User:JrandWP/sandbox/List of googolisms/Polynomial omega level

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

Smaller numbers

\(f_{\omega^\omega}(10^{10^6})\) ~ \(f_{\omega^\omega + \omega}(10^{10^6})\)

• pete-7.c, \(f_{\omega^\omega}(2\uparrow\uparrow36)\)
• Dupertri, {3,3,2 (1) 2}
• Duperdecal, {10,3,2 (1) 2}
• Linelplex, s(3,3,2{2}2)
• Goobolplex, {10,{10,100 (1) 2} (1) 2}
• Grand godgahlah, E100#^#100#2
• Grand godgahlahgong, E100000#^#100000#2
• Truperdecal, {10,4,2 (1) 2}
• Grand grand godgahlah / two-ex-grand godgahlah, E100#^#100#3
• Grand grand godgahlahgong, E100000#^#100000#3
• Quadruperdecal, {10,5,2 (1) 2}
• Grand grand grand godgahlah / three-ex-grand godgahlah, E100#^#100#4
• Grand grand grand grand godgahlah / four-ex-grand godgahlah, E100#^#100#5
• Gibbol, {10,100,2 (1) 2}
• Lin-Googol, 10[1{1}1]100
• Grandgahlah, E100#^#100#100
• Titanicoltrex, #{0:1}*((10))*100
• Hundred-ex-grand godgahlah, E100#^#100#101
• Eleven-thousand-eight-hundred-sixty-two-ex-grand godgahlahgong, E100000#^#100000#11863
• Superis-Terribuporcal, Forcal_2[2]2(1)
• Godgahlah-ex-grand godgahlah, E100#^#100#(1+E100#^#100)
• Latri, {3,3,3 (1) 2}
• Lintrienel, s(3,3,3{2}2)
• Gabbol, {10,100,3 (1) 2}
• Lin-Doogol, 10[2{1}1]100
• Greagahlah, E100#^#100#100#100
• Superis-Terribmegocal, Forcal_3[2]2(1)
• Geebol, {10,100,4 (1) 2}
• Gigangahlah, E100#^#100#100#100#100
• Superis-Terribypercal, Forcal_4[2]2(1)
• Gibol, {10,100,5 (1) 2}
• Gorgegahlah, E100#^#100#100#100#100#100
• Gobbol, {10,100,6 (1) 2}
• Gulgahlah, E100#^#100#100#100#100#100#100
• Gabol, {10,100,7 (1) 2}
• Gaspgahlah, E100#^#100##7
• Ginorgahlah, E100#^#100##8
• Gargangahlah, E100#^#100##9
• Googongahlah, E100#^#100##10
• Boobol, {10,10,100 (1) 2}
• Gugoldgahlah, E100#^#100##100
• Lin-Kiloogol, 10[0,1{1}1]100

\(f_{\omega^\omega + \omega}(10^{10^6})\) ~ \(f_{\omega^\omega 2}(10^{10^6})\)

• Graatagoldgahlah, E100#^#100##100#100
• Titanicolgoltrex, #{0:1}^*((10))*100
• Greegoldgahlah, E100#^#100##100#100#100
• Grinningoldgahlah, E100#^#100##100#100#100#100
• Golaagoldgahlah, E100#^#100##100#100#100#100#100
• Gruelohgoldgahlah, E100#^#100##100##6
• Gaspgoldgahlah, E100#^#100##100##7
• Ginorgoldgahlah, E100#^#100##100##8
• Gargantuuldgahlah, E100#^#100##100##9
• Googondoldgahlah, E100#^#100##100##10
• Gugolthragahlah, E100#^#100##100##100
• Bibbol, {10,10,100,2 (1) 2}
• Lintetenel, s(3,3,3,3{2}2)
• Gugolteslagahlah, E100#^#100##100##100##100
• Babbol, {10,10,100,3 (1) 2}
• Gugolpetagahlah, E100#^#100###5
• Beebol, {10,10,100,4 (1) 2}
• Gugolhexagahlah, E100#^#100###6
• Bibol, {10,10,100,5 (1) 2}
• Gugolheptagahlah, E100#^#100###7
• Bobbol, {10,10,100,6 (1) 2}
• Gugoloctagahlah, E100#^#100###8
• Babol, {10,10,100,7 (1) 2}
• Gugolennagahlah, E100#^#100###9
• Gugoldekagahlah, E100#^#100###10
• Throogahlah / throogogahlah, E100#^#100###100
• Troobol, {10,10,10,100 (1) 2}
• Lin-Megoogol, 10[0,0,1{1}1]100
• Titanic Astuul, #{0:1}{1}((10))*100
• Tribbol, {10,10,10,100,2 (1) 2}
• Linpentenel, s(3,3,3,3,3{2}2)
• Throotergahlah, E100#^#100###100###100###100
• Trabbol, {10,10,10,100,3 (1) 2}
• Treebol, {10,10,10,100,4 (1) 2}
• Tribol, {10,10,10,100,5 (1) 2}
• Trobbol, {10,10,10,100,6 (1) 2}
• Trabol, {10,10,10,100,7 (1) 2}
• Tetroogahlah / teroogahlah / teroogogahlah, E100#^#100####100
• Quadroobol, {10,10,10,10,100 (1) 2}
• Lin-Gigoogol, 10[0,0,0,1{1}1]100
• Titanic Galaxiol, #{0:1}{2}((10))*100
• Quadribbol, {10,10,10,10,100,2 (1) 2}
• Quadrabbol, {10,10,10,10,100,3 (1) 2}
• Quadreebol, {10,10,10,10,100,4 (1) 2}
• Quadribol, {10,10,10,10,100,5 (1) 2}
• Quadrobbol, {10,10,10,10,100,6 (1) 2}
• Quadrabol, {10,10,10,10,100,7 (1) 2}
• Pentoogahlah / petoogahlah / petoogogahlah, E100#^#100#####100
• Quintoobol, {10,10,10,10,10,100 (1) 2}
• Titanic Cosmol, #{0:1}{3}((10))*100
• Hexoogahlah / ectoogahlah / ectoogogahlah, E100#^#100######100
• Titanic Hyperiol, #{0:1}{4}((10))*100
• Heptoogahlah / zettoogahlah / zettoogogahlah, E100#^#100#######100
• Ogdoogahlah / yottoogahlah / yottoogogahlah, E100#^#100########100
• Entoogahlah, E100#^#100#^#9
• Dektoogahlah, E100#^#100#^#10
• Lvapofrbi, 1^[(3)[1]]₀(76)
• Gootrol, {10,100 (1) 3}
• Gotrigahlah, E100#^#100#^#100
• Dulinoogol, 10[0{1}2]100

\(f_{\omega^\omega 2}(10^{10^6})\) ~ \(f_{\omega^{\omega+1}}(10^{10^6})\)

• Dulinel, s(3,2,2{2}3)
• Dulinelplex, s(3,3,2{2}3)
• Gitrol, {10,100,2 (1) 3}
• Dulin-Googol, 10[1{1}2]100
• Grangotrigahlah / grantrigahlah, E100#^#100#^#100#100
• Dulintrienel, s(3,3,3{2}3)
• Gatrol, {10,100,3 (1) 3}
• Greagotrigahlah / greatrigahlah, E100#^#100#^#100#100#100
• Geetrol, {10,100,4 (1) 3}
• Gigangotrigahlah / gigantrigahlah, E100#^#100#^#100#100#100#100
• Gietrol, {10,100,5 (1) 3}
• Gorgegotrigahlah / gorgetrigahlah, E100#^#100#^#100#100#100#100#100
• Gotrol, {10,100,6 (1) 3}
• Gulgotrigahlah / gultrigahlah, E100#^#100#^#100##6
• Gaitrol, {10,100,7 (1) 3}
• Gaspgotrigahlah / gasptrigahlah, E100#^#100#^#100##7
• Ginorgotrigahlah, E100#^#100#^#100##8
• Bootrol, {10,10,100 (1) 3}
• Gugoldgotrigahlah / gugoldtrigahlah, E100#^#100#^#100##100
• Dulintetenel, s(3,3,3,3{2}3)
• Throogotrigahlah / throotrigahlah, E100#^#100#^#100###100
• Trootrol, {10,10,10,100 (1) 3}
• Tetroogotrigahlah / terootrigahlah / teroogotrigahlah, E100#^#100#^#100####100
• Quadrootrol, {10,10,10,10,100 (1) 3}
• Pentoogotrigahlah / petootrigahlah / petoogotrigahlah, E100#^#100#^#100#####100
• Hexoogotrigahlah / ectootrigahlah / ectoogotrigahlah, E100#^#100#^#100######100
• Heptoogotrigahlah / zettootrigahlah / zettoogotrigahlah, E100#^#100#^#100#######100
• Ogdoogotrigahlah / yottootrigahlah / yottoogotrigahlah, E100#^#100#^#100########100
• Gooquadrol, {10,100 (1) 4}
• Gotergahlah, E100#^#100#^#100#^#100
• Trulinoogol, 10[0{1}3]100
• Booquadrol, {10,10,100 (1) 4}
• Trooquadrol, {10,10,10,100 (1) 4}
• Quadrooquadrol, {10,10,10,10,100 (1) 4}
• Quadreequadrol, {10,10,10,10,100,4 (1) 4}
• Gooquintol, {10,100 (1) 5}
• Goppegahlah, E100#^#100#^#100#^#100#^#100
• Gohexgahlah / gohexahlah, E100#^#*#6
• Gohepgahlah, E100#^#*#7
• Go-ahtgahlah, E100#^#*#8
• Go-enngahlah, E100#^#*#9
• Emperal, {10,10 (1) 10}
• Godekahlah, E100#^#*#10
• Gossol, {10,10 (1) 100}
• Godgoldgahlah / gohectgahlah / godgoldahlah, E100#^#*#100
• Kilulinoogol, 10[0{1}0,1]100
• Titaniprimol, #{1:1}((10))*100

\(f_{\omega^{\omega+1}}(10^{10^6})\) ~ \(f_{\omega^{\omega+2}}(10^{10^6})\)

• Emperalplex, {10,10 (1) {10,10 (1) 10}}
• Gossolplex, {10,10 (1) {10,10 (1) 100}}
• Kilulin-Googol, 10[1{1}0,1]100
• Kilulin-Linoogol, 10[0{1}1,1]100
• Kilulin-Dulinoogol, 10[0{1}2,1]100
• Gissol, {10,10 (1) 100,2}
• Gotrigoldgahlah / gotrigoldahlah, E100#^#*##3
• Dukilulinoogol, 10[0{1}0,2]100
• Gissolplex, {10,10 (1) {10,10 (1) 100,2},2}
• Dienlinel, s(3,2,2{2}3,3)
• Dienlintrienel, s(3,3,3{2}3,3)
• Gassol, {10,10 (1) 100,3}
• Gotergoldgahlah / gotergoldahlah, E100#^#*##4
• Gassolplex, {10,10 (1) {10,10 (1) 100,3},3}
• Geesol, {10,10 (1) 100,4}
• Goppegoldgahlah / goppegoldahlah, E100#^#*##5
• Geesolplex, {10,10 (1) {10,10 (1) 100,4},4}
• Gussol, {10,10 (1) 100,5}
• Gohexgoldgahlah / gohexgoldahlah, E100#^#*##6
• Gussolplex, {10,10 (1) {10,10 (1) 100,5},5}
• Gohepgoldgahlah / gohepgoldahlah, E100#^#*##7
• Go-ahtgoldgahlah / go-ahtgoldahlah, E100#^#*##8
• Go-enngoldgahlah / go-enngoldahlah, E100#^#*##9
• Godekagoldgahlah / godekagoldahlah, E100#^#*##10
• Hyperal, {10,10 (1) 10,10}
• Fish number 3, \(\approx f_{(\omega^{\omega+1}) 63+1}(63)\)
• Godthroogahlah / godthroldahlah, E100#^#*##100
• Mossol, {10,10 (1) 10,100}
• Megulinoogol, 10[0{1}0,0,1]100

\(f_{\omega^{\omega+2}}(10^{10^6})\) ~ \(f_{\omega^{\omega 2}}(10^{10^6})\)

• Hyperalplex, {10,10 (1) 10,{10,10 (1) 10,10}}
• Mossolplex, {10,10 (1) 10,{10,10 (1) 10,100}}
• Megulin-Kilulinoogol, 10[0{1}0,1,1]100
• Missol, {10,10 (1) 10,100,2}
• Dumegulinoogol, 10[0{1}0,0,2]100
• Trienlinel, s(3,2,2{2}3,3,3)
• Massol, {10,10 (1) 10,100,3}
• Meesol, {10,10 (1) 10,100,4}
• Mussol, {10,10 (1) 10,100,5}
• Godtetroogahlah / godteroogahlah / godteroldahlah, E100#^#*###100
• Bossol, {10,10 (1) 10,10,100}
• Gigulinoogol, 10[0{1}0,0,0,1]100
• Titanitrol, #{3:1}((10))*100
• Bissol, {10,10 (1) 10,10,100,2}
• Tetenlinel, s(3,2,2{2}3,3,3,3)
• Bassol, {10,10 (1) 10,10,100,3}
• Beesol, {10,10 (1) 10,10,100,4}
• Bussol, {10,10 (1) 10,10,100,5}
• Godpentoogahlah / godpetoogahlah / godpetoldahlah, E100#^#*####100
• Trossol, {10,10 (1) 10,10,10,100}
• Terulinoogol, 10[0{1}0,0,0,0,1]100
• Titaniterol, #{4:1}((10))*100
• Trissol, {10,10 (1) 10,10,10,100,2}
• Pentenlinel, s(3,2,2{2}3,3,3,3,3)
• Trassol, {10,10 (1) 10,10,10,100,3}
• Treesol, {10,10 (1) 10,10,10,100,4}
• Trussol, {10,10 (1) 10,10,10,100,5}
• Godhexoogahlah / go-ectoogahlah / go-ectolgahlah, E100#^#*#####100
• Quadrossol, {10,10 (1) 10,10,10,10,100}
• Petulinoogol, 10[0{1}0,0,0,0,0,1]100
• Godheptoogahlah / godzettoogahlah / godzettolgahlah, E100#^#*######100
• Quintossol, {10,10 (1) 10,10,10,10,10,100}
• Ectulinoogol, 10[0{1}0,0,0,0,0,0,1]100
• Godogdoogahlah / godyottoogahlah / godyottolgahlah, E100#^#*#######100
• Zettulinoogol, 10[0{1}0,0,0,0,0,0,0,1]100
• Godgahgridgahthroogahteroogahpetoogah-ectoogahzetoogahyottoogahlah, E100#^#*#######100#^#*######100#^#*#####100#^#*####100#^#*###100#^#*##100#^#*#100#^#100
• Godentoogahlah, E100#^#*########100
• Yottulinoogol, 10[0{1}0,0,0,0,0,0,0,0,1]100
• Goddektoogahlah, E100#^#*#########100
• Xennulinoogol, 10[0{1}0,0,0,0,0,0,0,0,0,1]100
• Diteral, {10,10 (1)(1) 2}
• Wekulinoogol, 10[0{1}0,0,0,0,0,0,0,0,0,0,1]100
• Dubol, {10,100 (1)(1) 2}
• Deutero-godgahlah, E100#^#*#^#100
• Behemicol, #{0:2}((10))*100

\(f_{\omega^{\omega 2}}(10^{10^6})\) ~ \(f_{\omega^{\omega 3}}(10^{10^6})\)

• Linbel, s(3,2,2{2}1{2}2)
• Diteralplex, {10,3,2 (1)(1) 2}
• Lintrienbel, s(3,3,3{2}1{2}2)
• Linblinel, s(3,2,2{2}2{2}2)
• Linbdulinel, s(3,2,2{2}3{2}2)
• Linbdienlinel, s(3,2,2{2}3,3{2}2)
• Dutrol, {10,100 (1)(1) 3}
• Dulinbel, s(3,2,2{2}1{2}3)
• Duquadrol, {10,100 (1)(1) 4}
• Admiral, {10,10 (1)(1) 10}
• Dossol, {10,10 (1)(1) 100}
• Deutero-godgoldgahlah / deutero-godgoldahlah, E100#^#*#^#*#100
• Dossolplex, {10,10 (1)(1) {10,10 (1)(1) 100}}
• Dienlinbel, s(3,2,2{2}1{2}3,3)
• Deutero-godthroogahlah / deutero-godthrolgahlah, E100#^#*#^#*##100
• Trienlinbel, s(3,2,2{2}1{2}3,3,3)
• Dimensol, s(3,3{1,2}2)
• Dutritri, {3,3,3 (1) 3,3,3 (1) 3,3,3}
• Dutridecal, {10,10,10 (1) 10,10,10 (1) 10,10,10}
• Deutero-godtetroogahlah / deutero-godteroogahlah / deutero-godterolgahlah, E100#^#*#^#*###100
• Deutero-godpentoogahlah / deutero-godpetoogahlah / deutero-godpetolgahlah, E100#^#*#^#*####100
• Deutero-godhexoogahlah / deutero-go-ectoogahlah / deutero-go-ectolgahlah, E100#^#*#^#*#####100
• Deutero-godheptoogahlah / deutero-godzettoogahlah / deutero-gozettolgahlah, E100#^#*#^#*######100
• Deutero-godogdoogahlah / deutero-godyottoogahlah / deutero-goyottolgahlah, E100#^#*#^#*#######100
• Triubol, {10,100(1)(1)(1)2}
• Trito-godgahlah, E100#^#*#^#*#^#100
• Leviathol, #{0:3}((10))*100

\(f_{\omega^{\omega 3}}(10^{10^6})\) ~ \(f_{\omega^{\omega^2}}(10^{10^6})\)

• Lintrel, s(3,2,2{2}1{2}1{2}2)
• Tetrubol, {10,100 (1)(1)(1)(1) 2}
• Teterto-godgahlah, E100#^#*#^#*#^#*#^#100
• Lintetel, s(3,2,2{2}1{2}1{2}1{2}2)
• Pepto-godgahlah, E100#^##5
• Linpenel, s(3,2,2{2}1{2}1{2}1{2}1{2}2)
• Exto-godgahlah, E100#^##6
• Linhexel, s(3,2,2{2}1{2}1{2}1{2}1{2}1{2}2)
• Epto-godgahlah, E100#^##7
• Ogdo-godgahlah, E100#^##8
• Ento-godgahlah, E100#^##9
• Xappol, {10,10 (2) 2}
• Dekato-godgahlah, E100#^##10
• Isosto-godgahlah, E100#^##20
• Planel, s(3,2,2{3}2)
• Trianto-godgahlah, E100#^##30
• Saranto-godgahlah, E100#^##40
• Goxxol, {10,100 (2) 2}
• Triabiogodgahlah, E100+_##100
• Gridgahlah, E100#^##100
• Hyper-grid-hyperon, 100{X^X2}100
• Empiriol, #{0:0:1}((10))*100

Larger numbers