |
|- |
||
|[[BIGG]] |
|[[BIGG]] |
||
|200? |
|200? |
||
|- |
|- |
||
− | |[[ |
+ | |[[Loader's number]] |
+ | |D<sup>5</sup>(99) |
||
− | |{L2,100}<sub>100,100</sub> |
||
|- |
|- |
||
+ | |[[Bashicu matrix system|Bashicu matrix number]] with respect to Bashicu matrix system version 2.3 |
||
− | |[[Good goshomity]] |
||
+ | | |
||
− | |{L2,goshomity}<sub>goshomity,goshomity</sub> |
||
|- |
|- |
||
+ | |[[N primitive#Large_Number|6]] (N primitive) |
||
− | |[[Big Bukuwaha]] |
||
+ | | |
||
− | |{100,100 Bukuwaha 2} |
||
|- |
|- |
||
+ | |[[Y sequence|Y sequence number]] |
||
− | |[[Bongo Bukuwaha]] |
||
+ | |f<sup>2000</sup>(1) |
||
− | |{100,100 Big Bukuwaha 2} |
||
|- |
|- |
||
+ | |[[Transcendental integer|the least transcendental integer]] |
||
− | |[[Quabinga Bukuwaha]] |
||
+ | | |
||
− | |{100,100 Bongo Bukuwaha 2} |
||
− | |- |
||
− | |[[Meameamealokkapoowa]] |
||
− | |{L100,10}<sub>10,10</sub> |
||
− | |- |
||
− | |[[Meameamealokkapoowa oompa]] |
||
− | |{LLL … A … LLL,10}<sub>10,10</sub> |
||
− | |- |
||
− | |[[Loader's number]] |
||
− | |D<sup>5</sup>(99) |
||
|} |
|} |
||
[[List of googologisms/Higher computable level|'''More...''']] |
[[List of googologisms/Higher computable level|'''More...''']] |
||
− | <!-- |
||
− | There is no such thing as meameamealokkapoowa oompa boompa. Do not add it. |
||
− | |||
− | Instead of making cheesy expansions to other people's number systems, go make up your own function. Don't be a googological parasite. -FB100Z |
||
− | |||
− | If you still want it, please contact Jonathan Bowers or Sbiis Saibian. ^_^ |
||
− | |||
− | Because Jabe and Sbiis can just snap their fingers and we'll write article about it :D -FB |
||
− | --> |
||
==Uncomputable numbers== |
==Uncomputable numbers== |
||
+ | |||
+ | The term "uncomputable number" here refers to the numbers defined in terms of [[Uncomputable function|uncomputably fast-growing functions]]. This table contains large numbers which are known to be ill-defined. For more details on the ill-definedness, click the "More..." link below. |
||
{| |
{| |
||
!Name |
!Name |
||
!Value |
!Value |
||
+ | !Ill-defined? |
||
|- |
|- |
||
− | |[[Rado's sigma function| |
+ | |1919-th [[Rado's sigma function|busy beaver]] |
+ | |\(\Sigma(1919)\) |
||
− | | |
||
+ | |No |
||
|- |
|- |
||
|[[Fish number 4]] |
|[[Fish number 4]] |
||
|F<sub>4</sub><sup>63</sup>(3) |
|F<sub>4</sub><sup>63</sup>(3) |
||
+ | |No |
||
|- |
|- |
||
|[[Xi function|\(\Xi(10^6)\)]] |
|[[Xi function|\(\Xi(10^6)\)]] |
||
| |
| |
||
+ | |No |
||
+ | |- |
||
+ | |[[Infinite_time_Turing_machine|\(\Sigma_\infty(10^9)\)]] |
||
+ | | |
||
+ | |No |
||
|- |
|- |
||
|[[Rayo's number]] |
|[[Rayo's number]] |
||
|Rayo(10<sup>100</sup>) |
|Rayo(10<sup>100</sup>) |
||
+ | |Partially |
||
|- |
|- |
||
|[[Fish number 7]] |
|[[Fish number 7]] |
||
|F<sub>7</sub><sup>63</sup>(10<sup>100</sup>) |
|F<sub>7</sub><sup>63</sup>(10<sup>100</sup>) |
||
+ | |Partially |
||
|- |
|- |
||
|[[BIG FOOT]] |
|[[BIG FOOT]] |
||
|FOOT<sup>10</sup>(10<sup>100</sup>) |
|FOOT<sup>10</sup>(10<sup>100</sup>) |
||
+ | |Yes |
||
|- |
|- |
||
|[[Little Bigeddon]] |
|[[Little Bigeddon]] |
||
+ | | |
||
− | |(Largest valid googologism) |
||
+ | |Yes |
||
|- |
|- |
||
|[[Sasquatch]] |
|[[Sasquatch]] |
||
+ | | |
||
− | |(Unconfirmed, largest if confirmed) |
||
+ | |Yes |
||
+ | |- |
||
+ | |[[Large Number Garden Number]] |
||
+ | |\(f^{10}(10 \uparrow^{10} 10)\) |
||
+ | |Not determined yet |
||
|} |
|} |
||
Line 2,033: | Line 2,270: | ||
== Notes == |
== Notes == |
||
− | <references /> |
+ | <references />[[ja:数の一覧]] |
− | |||
− | [[ja:数の一覧]] |
||
[[zh:大數列表]] |
[[zh:大數列表]] |
||
+ | [[cs:Seznam googolismů]] |
||
[[Category:Lists]] |
[[Category:Lists]] |
||
[[Category:Classes]] |
[[Category:Classes]] |
Revision as of 13:09, 29 March 2020
List of googolisms
- Class 0 and 1
- Class 2
- Class 3
- Class 4
- Class 5
- Tetration level
- Up-arrow notation level
- Linear omega level
- Quadratic omega level
- Polynomial omega level
- Exponentiated linear omega level
- Exponentiated polynomial omega level
- Double exponentiated polynomial omega level
- Triple exponentiated polynomial omega level
- Iterated Cantor normal form level
- Epsilon level
- Binary phi level
- Bachmann's collapsing level
- Higher computable level
- Uncomputable numbers
This is a list of googolisms in ascending order.
This list contains ill-defined large numbers, e.g. BEAF numbers beyond tetrational arrays, BIG FOOT, Little Bigeddon, Sasquatch, and large numbers whose well-definedness is not known, e.g. large numbers defined by Taranovsky's ordinal notation and Bashicu matrix number with respect to Bashicu matrix system version 2.3.
This page (the main list) lists the more notable googolisms on each class; click the "More..." link at the end of each section to see more googolisms in that class.
Class 0 (0 - 6)
Name | Value |
---|---|
Zero | 0 |
Googolplexianminex | \(10^{-(10^{10^{10^{100}}})}\) |
Googolplexminex | \(10^{-(10^{10^{100}})}\) |
Googolminex | \(10^{-(10^{100})}\) or 1/googolplex |
One | 1 |
Two | 2 |
Three | 3 |
Four | 4 |
Five | 5 |
Six | 6 |
Class 1 (7 - 1,000,000)
Name | Value |
---|---|
Seven | 7 |
Eight | 8 |
Nine | 9 |
Ten | 10 |
Dozen | 12 |
Hundred | 100 (102) |
Eleventy | 110 |
Twelfty (or long hundred) | 120 |
Gross | 144 (122) |
Baker's gross | 169 (132) |
Poulter's gross | 196 (142) |
Short ream | 480 |
Ream | 500 |
Beast number | 666 |
Thousand / Niloogol | 1,000 (103) |
Great gross | 1,728 (123) |
Great Baker's gross | 2,197 (133) |
Poulter's great gross | 2,744 (143) |
Myriad | 10,000 |
Lakh | 100,000 |
Class 2 (1,000,000 - \(10^{1,000,000}\))
Name | Value |
---|---|
Million | 1,000,000 |
Crore | 10,000,000 |
Myllion | 100,000,000 |
Billion(S)[1] / Milliard | 1,000,000,000 |
Dialogue | 1010 |
Trillion(S) / Billion(L) | 1012 |
Quadrillion(S) / Billiard | 1015 |
Byllion | 1016 |
Trillion(L) / Quintillion(S) | 1018 |
Sextillion(S) / Trilliard | 1021 |
Avogadro's number | 6.02214076*1023 |
Septillion(S) / Quadrillion(L) | 1024 |
Octillion(S) / Quadrilliard | 1027 |
Nonillion(S) / Quintillion(L) | 1030 |
Tryllion | 1032 |
Decillion(S) / Quintilliard | 1033 |
Undecillion(S) / Sextillion(L) | 1036 |
Duodecillion(S) / Sextilliard | 1039 |
Tredecillion(S) / Septillion(L) | 1042 |
Quattuordecillion(S) / Septilliard | 1045 |
Quindecillion(S) / Octillion(L) | 1048 |
Sexdecillion(S) / Octilliard | 1051 |
Septendecillion(S) / Nonillion(L) | 1054 |
Octodecillion(S) / Nonilliard | 1057 |
Novemdecillion(S) / Decillion(L) | 1060 |
Vigintillion(S) / Decilliard | 1063 |
Quadryllion | 1064 |
Eddington number | 136*2256 ~ 1.5747724136275*1079 |
Trigintillion(S) | 1093 |
Googol | 10100 |
Vigintillion(L) | 10120 |
Quadragintillion(S) | 10123 |
Googolex | 12060 ~ 5.6347514353165*10124 |
Quintyllion | 10128 |
Quinquagintillion(S) | 10153 |
Trigintillion(L) | 10180 |
Sexagintillion(S) | 10183 |
Gargoogol | 10200 |
Septuagintillion(S) | 10213 |
Hundertime | 4.71193079990*10219 |
Googoc | 200100 ~ 1.2676506002282*10230 |
Quadragintillion(L) | 10240 |
Octogintillion(S) | 10243 |
Nonagintillion(S) | 10273 |
Quinquagintillion(L) | 10300 |
Centillion(S) | 10303 |
Sexagintillion(L) | 10360 |
Primo-vigesimo-centillion(S) | 10366 |
Faxul | 200! ~ 7.88657867364*10374 |
Septuagintillion(L) | 10420 |
Octogintillion(L) | 10480 |
Googocci | 402201 ~ 2.814729533583*10523 |
Nonagintillion(L) | 10540 |
Centillion(L) | 10600 |
Primo-vigesimo-centillion(L) | 10726 |
Googolchime | 101,000 |
Millillion(S) | 103,003 |
Decyllion | 104,096 |
Millillion(L) | 106,000 |
Googoltoll | 1010,000 |
Hitchhiker's number | 2276,709 ~ 5.117645330517*1083,297 |
Googolgong | 10100,000 |
Class 3 (\(10^{1,000,000} - 10^{10^{1,000,000}}\))
Name | Value |
---|---|
Maximusmillion | 101,000,000 |
Milli-millillion(S) | 103,000,003 |
Vigintyllion | 104,194,304 |
Milli-millillion(L) | 106,000,000 |
Largest known prime | 282,589,933-1 ~ 1.488944*1024,862,047 |
Nanillion | 103,000,000,003 |
Trialogue | 101010 |
Ballium's number | ~ 2.03542*10138,732,019,349 |
Picillion | 103*1012+3 |
Femtillion | 103*1015+3 |
Attillion | 103*1018+3 |
Zeptillion | 103*1021+3 |
Yoctillion | 103*1024+3 |
Xonillion | 103*1027+3 |
Vecillion | 103*1030+3 |
Mecillion | 103*1033+3 |
Duecillion | 103*1036+3 |
Trecillion | 103*1039+3 |
Tetrecillion | 103*1042+3 |
Icosillion | 103*1060+3 |
Triacontillion | 103*1090+3 |
Googolplex | 1010100 |
Gargoogolplex | googolplex2 = 102*10100 |
Googolbang | (10100)! ~ 109.957*10101 |
Tetracontillion | 103*10120+3 |
Pentacontillion | 103*10150+3 |
Hexacontillion | 103*10180+3 |
Heptacontillion | 103*10210+3 |
Octacontillion | 103*10240+3 |
Ennacontillion | 103*10270+3 |
Hectillion | 103*10300+3 |
Ecetonplex | 1010303 |
Kilofaxul | (200!)! ~ 1010379 |
Dohectillion | 103*10600+3 |
Googolplexichime | 10101,000 |
Killillion | 103*103,000+3 |
Googolplexigong | 1010100,000 |
Class 4
Name | Value |
---|---|
Millionduplex | 10101,000,000 |
Megillion | 103*103,000,000+3 |
Gigillion | 103*103,000,000,000+3 |
Tetralogue | 10101010 |
Terillion | 103*103*1012+3 |
Petillion | 103*103*1015+3 |
Exillion | 103*103*1018+3 |
Zettillion | 103*103*1021+3 |
Yottillion | 103*103*1024+3 |
Xennillion | 103*103*1027+3 |
Dakillion | 103*103*1030+3 |
Hendillion | 103*103*1033+3 |
First Skewes number | eee79 ~ 10101034 |
Dokillion | 103*103*1036+3 |
Tradakillion | 103*103*1042+3 |
Ikillion | 103*103*1060+3 |
Trakillion | 103*103*1090+3 |
Googolduplex | 101010100 |
Fzgoogolplex | (1010100)1010100 = 101010100+100 |
Tekillion | 103*103*10120+3 |
Hotillion | 103*103*10300+3 |
Ecetonduplex | 101010303 |
Megafaxul | ((200!)!)! ~ 101010379 |
Botillion | 103*103*10600+3 |
Trotillion | 103*103*10900+3 |
Second Skewes number | eeee7.705 ~ 101010963 |
Totillion | 103*103*101,200+3 |
Kalillion | 103*103*103,000+3 |
Dalillion | 103*103*106,000+3 |
Tralillion | 103*103*109,000+3 |
Talillion | 103*103*1012,000+3 |
Dakalillion | 103*103*1030,000+3 |
Googolduplexigong | 101010100,000 |
Hotalillion | 103*103*10300,000+3 |
Class 5
Name | Value |
---|---|
Mejillion | 103*103*103,000,000+3 |
Gijillion | 103*103*10300,000,0000+3 |
Pentalogue | 1010101010 |
Astillion | 103*103*103*1012+3 |
Lunillion | 103*103*103*1015+3 |
Fermillion | 103*103*103*1018+3 |
Multillion | 103*103*103*1042+3 |
Googoltriplex | 10101010100 |
Fzgargoogolplex | googolduplexgoogolduplex |
Ecetontriplex | 10101010303 |
Gigafaxul | (((200!)!)!)! ~ 10101010379 |
Googoltriplexigong | 10101010100,000 |
Tetration level
Name | Value |
---|---|
Hexalogue | 10↑↑6 |
Googolquadriplex | E100#5 |
Fzgargantugoogolplex | googoltriplexgoogoltriplex |
Heptalogue | 10↑↑7 |
Googolquinplex | E100#6 |
Octalogue | 10↑↑8 |
Googolsextiplex | E100#7 |
Ennalogue | 10↑↑9 |
Bentley's Number | \(\sum^{9}_{i = 0} 10 \uparrow\uparrow i\) |
Googolseptiplex | E100#8 |
Decker | {10,10,2} = 10↑↑10 |
Googoloctiplex | E100#9 |
Endekalogue | 10↑↑11 |
Equinoxal | 10(≡) = 10(10)(10) |
Googolnoniplex | E100#10 |
Dodekalogue | 10↑↑12 |
Googoldeciplex | E100#11 |
Triadekalogue | 10↑↑13 |
Tetradekalogue | 10↑↑14 |
Giggol | {10,100,2} = 10↑↑100 |
Grangol | E100#100 |
Expofaxul | 200!1 |
Mega | 2[5] = 256[4] ~ 10↑↑258 |
Chilialogue | 10↑↑1,000 |
Grangolgong | E100,000#100,000 |
Tritri | {3,3,3} = {3,7625597484987,2} = 3↑↑7,625,597,484,987 |
Googolgoogolplex | 10↑↑(10100) |
Googoldex | E100#(10100) = E100#1#2 |
Ecetondex | E303#1#2 |
Grand Faxul | ~ 10↑↑10379 |
Up-arrow notation level
Name | Value |
---|---|
Zootzootplex | Exponential factorial of googolplex = googolplexgoogolplex-1googolplex-2...432. |
Googolplexstack | 10↑↑1010100 |
Googolplexidex | E100#(1010100) = E100#2#2 |
Grand Kilofaxul | ~ 10↑↑1010379 |
Tria-teraksys | E1#1#3 = 10↑↑↑3 = 10↑↑10↑↑10 |
Equiduoxal | 10(≡≡) = 10(10(≡))(10(≡)) |
Giggolplex | {10,giggol,2} = 10↑↑10↑↑100 |
Grangoldex | E100#100#2 |
Kiloexpofaxul | (200!1)!1 |
Grangoldexigong | E100,000#100,000#2 |
Googolgoogolduplex | 10↑↑10↑↑(10100) |
Ecetondudex | E303#1#3 |
Bigrand Faxul | ~ 10↑↑10↑↑(10379) |
Tetra-teraksys | E1#1#4 = 10↑↑↑4 |
Giggolduplex | {10,giggolplex,2} = 10↑↑10↑↑10↑↑100 |
Grangoldudex | E100#100#3 |
Megaexpofaxul | ((200!1)!1)!1 |
Grangoldudexigong | E100,000#100,000#3 |
Googolgoogoltriplex | 10↑↑10↑↑10↑↑(10100) |
Deka-teraksys | E1#1#10 = 10↑↑↑10 |
Megiston | 10[5] ~ 10↑↑↑11 |
Gaggol | {10,100,3} = 10↑↑↑100 |
Greagol | E100#100#100 |
Tetrofaxul | 200!2 |
Greagolgong | E100,000#100,000#100,000 |
Googol-3-flex | 10↑↑↑(10100) |
Ecetonthrex | E303#1#1#2 |
Folkman's number | 2↑↑↑(2901) |
Grand expofaxul | ~ 10↑↑↑10↑↑198 |
A-ooga | 2[6] |
Grahal | g1 = 3↑↑↑↑3 |
Tria-petaksys | 10↑↑↑↑3 |
Gaggolplex | {10,gaggol,3} |
Greagolthrex | E100#100#100#2 |
Kilotetrofaxul | (200!2)!2 |
Greagolthrexigong | E100,000#100,000#100,000#2 |
Ecetonduthrex | E303#1#1#3 |
Tritet | {4,4,4} = 4↑↑↑↑4 |
Greagolduthrex | E100#100#100#3 |
Greagolduthrexigong | E100,000#100,000#100,000#3 |
Equitrioxal | 10(≡≡≡) = 10(10(≡≡))(10(≡≡)) |
Hexar | \(Q_{1,0}(6)\) = 6↑↑↑↑6 |
Geegol | {10,100,4} = 10↑↑↑↑100 |
Gigangol | E100#100#100#100 |
Pentofaxul | 200!3 |
Geegolplex | {10,geegol,4} |
Gigangoltetrex | E100#100#100#100#2 |
Tripent | {5,5,5} = 5↑↑↑↑↑5 |
Gigol | {10,100,5} = 10↑↑↑↑↑100 |
Gorgegol | E100#100#100#100#100 |
Hexofaxul | 200!4 |
Gigolplex | {10,gigol,5} |
Gorgegolpentex | E100#100#100#100#100#2 |
Goggol | {10,100,6}= 10↑↑↑↑↑↑100 |
Gulgol | E100#100#100#100#100#100 |
Goggolplex | {10,goggol,6} |
Gulgolhex | E100#100#100#100#100#100#2 |
Trisept | {7,7,7} = 7↑77 |
Gagol | {10,100,7} = 10↑7100 |
Gaspgol | E100#100#100#100#100#100#100 |
Gagolplex | {10,gagol,7} |
Gaspgolheptex | E100#100#100#100#100#100#100#2 |
Ginorgol | E100#100#100#100#100#100#100#100 |
Ginorgoloctex | E100#100#100#100#100#100#100#100#2 |
Tridecal | {10,10,10} |
Boogol | {10,10,100} |
Gugold | E100##100 |
Hyperfaxul | 200![1] |
Gugoldagong | E100,000##100,000 |
Gongol | hyper(10,10100,100) |
Googoldiflux | \(10 \underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_{10^{100}} (10^{100})\) |
Equiquioxal | 10(≡{≡}≡) |
Linear omega level
Name | Value |
---|---|
\(q(6)\) (lower bound) | |
Moser | 2[2[5]] using Steinhaus-Moser notation, ~ 3 ↑Mega 3 |
Boogolplex | {10,10,{10,10,100}} |
Gugolda-suplex | E100##100#2 |
Kilohyperfaxul | (200![1])![1] |
Gongolplex | hyper(10,gongol,100) |
Dihexar | \(Q_{1,1}(6) \approx 6\rightarrow 6\rightarrow 6\rightarrow 2\) |
Graham's number | g64, where g1 = 3 ↑4 3 and gn = 3 ↑gn-1 3, ~ {4,65,1,2} |
xkcd number | A(G,G), where G is Graham's number, ~ {4,66,1,2} |
Corporal | {10,100,1,2} |
Graatagold | E100##100#100 |
Forcal | g1,000,000 |
Conway's Tetratri | 3→3→3→3 ~ {33,3,2,2} |
Corporalplex | {10,{10,100,1,2},1,2} |
Graatagolda-sudex | E100##100#100#2 |
Force forcal | gforcal |
Trihexar | \(Q_{1,2}(6)\) |
Greegold | E100##100#100#100 |
Suporcal | Forcal(1,000,000) |
Greegolda-suthrex | E100##100#100#100#2 |
Grinningold | E100##100##4 |
Megocal | Forcal2(1,000,000) |
Golaagold | E100##100##5 |
Gruelohgold | E100##100##6 |
Gaspgold | E100##100##7 |
Ginorgold | E100##100##8 |
Grand tridecal | {10,10,10,2} |
Gugolthra | E100##100##100 |
Biggol | {10,10,100,2} |
Giaxul | 200![200] = 200![1,2] |
Ultron | \(\approx f_{\omega+200} (100)\) |
Terribocal | Forcal1,2(1) |
Biggolplex | {10,10,{10,10,100,2},2} |
Graatagolthra | E100##100##100##2 |
Tetratri | {3,3,3,3} |
Septasexahexar | \(Q_{3,0}(6)\) |
Gugoltesla | E100##100##100##100 |
Baggol | {10,10,100,3} |
Tribocal | Forcal1,3(1) |
Baggolplex | {10,10,{10,10,100,3},3} |
Graatagoltesla | E100##100##100##100##2 |
Supertet | {4,4,4,4} |
Gugolpeta | E100##100##100##100##100 |
Beegol | {10,10,100,4} |
Beegolplex | {10,10,{10,10,100,4},4} |
Gugolhexa | E100###6 |
Bigol | {10,10,100,5} |
Bigolplex | {10,10,{10,10,100,5},5} |
Gugolhepta | E100###7 |
Boggol | {10,10,100,6} |
Boggolplex | {10,10,{10,10,100,6},6} |
Gugolocta | E100###8 |
Bagol | {10,10,100,7} |
Bagolplex | {10,10,{10,10,100,7},7} |
General | {10,10,10,10} |
Kaboodol | \(\underbrace{10 \rightarrow\ldots\rightarrow 10}_{102} < \text{kaboodol} < \underbrace{10 \rightarrow\ldots\rightarrow 10}_{103}\) |
Throogol | E100###100 |
Troogol | {10,10,10,100} |
Giabixul | 200![200,200] |
Quadratic omega level
Name | Value |
---|---|
Generalplex | {10,10,10,{10,10,10,10}} = {10,3,1,1,2} |
Kaboodolplex | \(\underbrace{10 \rightarrow\ldots\rightarrow 10}_{\text{kaboodol}+2} < \text{kaboodolplex} < \underbrace{10 \rightarrow\ldots\rightarrow 10}_{\text{kaboodol}+3}\) |
Troogolplex | {10,10,10,{10,10,10,100}} |
BOX_M̃ | |
Thrangol | E100###100#100 |
Threagol | E100###100##3 |
Thrugold | E100###100##100 |
Thrugolthra | E100###100###3 |
Thrugoltesla | E100###100###4 |
Throotrigol | E100###100###100 |
Triggol | {10,10,10,100,2} |
Triggolplex | {10,10,10,{10,10,10,100,2},2} |
Thrantrigol | E100###100###100#100 |
Thrutrigold | E100###100###100##100 |
Pentatri | {3,3,3,3,3} |
Throotergol | E100###100###100###100 |
Traggol | {10,10,10,100,3} |
Throopetol | E100###100###100###100###100 |
Treegol | {10,10,10,100,4} |
Superpent | {5,5,5,5,5} |
Throohexol | E100####6 |
Trigol | {10,10,10,100,5} |
Throoheptgol | E100####7 |
Troggol | {10,10,10,100,6} |
Throogogdol | E100####8 |
Tragol | {10,10,10,100,7} |
Pentadecal | {10,10,10,10,10} |
Tetroogol | E100####100 |
Quadroogol | {10,10,10,10,100} |
Polynomial omega level
Name | Value |
---|---|
Pentadecalplex | {10,10,10,10,{10,10,10,10,10}} |
Quadroogolplex | {10,10,10,10,{10,10,10,10,100}} |
Tetrangol | E100####100#100 |
Tetrugold | E100####100##100 |
Tetrithroogol | E100####100###100 |
Tetrootrigol | E100####100####100 |
Quadriggol | {10,10,10,10,100,2} |
Hexatri | {3,3,3,3,3,3} |
Tetrootergol | E100####100####100####100 |
Quadraggol | {10,10,10,10,100,3} |
Tetroopetol | E100####100####100####100####100 |
Quadreegol | {10,10,10,10,100,4} |
Tetroohexol | E100#####6 |
Quadrigol | {10,10,10,10,100,5} |
Superhex | {6,6,6,6,6,6} |
Tetrooheptgol | E100#####7 |
Quadroggol | {10,10,10,10,100,6} |
Tetroogogdol | E100#####8 |
Quadragol | {10,10,10,10,100,7} |
Hexadecal | {10,10,10,10,10,10} |
Pentoogol | E100#####100 |
Quintoogol | {10,10,10,10,10,100} |
Quintiggol | {10,10,10,10,10,100,2} |
Quintaggol | {10,10,10,10,10,100,3} |
Quinteegol | {10,10,10,10,10,100,4} |
Quintigol | {10,10,10,10,10,100,5} |
Quintoggol | {10,10,10,10,10,100,6} |
Supersept | {7,7,7,7,7,7,7} |
Quintagol | {10,10,10,10,10,100,7} |
Heptadecal | {10,10,10,10,10,10,10} |
Hexoogol | E100######100 |
Sextoogol | {10,10,10,10,10,10,100} |
Superoct | {8,8,8,8,8,8,8,8} |
Octadecal | {10,10,10,10,10,10,10,10} |
Heptoogol | E100#######100 |
Septoogol | {10,10,10,10,10,10,10,100} |
Superenn | {9,9,9,9,9,9,9,9,9} |
Ennadecal | {10,10,10,10,10,10,10,10,10} |
Ogdoogol | E100########100 |
Octoogol | {10,10,10,10,10,10,10,10,100} |
Iteral | {10,10,10,10,10,10,10,10,10,10} = {10,10 (1) 2} = {10,2,2 (1) 2} |
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} = {3,27 (1) 2} |
Goobol | {10,100(1)2} |
Godgahlah | E100#100100 = E100#^#100 |
Giatrixul | 200![200,200,200] |
Godgahlahgong | E100,000#100,000100,000 |
Exponentiated linear omega level
Name | Value |
---|---|
Dupertri | {3,{3,3,3}(1)2} = {3,3,2 (1) 2} |
Duperdecal | {10,{10,10(1)2}(1)2} |
Goobolplex | {10,{10,100(1)2}(1)2} |
Grand godgahlah | E100#godgahlah100 = E100#^#100#2 |
Grand godgahlahgong | E100,000#godgahlahgong100,000 |
Grand grand godgahlah | E100#^#100#3 |
Gibbol | {10,100,2(1)2} |
Grandgahlah | E100#^#100#100 |
Latri | {3,3,3(1)2} |
Gabbol | {10,100,3(1)2} |
Greagahlah | E100#^#100#100#100 |
Boobol | {10,10,100(1)2} |
Gugoldgahlah | E100#^#100##100 |
Bibbol | {10,10,100,2(1)2} |
Gugolthragahlah | E100#^#100##100##100 |
Troobol | {10,10,10,100(1)2} |
Throogahlah | E100#^#100###100 |
Quadroobol | {10,10,10,10,100(1)2} |
Tetroogahlah | E100#^#100####100 |
Gootrol | {10,100(1)3} |
Gotrigahlah | E100#^#100#^#100 |
Bootrol | {10,10,100(1)3} |
Gooquadrol | {10,100(1)4} |
Gotergahlah | E100#^#100#^#100#^#100 |
Emperal | {10,10(1)10} |
Gossol | {10,10(1)100} |
Godgoldgahlah | E100#^#*#100 |
Emperalplex | {10,10(1){10,10(1)10}} |
Gossolplex | {10,10(1){10,10(1)100}} |
Gotrigoldgahlah | E100#^#*##3 |
Gissol | {10,10(1)100,2} |
Gassol | {10,10(1)100,3} |
Hyperal | {10,10(1)10,10} |
Mossol | {10,10(1)10,100} |
Godthroogahlah | E100#^#*##100 |
Mossolplex | {10,10(1)10,{10,10(1)10,100}} |
Bossol | {10,10(1)10,10,100} |
Godtetroogahlah | E100#^#*###100 |
Trossol | {10,10(1)10,10,10,100} |
Godpentoogahlah | E100#^#*####100 |
Quadrossol | {10,10(1)10,10,10,10,100} |
Quintossol | {10,10(1)10,10,10,10,10,100} |
Diteral | {10,10 (1)(1) 2} |
Dubol | {10,100 (1)(1) 2} |
Deutero-godgahlah | E100#^#*#^#100 |
Diteralplex | {10,diteral (1)(1) 2} |
Dutrol | {10,100 (1)(1) 3} |
Duquadrol | {10,100 (1)(1) 4} |
Admiral | {10,10 (1)(1) 10} |
Dossol | {10,10 (1)(1) 100} |
Deutero-godgoldgahlah | E100#^#*#^#*#100 |
Dossolplex | {10,10 (1)(1) dossol} |
Dutritri | {3,3,3 (1) 3,3,3 (1) 3,3,3} |
Dutridecal | {10,10,10 (1) 10,10,10 (1) 10,10,10} |
Trito-godgahlah | E100#^#*#^#*#^#100 |
Teterto-godgahlah | E100#^#*#^#*#^#*#^#100 |
Xappol | {10,10 (2) 2} |
Gridgahlah | E100#^##100 |
Exponentiated polynomial omega level
Name | Number |
---|---|
Xappolplex | {10,xappol (2) 2} |
Grand xappol | {10,10 (2) 3} |
Dimentri | {3,3 (3) 2} |
Colossol | {10,10 (3) 2} |
Kubikahlah | E100#^###100 |
Colossolplex | {10,colossol (3) 2} |
Terossol | {10,10 (4) 2} |
Quarticahlah | E100#^####100 |
Terossolplex | {10,terossol (4) 2} |
Petossol | {10,10 (5) 2} |
Quinticahlah | E100#^#^#5 |
Petossolplex | {10,petossol (5) 2} |
Ectossol | {10,10 (6) 2} |
Sexticahlah | E100#^#^#6 |
Ectossolplex | {10,ectossol (6) 2} |
Zettossol | {10,10 (7) 2} |
Septicahlah | E100#^#^#7 |
Zettossolplex | {10,zettossol (7) 2} |
Yottossol | {10,10 (8) 2} |
Octicahlah | E100#^#^#8 |
Yottossolplex | {10,yottossol (8) 2} |
Xennossol | {10,10 (9) 2} |
Xennossolplex | {10,xennossol (9) 2} |
Dimendecal | {10,10 (10) 2} |
Gongulus | {10,10 (100) 2} |
Godgathor | E100#^#^#100 |
Double exponentiated polynomial omega level
Name | Value |
---|---|
Gongulusplex | {10,10 (gongulus) 2} |
Gongulusduplex | {10,10 (gongulusplex) 2} |
Deutero-godgathor | E100#^#^#*#^#^#100 |
Trito-godgathor | E100#^#^#*#^#^#*#^#^#100 |
Hecato-godgathor | E100#^(#^#*#)100 |
Godgridgathor | E100#^(#^#*##)100 |
Dulatri | {3,3 (0,2) 2} |
Godkubikgathor | E100#^(#^#*###)100 |
Gingulus | {10,100 (0,2) 2} |
Godgathordeus | E100#^(#^#*#^#)100 |
Trilatri | {3,3 (0,3) 2} |
Gangulus | {10,100 (0,3) 2} |
Godgathortruce | E100#^(#^#*#^#*#^#)100 |
Geengulus | {10,100 (0,4) 2} |
Godgathorquad | E100#^(#^#*#^#*#^#*#^#)100 |
Gowngulus | {10,100 (0,5) 2} |
Gungulus | {10,100 (0,6) 2} |
Bongulus | {10,100 (0,0,1) 2} |
Gralgathor | E100#^#^##100 |
Bingulus | {10,100 (0,0,2) 2} |
Gralgathordeus | E100#^(#^##*#^##)100 |
Trimentri | {3,3 (0,0,0,1) 2} = {3,3 ((1)1) 2} |
Bangulus | {10,100 (0,0,3) 2} |
Gralgathortruce | E100#^(#^##*#^##*#^##)100 |
Beengulus | {10,100 (0,0,4) 2} |
Gralgathorquad | E100#^(#^##*#^##*#^##*#^##)100 |
Trongulus | {10,100 (0,0,0,1) 2} |
Thraelgathor | E100#^#^###100 |
Quadrongulus | {10,100 (0,0,0,0,1) 2} |
Terinngathor | E100#^#^####100 |
Pentaelgathor | E100#^#^#####100 |
Quintongulus | {10,100 (0,0,0,0,0,1) 2} |
Sextongulus | {10,100 (0,0,0,0,0,0,1) 2} |
Septongulus | {10,100 (0,0,0,0,0,0,0,1) 2} |
Octongulus | {10,100 (0,0,0,0,0,0,0,0,1) 2} |
Goplexulus | \(\lbrace10,100 (\underbrace{0,0,\ldots ,0,0,}_{100 \text{ zeroes}}1) 2\rbrace\) = {10,100 ((1)1) 2} |
Godtothol | E100#^#^#^#100 |
Triple exponentiated polynomial omega level
Name | Value |
---|---|
Extendol | s(3,3{1`2}2) |
Graltothol | E100#^#^#^##100 |
Goduplexulus | {10,100 ((100)1) 2} |
Thraeltothol | E100#^#^#^###100 |
Terinntothol | E100#^#^#^####100 |
Pentaeltothol | E100#^#^#^#####100 |
Godtertol | E100#^#^#^#^#100 |
Gotriplexulus | \(\lbrace 10,100 ((\underbrace{0,0,\ldots ,0,0,}_{100 \text{ zeroes}}1)1) 2\rbrace\) = {10,100 (((1)1)1) 2} |
Iterated Cantor normal form level
Name | Value |
---|---|
Graltertol | E100#^#^#^#^##100 |
Thraeltertol | E100#^#^#^#^###100 |
Godtopol | E100#^#^#^#^#^#100 |
Graltopol | E100#^#^#^#^#^##100 |
Godhathor | E100#^#^#^#^#^#^#100 |
Godheptol | E100#^#^#^#^#^#^#^#100 |
Godoctol | E100#^#^#^#^#^#^#^#^#100 |
Godentol | E100#^#^#^#^#^#^#^#^#^#100 |
Goddekathol | E100#^#^#^#^#^#^#^#^#^#^#100 |
Tethrathoth | E100#^^#100 |
Goppatoth | 10↑↑100 & 10 |
Giaquaxul | 200![200,200,200,200] |
Epsilon level
Name | Value |
---|---|
Grand tethrathoth | E100#^^#100#2 |
Goppatothplex | 10↑↑(goppatoth) & 10 |
Grantethrathoth | E100#^^#100#100 |
Tethratrithoth | E100#^^#100#^^#100 |
Deutero-tethrathoth | E100#^^#*#^^#100 |
Hecato-tethrathoth | E100(#^^#)^#100 |
Monster-Giant | E100(#^^#)^(#^^#)^#100 |
Super Monster-Giant | E100(#^^#)^(#^^#)^(#^^#)^#100 |
Terrible tethrathoth | E100(#^^#)^^#100 |
Terrible terrible tethrathoth | E100((#^^#)^^#)^^#100 |
Tethrathoth ba'al | E100#^^#>#100 |
Great and Terrible Tethrathoth | E100#^^#>#100#2 |
Gippatoth | 100↑↑(2 × 100) & 10 |
Gappatoth | 100↑↑(3 × 100) & 10 |
Geepatoth | 100↑↑(4 × 100) & 10 |
Grangol-carta-tethriterator | E100#^^#>#100#100 |
Tethriterhecate | E100#^^#>#*#100 |
Deutero-tethriterator | E100#^^#>#*#^^#>#100 |
Tethriterfact | E100(#^^#>#)^#100 |
Terrible tethriterator | E100(#^^#>#)^^#100 |
Tethriditerator | E100#^^#>(#+#)100 |
Tethrigriditerator | E100#^^#>##100 |
Tethrispatialator | E100#^^#>#^#100 |
Dustaculated-tethrathoth | E100#^^#>#^^#100 |
Tristaculated-tethrathoth | E100#^^#>#^^#>#^^#100 |
Tethracross | E100#^^##100 |
Boppatoth | 100↑↑(1002) & 10 |
Binary phi level
Name | Value |
---|---|
Terrible tethracross | E100(#^^##)^^#100 |
Secundotethrated-tethracross | E100(#^^##)^^##100 |
Tethritercross | E100#^^##>#100 |
Dustaculated-tethracross | E100#^^##>#^^##100 |
Tethracubor | E100#^^###100 |
Troppatoth | 100↑↑(1003) & 10 |
Terrible tethracubor | E100(#^^###)^^#100 |
Tethraducubor | E100(#^^###)^^###100 |
Tethritercubor | E100#^^###>#100 |
Dustaculated-tethracubor | E100#^^###>#^^###100 |
Tethrateron | E100#^^####100 |
Quadroppatoth | 100↑↑(1004) & 10 |
Terrible tethrateron | E100(#^^####)^^#100 |
Tethraduteron | E100(#^^####)^^####100 |
Tethra-hectateron | E100#^^####>#100 |
Dustaculated-tethrateron | E100#^^####>#^^####100 |
Tethrapeton | E100#^^#^#5 |
Tethrahexon | E100#^^#^#6 |
Tethrahepton | E100#^^#^#7 |
Tethra-ogdon | E100#^^#^#8 |
Tethrennon | E100#^^#^#9 |
Tethradekon | E100#^^#^#10 |
Tethrafact | E100#^^#^#100 |
Tethrato-tethrathoth | E100#^^#^^#100 |
Tethrarxitet | E100#^^#^^#^^#100 |
Pentacthulhum | E100#^^^#100 |
Bachmann's collapsing level
Name | Value |
---|---|
Pentacthuldugon | E100(#^^^#)^^^#100 |
Pentacthuliterator | E100#^^^#>#100 |
Hugexul | 200![200(1)200] |
Superior Hugexul | 200![200(1)200,200] |
Dustaculated-pentacthulhum | E100#^^^#>#^^^#100 |
Pentacthulcross | E100#^^^##100 |
Bisuperior Hugexul | 200![200(1)200,200,200] |
Pentacthulcubor | E100#^^^###100 |
Pentacthulteron | E100#^^^####100 |
Pentacthultope | E100#^^^#^#100 |
Pentacthularxitri | E100#^^^#^^^#100 |
Hexacthulhum | E100#^^^^#100 |
Hugebixul | 200![200(1)200(1)200] |
Hexacthuliterator | E100#^^^^#>#100 |
Superior Hugebixul | 200![200(1)200(1)200,200] |
Hexacthulcross | E100#^^^^##100 |
Heptacthulhum | E100#{5}#100 |
Hugetrixul | 200![200(1)200(1)200(1)200] |
Ogdacthulhum | E100#{6}#100 |
Hugequaxul | 200![200(1)200(1)200(1)200(1)200] |
Ennacthulhum | E100#{7}#100 |
Dekacthulhum | E100#{8}#100 |
Goliath | E100#{10}#100 |
Godsgodgulus | E100#{#}#100 |
Godsgodgulcross | E100#{#}##100 |
Godsgodeus | E100#{#+#}#100 |
The centurion | E100#{#^#}#100 |
Ohmygosh-ohmygosh-ohmygooosh | E100#{#{#}#}#100 |
Blasphemorgulus | E100{#,#,1,2}100 |
Hundrelasphemorgue | E100{#,#+1,1,2}100 |
Enormaxul | 200![200(2)200] |
Superior Enormaxul | 200![200(2)200,200] |
Bisuperior Enormaxul | 200![200(2)200,200,200] |
Enormabixul | 200![200(2)200(2)200] |
Enormatrixul | 200![200(2)200(2)200(2)200] |
Enormaquaxul | 200![200(2)200(2)200(2)200(2)200] |
Destruxul | 200![200(200)200] |
Great Destruxul | 200![200(200)200(200)200] |
Bigreat Destruxul | 200![200(200)200(200)200(200)200] |
Bird's number | \(f_{\vartheta(\Omega^{\omega})+2}(f_{\vartheta(\Omega^{\omega})+1}(f_{\vartheta(\Omega^{\omega})}(f_{\vartheta(\Omega^{\omega})}(7))))\) |
TREE[3] (lower bound) | |
Destrubixul | 200![200([200(200)200])200] |
Destrutrixul | 200![200([200([200(200)200])200])200] |
Destruquaxul | 200![200([200([200([200(200)200])200])200])200] |
Golapulus | 10100&10&10 |
Extremexul | 200![1(1)[2200,200,200,200]] |
Higher computable level
Since the comparison (or even the well-definedness) of numbers of this level is unknown, the order of entries does not necessarily imply the order of the sizes. Also, several numbers are defined by an OCF, which is uncomputable, and are not known to be computable.
Name | Value |
---|---|
Extremebixul | 200![1(1)[2200,200,200,200,200]] |
Extremetrixul | 200![1(1)[2200,200,200,200,200,200]] |
Extremequaxul | 200![1(1)[2200,200,200,200,200,200,200]] |
Gigantixul | 200![1(1)[3200,200,200]] |
Gigantibixul | 200![1(1)[3200,200,200,200]] |
Gigantitrixul | 200!1(1)[3200,200,200,200,200]] |
Gigantiquaxul | 200![1(1)[3200,200,200,200,200,200]] |
Nucleaxul | 200![200200] |
Nucleabixul | 200![[200200]200] |
SCG(13) (lower bound) | |
Nucleatrixul | 200![[[200200]200]200] |
Nucleaquaxul | 200![[[[200200]200]200]200] |
BIGG | 200? |
Loader's number | D5(99) |
Bashicu matrix number with respect to Bashicu matrix system version 2.3 | |
6 (N primitive) | |
Y sequence number | f2000(1) |
the least transcendental integer |
Uncomputable numbers
The term "uncomputable number" here refers to the numbers defined in terms of uncomputably fast-growing functions. This table contains large numbers which are known to be ill-defined. For more details on the ill-definedness, click the "More..." link below.
Name | Value | Ill-defined? |
---|---|---|
1919-th busy beaver | \(\Sigma(1919)\) | No |
Fish number 4 | F463(3) | No |
\(\Xi(10^6)\) | No | |
\(\Sigma_\infty(10^9)\) | No | |
Rayo's number | Rayo(10100) | Partially |
Fish number 7 | F763(10100) | Partially |
BIG FOOT | FOOT10(10100) | Yes |
Little Bigeddon | Yes | |
Sasquatch | Yes | |
Large Number Garden Number | \(f^{10}(10 \uparrow^{10} 10)\) | Not determined yet |
Notes
- ↑ (S) means "in the short scale", and (L) means "in the long scale".