FANDOM


heFunctions Edit

3 entry arrays Edit

  • Division, a/b
  • Subtraction, a-b
  • Addition, a+b
  • Multiplication, a*b
  • Exponentiation, ab = a**b
  • Tetration, ba
  • Pentation, {a,b,3}
  • Hexation, {a,b,4}
  • Heptation, {a,b,5}
  • Octation, {a,b,6}
  • Enneation, {a,b,7}
  • Decation, {a,b,8}
  • Hendecation, {a,b,9}
  • Dodecation, {a,b,10}
  • Tridecation, {a,b,11}
  • Tetradecation, {a,b,12}
  • Pentadecation, {a,b,13}
  • Hexdecation, {a,b,14}
  • Heptadecation, {a,b,15}
  • Octadecation, {a,b,16}
  • Enneadecation, {a,b,17}
  • Icosation, {a,b,18}
  • Henicosation, {a,b,19}
  • Doicosation, {a,b,20}
  • Triaicosation, {a,b,21}
  • Tetraicosation, {a,b,22}
  • Pentaicosation, {a,b,23}
  • Hexaicosation, {a,b,24}
  • Heptaicosation, {a,b,25}
  • Octaicosation, {a,b,26}
  • Enneaicosation, {a,b,27}
  • Triacontation, {a,b,28}
  • Tetracontation, {a,b,38}
  • Pentacontation, {a,b,48}
  • Hexacontation, {a,b,58}
  • Octacontation, {a,b,78}
  • Enneacontation, {a,b,88}
  • Hectation, {a,b,98}
  • Chiliation, {a,b,998}
  • Milliation, {a,b,999998}
  • Billiation, {a,b,999999998}
  • Trilliation, {a,b,1012-2}
  • Quadrilliation, {a,b,1015-2}
  • Quintilliation, {a,b,1018-2}
  • Sextilliation, {a,b,1021-2}
  • Septilliation, {a,b,1024-2}
  • Octilliation, {a,b,1027-2}
  • Nonilliation, {a,b,1030-2}
  • Decilliation, {a,b,1033-2}
  • Undecilliation, {a,b,1036-2}
  • Duodecilliation, {a,b,1039-2}
  • Tredecilliation, {a,b,1042-2}
  • Quattuordecilliation, {a,b,1045-2}
  • Quindecilliation, {a,b,1048-2}
  • Sexdecilliation, {a,b,1051-2}
  • Septendecilliation, {a,b,1054-2}
  • Octodecilliation, {a,b,1057-2}
  • Novemdecilliation, {a,b,1060-2}
  • Vigintilliation, {a,b,1063-2}
  • Trigintilliation, {a,b,1093-2}
  • Quadragintilliation, {a,b,10123-2}
  • Quinquagintilliation, {a,b,10153-2}
  • Sexagintilliation, {a,b,10183-2}
  • Septuagintilliation, {a,b,10213-2}
  • Octogintilliation, {a,b,10243-2}
  • Nonagintilliation, {a,b,10273-2}
  • Centilliation, {a,b,10303-2}
  • Millilliation, {a,b,103003-2}
  • Micrilliation, {a,b,103000003-2}
  • Nanilliation, {a,b,103000000003-2}
  • Picilliation, {a,b,103*1012+3-2}
  • Femtilliation, {a,b,103*1015+3-2}
  • Attilliation, {a,b,103*1018+3-2}
  • Zeptilliation, {a,b,103*1021+3-2}
  • Yoctilliation, {a,b,103*1024+3-2}
  • Xonilliation, {a,b,103*1027+3-2}
  • Vecilliation, {a,b,103*1030+3-2}
  • Mecilliation, {a,b,103*1033+3-2}
  • Duecilliation, {a,b,103*1036+3-2}
  • Trecilliation, {a,b,103*1039+3-2}
  • Tetrecilliation, {a,b,103*1042+3-2}
  • Pentecilliation, {a,b,103*1045+3-2}
  • Hexecilliation, {a,b,103*1048+3-2}
  • Heptecilliation, {a,b,103*1051+3-2}
  • Octecilliation, {a,b,103*1054+3-2}
  • Ennecilliation, {a,b,103*1057+3-2}
  • Icosilliation, {a,b,103*1060+3-2}
  • Triacontilliation, {a,b,103*1090+3-2}
  • Tetracontilliation, {a,b,103*10120+3-2}
  • Pentacontilliation, {a,b,103*10150+3-2}
  • Hexacontilliation, {a,b,103*10180+3-2}
  • Heptacontilliation, {a,b,103*10210+3-2}
  • Octacontilliation, {a,b,103*10240+3-2}
  • Ennacontilliation, {a,b,103*10270+3-2}
  • Hectilliation, {a,b,103*10300+3-2}
  • Killilliation, {a,b,103*103000+3-2}
  • Megilliation, {a,b,103*103,000,000+3-2}
  • Gigilliation, {a,b,103*103,000,000,000+3-2}
  • Terilliation, {a,b,103*103*1012+3-2}
  • Petilliation, {a,b,103*103*1015+3-2}
  • Exilliation, {a,b,103*103*1018+3-2}
  • Zettilliation, {a,b,103*103*1021+3-2}
  • Yottilliation, {a,b,103*103*1024+3-2}
  • Xennilliation, {a,b,103*103*1027+3-2}
  • Dakilliation, {a,b,103*103*1030+3-2}
  • Hendilliation, {a,b,103*103*1033+3-2}
  • Dokilliation, {a,b,103*103*1036+3-2}
  • Tradakilliation, {a,b,103*103*1039+3-2}
  • Tedakilliation, {a,b,103*103*1042+3-2}
  • Pedakilliation, {a,b,103*103*1045+3-2}
  • Exdakilliation, {a,b,103*103*1048+3-2}
  • Zedakilliation, {a,b,103*103*1051+3-2}
  • Yodakilliation, {a,b,103*103*1054+3-2}
  • Nedakilliation, {a,b,103*103*1057+3-2}
  • Ikilliation, {a,b,103*103*1060+3-2}
  • Ikenilliation, {a,b,103*103*1063+3-2}
  • Icodilliation, {a,b,103*103*1066+3-2}
  • Ictrilliation, {a,b,103*103*1069+3-2}
  • Icterilliation, {a,b,103*103*1072+3-2}
  • Icpetilliation, {a,b,103*103*1075+3-2}
  • Ikectilliation, {a,b,103*103*1078+3-2}
  • Iczetilliation, {a,b,103*103*1081+3-2}
  • Ikyotilliation, {a,b,103*103*1084+3-2}
  • Icxenilliation, {a,b,103*103*1087+3-2}
  • Trakilliation, {a,b,103*103*1090+3-2}
  • Tekilliation, {a,b,103*103*10120+3-2}
  • Pekilliation, {a,b,103*103*10150+3-2}
  • Exakilliation, {a,b,103*103*10180+3-2}
  • Zakilliation, {a,b,103*103*10210+3-2}
  • Yokilliation, {a,b,103*103*10240+3-2}
  • Nekilliation, {a,b,103*103*10270+3-2}
  • Hotilliation, {a,b,103*103*10300+3-2}
  • Botilliation, {a,b,103*103*10600+3-2}
  • Trotilliation, {a,b,103*103*10900+3-2}
  • Totilliation, {a,b,103*103*101200+3-2}
  • Potilliation, {a,b,103*103*101500+3-2}
  • Exotilliation, {a,b,103*103*101800+3-2}
  • Zotilliation, {a,b,103*103*102100+3-2}
  • Yootilliation, {a,b,103*103*102400+3-2}
  • Notilliation, {a,b,103*103*102700+3-2}
  • Kalilliation, {a,b,103*103*103000+3-2}
  • Dalilliation, {a,b,103*103*106000+3-2}
  • Tralilliation, {a,b,103*103*109000+3-2}
  • Talilliation, {a,b,103*103*1012,000+3-2}
  • Palilliation, {a,b,103*103*1015,000+3-2}
  • Exalilliation, {a,b,103*103*1018,000+3-2}
  • Zalilliation, {a,b,103*103*1021,000+3-2}
  • Yalilliation, {a,b,103*103*1024,000+3-2}
  • Nalilliation, {a,b,103*103*1027,000+3-2}
  • Dakalilliation, {a,b,103*103*1030,000+3-2}
  • Hotalilliation, {a,b,103*103*1030,0000+3-2}
  • Mejilliation, {a,b,103*103*103,000,000+3-2}
  • Dakejilliation, {a,b,103*103*1030,000,000+3-2}
  • Hotejilliation, {a,b,103*103*10300,000,000+3-2}
  • Gijilliation, {a,b,103*103*103,000,000,000+3-2}
  • Astilliation, {a,b,103*103*103*1012+3-2}
  • Lunilliation, {a,b,103*103*103*1015+3-2}
  • Fermilliation, {a,b,103*103*103*1018+3-2}
  • Jovilliation, {a,b,103*103*103*1021+3-2}
  • Solilliation, {a,b,103*103*103*1024+3-2}
  • Betilliation, {a,b,103*103*103*1027+3-2}
  • Glocilliation, {a,b,103*103*103*1030+3-2}
  • Gaxilliation, {a,b,103*103*103*1033+3-2}
  • Supilliation, {a,b,103*103*103*1036+3-2}
  • Versilliation, {a,b,103*103*103*1039+3-2}
  • Multilliation, {a,b,103*103*103*1042+3-2}
  • Nonekyotultilliation, {a,b,103*103*102.994*1045+3-2}

4 entry arrays Edit

  • Expansion, {a,b,1,2}
  • Multiexpansion, {a,b,2,2}
  • Powerexpansion, {a,b,3,2}
  • Expandotetration, {a,b,4,2}
  • Expandopentation, {a,b,5,2}
  • Expandohexation, {a,b,6,2}
  • Expandoheptation, {a,b,7,2}
  • Expandooctation, {a,b,8,2}
  • Expandoenneation, {a,b,9,2}
  • Expandodecation, {a,b,10,2}
  • Expandohendecation, {a,b,11,2}
  • Expandododecation, {a,b,12,2}
  • Expandotridecation, {a,b,13,2}
  • Expandotetradecation, {a,b,14,2}
  • Expandopentadecation, {a,b,15,2}
  • Expandohexadecation, {a,b,16,2}
  • Expandoheptadecation, {a,b,17,2}
  • Expandooctadecation, {a,b,18,2}
  • Expandoenneadecation, {a,b,19,2}
  • Expandoicosation, {a,b,20,2}
  • Expandohectation, {a,b,100,2}
  • Explosion, {a,b,1,3}
  • Multiexplosion, {a,b,2,3}
  • Powerexplosion, {a,b,3,3}
  • Explodotetration, {a,b,4,3}
  • Explodopentation, {a,b,5,3}
  • Explodohexation, {a,b,6,3}
  • Explodoheptation, {a,b,7,3}
  • Explodooctation, {a,b,8,3}
  • Explodoenneation, {a,b,9,3}
  • Explododecation, {a,b,10,3}
  • Explodohendecation, {a,b,11,3}
  • Explodododecation, {a,b,12,3}
  • Explodotridecation, {a,b,13,3}
  • Explodotetradecation, {a,b,14,3}
  • Explodopentadecation, {a,b,15,3}
  • Explodohexadecation, {a,b,16,3}
  • Explodoheptadecation, {a,b,17,3}
  • Explodooctadecation, {a,b,18,3}
  • Explodoenneadecation, {a,b,19,3}
  • Explodoicosation, {a,b,20,3}
  • Explodoohectation, {a,b,100,3}
  • Detonation, {a,b,1,4}
  • Multidetonation, {a,b,2,4}
  • Powerdetonation, {a,b,3,4}
  • Detonotetration, {a,b,4,4}
  • Detonopentation, {a,b,5,4}
  • Detonohexation, {a,b,6,4}
  • Detonoheptation, {a,b,7,4}
  • Detonooctation, {a,b,8,4}
  • Detonoenneation, {a,b,9,4}
  • Detonodecation, {a,b,10,4}
  • Detonohendecation, {a,b,11,4}
  • Detonododecation, {a,b,12,4}
  • Detonotridecation, {a,b,13,4}
  • Detonotetradecation, {a,b,14,4}
  • Detonopentadecation, {a,b,15,4}
  • Detonohexadecation, {a,b,16,4}
  • Detonoheptadecation, {a,b,17,4}
  • Detonooctadecation, {a,b,18,4}
  • Detonoenneadecation, {a,b,29,4}
  • Detonoicosation, {a,b,20,4}
  • Detonocentation, {a,b,100,4}
  • Pentonation, {a,b,1,5}
  • Multipentonation, {a,b,2,5}
  • Powerpentonation, {a,b,3,5}
  • Pentonotetration, {a,b,4,5}
  • Pentonopentation, {a,b,5,5}
  • Pentonohexation, {a,b,6,5}
  • Pentonoheptation, {a,b,7,5}
  • Pentonooctation, {a,b,8,5}
  • Pentonoenneation, {a,b,9,5}
  • Pentonodecation, {a,b,10,5}
  • Hexonation, {a,b,1,6}
  • Multihexonation, {a,b,2,6}
  • Powerhexonation, {a,b,3,6}
  • Hexonotetration, {a,b,4,6}
  • Hexonopentation, {a,b,5,6}
  • Hexonohexation, {a,b,6,6}
  • Hexonoheptation, {a,b,7,6}
  • Hexonooctation, {a,b,8,6}
  • Hexonoenneation, {a,b,9,6}
  • Hexonodecation, {a,b,10,6}
  • Heptonation, {a,b,1,7}
  • Multiheptonation, {a,b,2,7}
  • Powerheptonation, {a,b,3,7}
  • Heptonotetration, {a,b,4,7}
  • Heptonopentation, {a,b,5,7}
  • Heptonohexation, {a,b,6,7}
  • Heptonoheptation, {a,b,7,7}
  • Heptonooctation, {a,b,8,7}
  • Heptonoenneation, {a,b,9,7}
  • Heptonodecation, {a,b,10,7}
  • Octonation, {a,b,1,8}
  • Multioctonation, {a,b,2,8}
  • Poweroctonation, {a,b,3,8}
  • Octonotetration, {a,b,4,8}
  • Octonopentation, {a,b,5,8}
  • Octonohexation, {a,b,6,8}
  • Octonoheptation, {a,b,7,8}
  • Octonooctation, {a,b,8,8}
  • Octonoenneation, {a,b,9,8}
  • Octonodecation, {a,b,10,8}
  • Ennonation or Nononation, {a,b,1,9}
  • Multiennonation, {a,b,2,9}
  • Powerennonation, {a,b,3,9}
  • Ennonotetration, {a,b,4,9}
  • Ennonopentation, {a,b,5,9}
  • Ennonohexation, {a,b,6,9}
  • Ennonoheptation, {a,b,7,9}
  • Ennonooctation, {a,b,8,9}
  • Ennonoenneation, {a,b,9,9}
  • Ennonodecation, {a,b,10,9}
  • Deconation, {a,b,1,10}
  • Multideconation, {a,b,2,10}
  • Powerdeconation, {a,b,3,10}
  • Deconotetration, {a,b,4,10}
  • Deconopentation, {a,b,5,10}
  • Deconohexation, {a,b,6,10}
  • Deconoheptation, {a,b,7,10}
  • Deconooctation, {a,b,8,10}
  • Deconoenneation, {a,b,9,10}
  • Deconodecation, {a,b,10,10}
  • Hendeconation, {a,b,1,11}
  • Multihendeconation, {a,b,2,11}
  • Powerhendeconation, {a,b,3,11}
  • Hendeconotetration, {a,b,4,11}
  • Hendeconopentation, {a,b,5,11}
  • Hendeconohexation, {a,b,6,11}
  • Hendeconoheptation, {a,b,7,11}
  • Hendeconooctation, {a,b,8,11}
  • Hendeconononation, {a,b,9,11}
  • Hendeconodecation, {a,b,10,11}
  • Dodeconation, {a,b,1,12}
  • Multidodeconation, {a,b,2,12}
  • Powerdodeconation, {a,b,3,12}
  • Dodeconotetration, {a,b,4,12}
  • Dodeconopentation, {a,b,5,12}
  • Dodeconohexation, {a,b,6,12}
  • Dodeconoheptation, {a,b,7,12}
  • Dodeconooctation, {a,b,8,12}
  • Dodeconononation, {a,b,9,12}
  • Dodeconodecation, {a,b,10,12}
  • Trideconation, {a,b,1,13}
  • Multitrideconation, {a,b,2,13}
  • Powertrideconation, {a,b,3,13}
  • Trideconotetration, {a,b,4,13}
  • Trideconopentation, {a,b,5,13}
  • Trideconohexation, {a,b,6,13}
  • Trideconoheptation, {a,b,7,13}
  • Trideconooctation, {a,b,8,13}
  • Trideconononation, {a,b,9,13}
  • Trideconodecation, {a,b,10,13}
  • Tetradeconation, {a,b,1,14}
  • Multitetradeconation, {a,b,2,14}
  • Powertetradeconation, {a,b,3,14}
  • Tetradeconotetration, {a,b,4,14}
  • Tetradeconopentation, {a,b,5,14}
  • Tetradeconohexation, {a,b,6,14}
  • Tetradeconoheptation, {a,b,7,14}
  • Tetradeconooctation, {a,b,8,14}
  • Tetradeconononation, {a,b,9,14}
  • Tetradeconodecation, {a,b,10,14}
  • Pentadeconation, {a,b,1,15}
  • Multipentadeconation, {a,b,2,15}
  • Powerpentadeconation, {a,b,3,15}
  • Hexdeconation, {a,b,1,16}
  • Multihexdeconation, {a,b,2,16}
  • Powerhexdeconation, {a,b,3,16}
  • Heptadeconation, {a,b,1,17}
  • Multiheptadeconation, {a,b,2,17}
  • Powerheptadeconation, {a,b,3,17}
  • Octadeconation, {a,b,1,18}
  • Multioctadeconation, {a,b,2,18}
  • Poweroctadeconation, {a,b,3,18}
  • Enneadeconation, {a,b,1,19}
  • Multienneadeconation, {a,b,2,19}
  • Powerenneadeconation, {a,b,3,19}
  • Icosonation, {a,b,1,20}
  • Multiicosonation, {a,b,2,20}
  • Powericosonation, {a,b,3,20}
  • Triacontonation, {a,b,1,30}
  • Multitriacontonation, {a,b,2,30}
  • Powertriacontonation, {a,b,3,30}
  • Tetracontonation, {a,b,1,40}
  • Multitetracontonation, {a,b,2,40}
  • Powertetracontonation, {a,b,3,40}
  • Pentacontonation, {a,b,1,50}
  • Multipentacontonation, {a,b,2,50}
  • Powerpentacontonation, {a,b,3,50}
  • Hexacononation, {a,b,1,60}
  • Multihexacontonation, {a,b,2,60}
  • Powerhexacontonation, {a,b,3,60}
  • Heptacontonation, {a,b,1,70}
  • Multiheptacontonation, {a,b,2,70}
  • Powerheptacontonation, {a,b,3,70}
  • Octacontonation, {a,b,1,80}
  • Multioctacontonation, {a,b,2,80}
  • Poweroctacontonation, {a,b,3,80}
  • Enneacontonation, {a,b,1,90}
  • Multienneacontonation, {a,b,2,90}
  • Powerenneacontonation, {a,b,3,90}
  • Hectonation, {a,b,1,100}
  • Multihectonation, {a,b,2,100}
  • Powerhectonation, {a,b,3,100}
  • Chilionation, {a,b,1,1000}
  • Multichilionation, {a,b,2,1000}
  • Powerchilionation, {a,b,3,1000}
  • Millionation, {a,b,1,1000000}
  • Multimillionation, {a,b,2,1000000}
  • Powermillionation, {a,b,3,1000000}
  • Billonation, {a,b,1,1000000000}
  • Multibillionation, {a,b,2,1000000000}
  • Powerbillionation, {a,b,3,1000000000}
  • Trillionation, {a,b,1,1012}
  • Multitrillionation, {a,b,2,1012}
  • Powertrillionation, {a,b,3,1012}
  • Quadrillionation, {a,b,1,1015}
  • Multiquadrillionation, {a,b,2,1015}
  • Powerquadrillionation, {a,b,3,1015}
  • Quintillionation, {a,b,1,1018}
  • Multiquintillionation, {a,b,2,1018}
  • Powerquintillionation, {a,b,3,1018}
  • Sextillionation, {a,b,1,1021}
  • Multisextillionation, {a,b,2,1021}
  • Powersextillionation, {a,b,3,1021}
  • Septillionation, {a,b,1,1024}
  • Multiseptillionation, {a,b,2,1024}
  • Powerseptillionation, {a,b,3,1024}
  • Octillionation, {a,b,1,1027}
  • Multioctillionation, {a,b,2,1027}
  • Poweroctillionation, {a,b,3,1027}
  • Nonillionation, {a,b,1,1030}
  • Multinonillionation, {a,b,2,1030}
  • Powernonillionation, {a,b,3,1030}
  • Decillionation, {a,b,1,1033}
  • Multidecillionation, {a,b,2,1033}
  • Powerdecillionation, {a,b,3,1033}
  • Undecillionation, {a,b,1,1036}
  • Duodecillionation, {a,b,1,1039}
  • Tredecillionation, {a,b,1,1042}
  • Quattuordecillionation, {a,b,1,1045}
  • Quindecillionation, {a,b,1,1048}
  • Sexdecillionation, {a,b,1,1051}
  • Septendecillionation, {a,b,1,1054}
  • Octodecillionation, {a,b,1,1057}
  • Novemdecillionation, {a,b,1,1060}
  • Vigintillionation, {a,b,1,1063}

5 entry arrays Edit

  • Multexponentiation, {a,b,1,1,2}
  • Multtetration, {a,b,2,1,2}
  • Multexpansion, {a,b,1,2,2}
  • Multmultiexpansion, {a,b,2,2,2}
  • Multexplosion, {a,b,1,3,2}
  • Multdetonation, {a,b,1,4,2}
  • Multpentonation, {a,b,1,5,2}
  • Multhexonation, {a,b,1,6,2}
  • Multheptonation, {a,b,1,7,2}
  • Multoctonation, {a,b,1,8,2}
  • Multennonation, {a,b,1,9,2}
  • Multdeconation, {a,b,1,10,2}
  • Metaexponentiation, {a,b,1,1,3}
  • Metaexpansion, {a,b,1,2,3}
  • Metaexplosion, {a,b,1,3,3}
  • Metadetonation, {a,b,1,4,3}
  • Metapentonation, {a,b,1,5,3}
  • Metahexonation, {a,b,1,6,3}
  • Metaheptonation, {a,b,1,7,3}
  • Xenoexponentiation, {a,b,1,1,4}
  • Xenoexpansion, {a,b,1,2,4}
  • Xenoexplosion, {a,b,1,3,4}
  • Xenodetonation, {a,b,1,4,4}
  • Xenopentonation, {a,b,1,5,4}
  • Xenohexonation, {a,b,1,6,4}
  • Xenoheptonation, {a,b,1,7,4}
  • Hyperexponentiation, {a,b,1,1,5}
  • Hyperexpansion, {a,b,1,2,5}
  • Hyperexplosion, {a,b,1,3,5}
  • Hyperdetonation, {a,b,1,4,5}
  • Hyperpentonation, {a,b,1,5,5}
  • Hyperhexonation, {a,b,1,6,5}
  • Hyperheptonation, {a,b,1,7,5}
  • Omniexponentiation, {a,b,1,1,6}
  • Omniexpansion, {a,b,1,2,6}
  • Omniexplosion, {a,b,1,3,6}
  • Omnidetonation, {a,b,1,4,6}
  • Omnipentonation, {a,b,1,5,6}
  • Omnihexonation, {a,b,1,6,6}
  • Omniheptonation, {a,b,1,7,6}
  • Heptaexponentiation, {a,b,1,1,7}
  • Heptaexpansion, {a,b,1,2,7}
  • Heptaexplosion, {a,b,1,3,7}
  • Heptadetonation, {a,b,1,4,7}
  • Heptapentonation, {a,b,1,5,7}
  • Heptahexonation, {a,b,1,6,7}
  • Heptaheptonation, {a,b,1,7,7}
  • Octaexponentiation, {a,b,1,1,8}
  • Octaexpansion, {a,b,1,2,8}
  • Octaexplosion, {a,b,1,3,8}
  • Octadetonation, {a,b,1,4,8}
  • Octapentonation, {a,b,1,5,8}
  • Octahexonation, {a,b,1,6,8}
  • Octaheptonation, {a,b,1,7,8}
  • Ennaexponentiation, {a,b,1,1,9}
  • Decaexponentiation, {a,b,1,1,10}
  • Icosaexponentiation, {a,b,1,1,20}
  • Triacontaexponentiation, {a,b,1,1,30}
  • Tetracontaexponentiation, {a,b,1,1,40}
  • Pentacontaexponentiation, {a,b,1,1,50}
  • Hexacontaexponentiation, {a,b,1,1,60}
  • Heptacontaexponentiation, {a,b,1,1,70}
  • Octacontaexponentiation, {a,b,1,1,80}
  • Ennacontaexponentiation, {a,b,1,1,90}
  • Hectaexponentiation, {a,b,1,1,100}
  • Chiliaexponentiation, {a,b,1,1,1000}
  • Milliaexponentiation, {a,b,1,1,1000000}
  • Billiaexponentiation, {a,b,1,1,1000000000}

6 entry arrays and higher Edit

  • Biexponentiation, {a,b,1,1,1,2}
  • Bitetration, {a,b,2,1,1,2}
  • Biexpansion, {a,b,1,2,1,2}
  • Bimultexpansion, {a,b,2,2,1,2}
  • Bimultexponentiation, {a,b,1,1,2,2}
  • Bimultexpansion, {a,b,1,2,2,2}
  • Bimultexpansion, {a,b,2,2,2,2}
  • Bimetaexponentiation, {a,b,1,1,3,2}
  • Bixenoexponentiation, {a,b,1,1,4,2}
  • Bihyperexponentiation, {a,b,1,1,5,2}
  • Biomniexponentiation, {a,b,1,1,6,2}
  • Biheptaexponentiation, {a,b,1,1,7,2}
  • Bioctaexponentiation, {a,b,1,1,8,2}
  • Triexponentiation, {a,b,1,1,1,3}
  • Trimultexponentiation, {a,b,1,1,2,3}
  • Trimetaexponentiation, {a,b,1,1,3,3}
  • Trixenoexponentiation, {a,b,1,1,4,3}
  • Trihyperexponentiation, {a,b,1,1,5,3}
  • Triomniexponentiation, {a,b,1,1,6,3}
  • Triheptaexponentiation, {a,b,1,1,7,3}
  • Trioctaexponentiation, {a,b,1,1,8,3}
  • Quadriexponentiation, {a,b,1,1,1,4}
  • Quadrimultexponentiation, {a,b,1,1,2,4}
  • Quadrimetaexponentiation, {a,b,1,1,3,4}
  • Quadrixenoexponentiation, {a,b,1,1,4,4}
  • Quadrihyperexponentiation, {a,b,1,1,5,4}
  • Quadriomniexponentiation, {a,b,1,1,6,4}
  • Quadriheptaexponentiation, {a,b,1,1,7,4}
  • Quadrioctaexponentiation, {a,b,1,1,8,4}
  • Quintiexponentiation, {a,b,1,1,1,5}
  • Sextiexponentiation, {a,b,1,1,1,6}
  • Septiexponentiation, {a,b,1,1,1,7}
  • Octiexponentiation, {a,b,1,1,1,8}
  • Noniexponentiation, {a,b,1,1,1,9}
  • Deciexponentiation, {a,b,1,1,1,10}
  • Bi-uniexponentiation, {a,b,1,1,1,1,2}
  • Bi-biexponentiation, {a,b,1,1,1,2,2}
  • Bi-triexponentiation, {a,b,1,1,1,3,2}
  • Bi-quadriexponentiation, {a,b,1,1,1,4,2}
  • Bi-quintiexponentiation, {a,b,1,1,1,5,2}
  • Bi-sextiexponentiation, {a,b,1,1,1,6,2}
  • Bi-septiexponentiation, {a,b,1,1,1,7,2}
  • Bi-octiexponentiation, {a,b,1,1,1,8,2}
  • Bi-noniexponentiation, {a,b,1,1,1,9,2}
  • Bi-deciexponentiation, {a,b,1,1,1,10,2}
  • Tri-uniexponentiation, {a,b,1,1,1,1,3}
  • Quadri-uniexponentiation, {a,b,1,1,1,1,4}
  • Quinti-uniexponentiation, {a,b,1,1,1,1,5}
  • Sexti-uniexponentiation, {a,b,1,1,1,1,6}
  • Septi-uniexponentiation, {a,b,1,1,1,1,7}
  • Octi-uniexponentiation, {a,b,1,1,1,1,8}
  • Noni-uniexponentiation, {a,b,1,1,1,1,9}
  • Deci-uniexponentiation, {a,b,1,1,1,1,10}
  • Bi-uni-uniexponentiation, {a,b,1,1,1,1,1,2}
  • Bi-uni-uni-uniexponentiation, {a,b,1,1,1,1,1,1,2}

2-rows arrays Edit

  • Bi-rowexponentiation, {a,b(1)2}
  • Bi-rowtetration, {a,b,2(1)2}
  • Bi-rowexpansion, {a,b,1,2(1)2}
  • Bi-rowmultexponentiation, {a,b,1,1,2(1)2}
  • Bi-row-biexponentiation, {a,b,1,1,1,2(1)2}
  • Bi-row-bi-uniexponentiation, {a,b,1,1,1,1,2(1)2}
  • Tri-rowexponentiation, {a,b(1)3}
  • Quadri-rowexponentiation, {a,b(1)4}
  • Quinti-rowexponentiation, {a,b(1)5}
  • Sexti-rowexponentiation, {a,b(1)6}
  • Septi-rowexponentiation, {a,b(1)7}
  • Octi-rowexponentiation, {a,b(1)8}
  • Noni-rowexponentiation, {a,b(1)9}
  • Deci-rowexponentiation, {a,b(1)10}
  • Bi-uni-rowexponentiation, {a,b(1)1,2}

M-i-us Edit

Exponentiation Edit

  • Minimus-, log10(n)
  • Uaximus-, 1n
  • Baximus-, 2n
  • Traximus-, 3n
  • Quadraximus-, 4n
  • Quintaximus-, 5n
  • Sextaximus-, 6n
  • Septaximus-, 7n
  • Octaximus-, 8n
  • Nonaximus-, 9n
  • Maximus-, 10n
  • -wo, 2n+1
  • -ree, 3n+1
  • -xclamation, n!
  • -illion (S), 103*n+3
  • -illion (L), 106*n
  • -illiard, 106*n+3
  • -yllion, 102n+2

Tetration Edit

  • -uogue, n1
  • -bogue, n2
  • -trogue, n3
  • -quadrogue, n4
  • -quintogue, n5
  • -sextogue, n6
  • -septogue, n7
  • -octogue, n8
  • -nonogue, n9
  • -logue, n10
  • -allion, n+11000

Pentation Edit

  • -uougent, {1,n,3}
  • -bougent, {2,n,3}
  • -trougent, {3,n,3}
  • -quadrougent, {4,n,3}
  • -quintougent, {5,n,3}
  • -sextougent, {6,n,3}
  • -septougent, {7,n,3}
  • -octougent, {8,n,3}
  • -nonougent, {9,n,3}
  • -taxis or -lougent, {10,n,3}
  • -eelion, {1000,n+1,3}

Hexation Edit

  • -petaxis, {10,n,4}
  • -ilion, {1000,n+1,4}

Heptation Edit

  • -exaxis, {10,n,5}
  • -ollion, {1000,n+1,5}

Octation Edit

  • -eptaxis, {10,n,6}
  • -alion, {1000,n+1,6}

Enneation Edit

  • -octaxis, {10,n,7}
  • -oulion, {1000,n+1,7}

Decation Edit

  • -ennaxis, {10,n,8}
  • -ullion, {1000,n+1,8}

Hendecation Edit

  • -dekaxis, {10,n,9}
  • -urlion, {1000,n+1,9}

Dodecation Edit

  • -endekaxis, {10,n,10}
  • -olion, {1000,n+1,10}

Tridecation Edit

  • -dodekaxis, {10,n,11}
  • -oilion, {1000,n+1,11}

Tetradecation and higher Edit

  • -uulion, {1000,n+1,12}
  • -eerlion, {1000,n+1,13}

Notations Edit

Primitive recursive Edit

  • Factorial, n!
  • Expofactorial, n!1
  • Tetrofactorial, n!2
  • Pentofactorial, n!3
  • Hexofactorial, n!4
  • Double factorial, n!!
  • Triple factorial, n!!!
  • Quadruple factorial, n!!!!
  • Quintuple factorial, n!!!!!
  • Sextuple factorial, n!!!!!!
  • Septuple factorial, n!!!!!!!
  • Octuple factorial, n!!!!!!!!
  • Nonuple factorial, n!!!!!!!!!
  • Subfactorial, !n
  • Mixed factorial, n*
  • Square factorial, nↅ
  • Latin square
  • Superfactorial (Sloane and Plouffe)
  • Hyperfactorial
  • 2nd factorial
  • Superfactorial (Pickover)
  • Left factorial, !n
  • Weak factorial, nw!
  • Ultrafactorial, n\
  • Torian, x!x
  • Exporian, x!x!x
  • Tetrorian, x!!4
  • Pentorian, x!!5
  • Hexorian, x!!6
  • Heptorian, x!!7
  • Octorian, x!!8
  • Ennorian, x!!9
  • Decorian, x!!10
  • Suxtorian, x!!x

RC0 Edit

The totality of these functions cannot be proved in RCA0 (see second-order arithmetic) and they eventually dominate all primitive recursive functions.

  • Weak goodstein function g(n) ≈ fω(n)
  • Ackermann function A(n,n) ≈ fω(n)
  • Ackermann numbers ≈ fω(n)
  • Friedman's vector reduction problem
  • Mythical tree problem
  • Pi-ation function, πn-2(a,b)
  • Sudan function Fn(x,y) ≈ fω(n)
  • Steinhaus-Moser notation ≈ fω(n)
  • Davenport-Schinzel sequence
  • Arrow notation (both variants) a↑nb
  • Psi Notation ≈ fω(n)
  • |T[k]| function, ≈ fω(n)
  • Hyper-E notation, E#
  • Graham's function, ≈ fω+1(n)
  • Exploding Tree Function, ≈ fω+1(n)

Peano arithmetic Edit

The following functions eventually dominate all multirecursive functions but are still provably recursive within Peano arithmetic.

  • Linear array notation
  • Extended hyper-E notation
  • n(k) function
  • The Q-supersystem
  • Taro's multivariable Ackermann function
  • SAN linear array notation
  • Planar array notation
  • Extended array notation (dimensional)
  • BEAF superdimensional arrays

ATR0 Edit

Starting from here, the totality of these functions is not provable in Peano arithmetic.

  • BEAF tetrational arrays
  • Notation Array Notation
  • Cascading-E notation
  • SAN extended array notation
  • Circle(n) functio
  • m(n) map
  • Goodstein function
  • Hydra(n) function
  • Worm(n) function
  • X-Sequence Hyper-Exponential Notation
  • m(m,n) map
  • Nested Cascading-E Notation
  • Three Bracket NaN

Faster computable functions Edit

These functions and all those that follow cannot be proved total in arithmetical transfinite induction.

  • Extended Cascading-E Notation
  • Hyper-Extended Cascading-E Notation
  • Extended Q-supersystem
  • tree(n) function
  • TREE(n) function
  • Bird's H(n) function
  • SAN expanding array notation
  • Bird's S(n) function (original)
  • Bird's U(n) function
  • SAN multiple expanding array notation
  • Pair(n) function
  • SCG(n) function
  • BH(n) function
  • Hyperfactorial array notation
  • Bird's array notation
  • Bird's S(n) function
  • Aarex's Array Notation
  • Strong array notation
  • Loader.c function
  • Friedman's finite promise games functions
  • Greedy clique sequence functions

Uncomputable functions Edit

These functions are uncomputable, and cannot be evaluated by computer programs in finite time.

  • Busy beaver function
  • Frantic frog function
  • Placid platypus function (slow-growing)
  • Weary wombat function (slow-growing)
  • mth order busy beaver function
  • Betti number
  • Doodle function
  • Xi function
  • Infinite time Turing machine busy beaver
  • Rayo's function
  • FOOT function
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