ULNL3

Back to Ultimate Large Numbers List Part II

ULTIMATE LARGE NUMBERS LIST

PART III

numbers of order type w^w to any number below infinity...

E100#^#100#(1+E100#^#100#2)

grand-godgahlah-ex-grand godgahlah

E100#^#100#(1+E100#^#100#3)

grand-grand-godgahlah-ex-grand godgahlah

E100#^#100#(1+E100#^#100#4)

grand-grand-grand-godgahlah-ex-grand godgahlah

E100#^#100#(1+E100#^#100#5)

grand-grand-grand-grand-godgahlah-ex-grand godgahlah

E100#^#100#100#2

grand grandgahlah

E100#^#100#100#2 = E100#^#100#(E100#^#100#100) = E100#^#100#(grandgahlah). The great grandgahlah is the grandgahlahth member of the godgahlah series.

E100#^#100#100#3

grand grand grandgahlah

E100#^#100#100#100

greagahlah

E100#^#100#100#100#2

grand greagahlah

E100#^#100#100#100#3

grand grand greagahlah

E100#^#100#100#100#100

gigangahlah

E100#^#100#100#100#100#2

grand gigangahlah

E100#^#100#100#100#100#100

gorgegahlah

E100#^#100#100#100#100#100#100

gulgahlah

E100#^#100#100#100#100#100#100#100

gaspgahlah

E100#^#100#100#100#100#100#100#100#100

ginorgahlah

E100#^#100##100

gugoldgahlah

E100#^#100##100#100

graatagoldgahlah

E100#^#100##100#100#100

greegoldgahlah

E100#^#100##100#100#100#100

grinningoldgahlah

E100#^#100##100#100#100#100#100

golaagoldgahlah

E100#^#100##100#100#100#100#100#100

gruelohgoldgahlah

E100#^#100##100#100#100#100#100#100#100

gaspgoldgahlah

E100#^#100##100#100#100#100#100#100#100#100

ginorgoldgahlah

E100#^#100##100##100

gugolthragahlah

E100#^#100##100##100##100

gugolteslagahlah

E100#^#100##100##100##100##100

gugolpetagahlah

E100#^#100##100##100##100##100##100

gugolhexagahlah

E100#^#100##100##100##100##100##100##100

gugolheptagahlah

E100#^#100##100##100##100##100##100##100##100

gugoloctagahlah

E100#^#100###100

throogahlah

E100#^#100####100

teroogahlah

E100#^#100#####100

petoogahlah

E100#^#100######100

ectoogahlah

E100#^#100#######100

zettoogahlah

E100#^#100########100

yottoogahlah

E100#^#100#^#100

gotrigahlah / tristo-godgahlah

E100#^#100#^#100#2

grand gotrigahlah

E100#^#100#^#100#3

grand grand gotrigahlah

E100#^#100#^#100#100

grantrigahlah

E100#^#100#^#100#100#2

great grantrigahlah

E100#^#100#^#100#100#100

greatrigahlah

E100#^#100#^#100#100#100#100

gigantrigahlah

E100#^#100#^#100##5

gorgetrigahlah

E100#^#100#^#100##6

gultrigahlah

E100#^#100#^#100##7

gasptrigahlah

E100#^#100#^#100##8

ginortrigahlah

E100#^#100#^#100##100

gugoldtrigahlah

E100#^#100#^#100###100

throotrigahlah

E100#^#100#^#100####100

terootrigahlah

E100#^#100#^#100#####100

petootrigahlah

E100#^#100#^#100######100

ectootrigahlah

E100#^#100#^#100#######100

zettootrigahlah

E100#^#100#^#100########100

yottootrigahlah

E100#^#100#^#100#^#100

gotergahlah / teristo-godgahlah

E100#^#100#^#100#^#100#2

grand gotergahlah

E100#^#100#^#100#^#100#100

grantergahlah

E100#^#100#^#100#^#100#100#2

grand grantergahlah

E100#^#100#^#100#^#100#100#100

greatergahlah

E100#^#100#^#100#^#100#100#100#100

gigantergahlah

E100#^#100#^#100#^#100##5

gorgetergahlah

E100#^#100#^#100#^#100##6

gultergahlah

E100#^#100#^#100#^#100##7

gasptergahlah

E100#^#100#^#100#^#100##8

ginortergahlah

E100#^#100#^#100#^#100###100

throotergahlah

E100#^#100#^#100#^#100####100

terootergahlah

E100#^#100#^#100#^#100#####100

petootergahlah

E100#^#100#^#100#^#100######100

ectootergahlah

E100#^#100#^#100#^#100#######100

zettootergahlah

E100#^#100#^#100#^#100########100

yottootergahlah

E100#^#100#^#100#^#100#^#100

gopeggahlah / pesto-godgahlah

E100#^#100#^#100#^#100#^#100#^#100

gohexgahlah / existo-godgahlah

E100#^#100#^#100#^#100#^#100#^#100#^#100

gohepgahlah / episto-godgahlah

E100#^#100#^#100#^#100#^#100#^#100#^#100#^#100

go-ahtgahlah / ogisto-godgahlah

E100#^#100#^#100#^#100#^#100#^#100#^#100#^#100#^#100

go-enngahlah / ennisto-godgahlah

E100#^#100#^#100#^#100#^#100#^#100#^#100#^#100#^#100#^#100

godekahlah / dekisto-godgahlah

E100#^#*#100

godgoldgahlah

E100#^#*#100#^#*#100

gotrigoldgahlah / tristo-godgoldgahlah

E100#^#*#100#^#*#100#^#*#100

gotergoldgahlah / teristo-godgoldgahlah

E100#^#*##5

gopeggoldgahlah / pesto-godgoldgahlah

E100#^#*##6

gohexgoldgahlah / existo-godgoldgahlah

E100#^#*##7

gohepgoldgahlah / episto-godgoldgahlah

E100#^#*##8

go-ahtgoldgahlah / ogisto-godgoldgahlah

E100#^#*##9

godenngoldgahlah / ennisto-godgoldgahlah

E100#^#*##10

godekagoldgahlah / dekisto-godgoldgahlah

E100#^#*##100

godthroogahlah

E100#^#*###100

godteroogahlah

E100#^#*####100

godpetoogahlah

E100#^#*#####100

go-ectoogahlah

E100#^#*######100

godzettoogahlah

E100#^#*#######100

godyottoogahlah

E100#^#*#^#100

deutero-godgahlah

E100#^#*#^#*#100

deutero-godgoldgahlah

E100#^#*#^#*##100

deutero-godthroogahlah

E100#^#*#^#*###100

deutero-godteroogahlah

E100#^#*#^#*####100

deutero-godpetoogahlah

E100#^#*#^#*#####100

deutero-go-ectoogahlah

E100#^#*#^#*######100

deutero-gozettoogahlah

E100#^#*#^#*#######100

deutero-goyottoogahlah

E100#^#*#^#*#^#100

trito-godgahlah

E100#^#*#^#*#^#*#^#100

teterto-godgahlah

E100#^#*#^#*#^#*#^#*#^#100

pepto-godgahlah

E100#^#*#^#*#^#*#^#*#^#*#^#100

exto-godgahlah

E100#^##7

epto-godgahlah

E100#^##8

ogdo-godgahlah

E100#^##9

ento-godgahlah

E100#^##10

dekato-godgahlah

E100#^##20

isosto-godgahlah

E100#^##100

gridgahlah / hecato-godgahlah

E100#^##100#^##100

gridtrigahlah

E100#^##100#^##100#^##100

gridtergahlah

E100#^##*#5

gridpeggahlah

E100#^##*#6

gridhexgahlah

E100#^##*#7

gridhepgahlah

E100#^##*#8

grid-ahtgahlah

E100#^##*#9

grid-enngahlah

E100#^##*#10

grid-dekgahlah

E100#^##*#^##100

deutero-gridgahlah

E100#^##*#^##*#^##100

trito-gridgahlah

E100#^##*#^##*#^##*#^##100

teterto-gridgahlah

E100#^###5

pepto-gridgahlah

E100#^###6

exto-gridgahlah

E100#^###7

epto-gridgahlah

E100#^###8

ogdo-gridgahlah

E100#^###9

ento-gridgahlah

E100#^###10

dekato-gridgahlah

E100#^###20

isosto-gridgahlah

E100#^###100

kubikahlah / hecato-gridgahlah

E100#^###100#^###100

kubitrigahlah

E100#^###100#^###100#^###100

kubitergahlah

E100#^###*#5

kubipeggahlah

E100#^###*#6

kubihexgahlah

E100#^###*#7

kubihepgahlah

E100#^###*#8

kubi-ahtgahlah

E100#^###*#9

kubi-enngahlah

E100#^###*#10

kubi-dekahlah

E100#^###*#^###100

deutero-kubikahlah

E100#^###*#^###*#^###100

trito-kubikahlah

E100#^###*#^###*#^###*#^###100

teterto-kubikahlah

E100#^####5

pepto-kubikahlah

E100#^####6

exto-kubikahlah

E100#^####7

epto-kubikahlah

E100#^####8

ogdo-kubikahlah

E100#^####9

ento-kubikahlah

E100#^####10

dekato-kubikahlah

E100#^####20

isosto-kubikahlah

E100#^####100

quarticahlah / hecato-kubikahlah

E100#^####100#^####100

quartitrigahlah

E100#^####100#^####100#^####100

quartitergahlah

E100#^####*#5

quartipeggahlah

E100#^####*#6

quartihexgahlah

E100#^####*#7

quartihepgahlah

E100#^####*#8

quarti-ahtgahlah

E100#^####*#9

quarti-enngahlah

E100#^####*#10

quarti-dekahlah

E100#^####*#^####100

deutero-quarticahlah

E100#^####*#^####*#^####100

trito-quarticahlah

E100#^####*#^####*#^####*#^####100

teterto-quarticahlah

E100#^#####5

pepto-quarticahlah

E100#^#####6

exto-quarticahlah

E100#^#####7

epto-quarticahlah

E100#^#####8

ogdo-quarticahlah

E100#^#####9

ento-quarticahlah

E100#^#####10

dekato-quarticahlah

E100#^#####20

isosto-quarticahlah

E100#^#####100

quinticahlah / hecato-quarticahlah

E100#^#####100#^#####100

quintitrigahlah

E100#^#####100#^#####100#^#####100

quintitergahlah

E100#^#####*#5

quintipeggahlah

E100#^#####*#6

quintihexgahlah

E100#^#####*#7

quintihepgahlah

E100#^#####*#8

quinti-ahtgahlah

E100#^#####*#9

quinti-enngahlah

E100#^#####*#10

quinti-dekahlah

E100#^#####*#^#####100

deutero-quinticahlah

E100#^#####*#^#####*#^#####100

trito-quinticahlah

E100#^#####*#^#####*#^#####*#^#####100

teterto-quinticahlah

E100#^######5

pepto-quinticahlah

E100#^######6

exto-quinticahlah

E100#^######7

epto-quinticahlah

E100#^######8

ogdo-quinticahlah

E100#^######9

ento-quinticahlah

E100#^######10

dekato-quinticahlah

E100#^######100

sexticahlah / hecato-quinticahlah

E100#^######100#^######100

sextitrigahlah

E100#^######100#^######100#^######100

sextitergahlah

E100#^######*#5

sextipeggahlah

E100#^######*#6

sextihexgahlah

E100#^######*#7

sextihepgahlah

E100#^######*#8

sexti-ahtgahlah

E100#^######*#9

sexti-enngahlah

E100#^######*#10

sexti-dekahlah

E100#^######*#^######100

deutero-sexticahlah

E100#^######*#^######*#^######100

trito-sexticahlah

E100#^######*#^######*#^######*#^######100

teterto-sexticahlah

E100#^#######5

pepto-sexticahlah

E100#^#######6

exto-sexticahlah

E100#^#######7

epto-sexticahlah

E100#^#######8

ogdo-sexticahlah

E100#^#######9

ento-sexticahlah

E100#^#######10

dekato-sexticahlah

E100#^#######100

septicahlah / hecato-sexticahlah

E100#^#######100#^#######100

septitrigahlah

E100#^#######100#^#######100#^#######100

septitergahlah

E100#^#######*#5

septipeggahlah

E100#^#######*#6

septihexgahlah

E100#^#######*#7

septihepgahlah

E100#^#######*#8

septi-ahtgahlah

E100#^#######*#9

septi-enngahlah

E100#^#######*#10

septi-dekahlah

E100#^#######*#^#######100

deutero-septicahlah

E100#^#######*#^#######*#^#######100

trito-septicahlah

E100#^#######*#^#######*#^#######*#^#######100

teterto-septicahlah

E100#^########5

pepto-septicahlah

E100#^########6

exto-septicahlah

E100#^########7

epto-septicahlah

E100#^########8

ogdo-septicahlah

E100#^########9

ento-septicahlah

E100#^########10

dekato-septicahlah

E100#^########100

octicahlah / hecato-septicahlah

E100#^########100#^########100

octitrigahlah

E100#^########100#^########100#^########100

octitergahlah

E100#^########*#5

octipeggahlah

E100#^########*#6

octihexgahlah

E100#^########*#7

octihepgahlah

E100#^########*#8

octi-ahtgahlah

E100#^########*#9

octi-enngahlah

E100#^########*#10

octi-dekgahlah

E100#^########*#^########100

deutero-octicahlah

E100#^########*#^########*#^########100

trito-octicahlah

E100#^########*#^########*#^########*#^########100

teterto-octicahlah

E100#^#########5

pepto-octicahlah

E100#^#########6

exto-octicahlah

E100#^#########7

epto-octicahlah

E100#^#########8

ogdo-octicahlah

E100#^#########9

ento-octicahlah

E100#^#########10

dekato-octicahlah

E100#^#########100

nonicahlah

E100#^##########100

decicahlah

E100#^#^#11

undecicahlah

E100#^#^#12

duodecicahlah

E100#^#^#13

tredecicahlah

E100#^#^#14

quattuordecicahlah

E100#^#^#15

quindecicahlah

E100#^#^#16

sexdecicahlah

E100#^#^#17

septendecicahlah

E100#^#^#18

octodecicahlah

E100#^#^#19

novemdecicahlah

E100#^#^#20

viginticahlah

E100#^#^#30

triginticahlah

E100#^#^#40

quadraginticahlah

E100#^#^#50

quinquaginticahlah

E100#^#^#60

sexaginticahlah

E100#^#^#70

septuaginticahlah

E100#^#^#80

octoginticahlah

E100#^#^#90

nonaginticahlah

Super Dimensional Array Epoch

E100#^#^#100 ~ E100#^#^#^#100

Entries: 79

E100#^#^#100

godgathor

A godgathor is comparable to Jonathan Bowers' gongulus. It's comparable to a 100-dimensional array. Evaluating godgathor we obtain:

E100#^#^#100 = E100#^#####...#####100 w/100 #s in a row

E100#^#¹⁰¹100

goober bunch

E100#^#^#100#2

grand godgathor

E100#^#^{(1+E100#^#^(101)100)}(E100#^#¹⁰¹100)

gibbering goober bunch

E100#^#^#100#3

grand grand godgathor

E100#^#^#100#^#^#100

gotrigathor

E100#^#^#100#^#^#100#^#^#100

gotergathor

E100#^#^#*#5

gopeggathor

E100#^#^#*#6

gohexgathor

E100#^#^#*#7

gohepgathor

E100#^#^#*#8

go-ahtgathor

E100#^#^#*#9

go-enngathor

E100#^#^#*#10

godekgathor

E100#^#^#*#^#^#100

deutero-godgathor

E100#^#^#*#^#^#*#^#^#100

trito-godgathor

E100#^#^#*#^#^#*#^#^#*#^#^#100

teterto-godgathor

E100#^(#^#*#)5

pepto-godgathor

E100#^(#^#*#)6

exto-godgathor

E100#^(#^#*#)7

epto-godgathor

E100#^(#^#*#)8

ogdo-godgathor

E100#^(#^#*#)9

ento-godgathor

E100#^(#^#*#)10

dekato-godgathor

E100#^(#^#*#)20

isosto-godgathor

E100#^(#^#*#)100

hecato-godgathor

E100#^(#^#*##)100

godgridgathor

E100#^(#^#*###)100

godkubikgathor

E100#^(#^#*####)100

godquarticgathor

E100#^(#^#*#####)100

godquinticgathor

E100#^(#^#*######)100

godsexticgathor

E100#^(#^#*#######)100

godsepticgathor

E100#^(#^#*########)100

godocticgathor

E100#^(#^#*#########)100

godnonicgathor

E100#^(#^#*##########)100

goddecicgathor

E100#^(#^#*#^#)100

godgathordeus

E100#^(#^#*#^#*#)100

hecato-godgathordeus

E100#^(#^#*#^#*##)100

godgridgathordeus

E100#^(#^#*#^#*###)100

godkubikgathordeus

E100#^(#^#*#^#*####)100

godquarticgathordeus

E100#^(#^#*#^#*#####)100

godquinticgathordeus

E100#^(#^#*#^#*######)100

godsexticgathordeus

E100#^(#^#*#^#*#######)100

godsepticgathordeus

E100#^(#^#*#^#*########)100

godocticgathordeus

E100#^(#^#*#^#*#########)100

godnonicgathordeus

E100#^(#^#*#^#*##########)100

goddecicgathordeus

E100#^(#^#*#^#*#^#)100

godgathortruce

E100#^(#^#*#^#*#^#*#^#)100

godgathorquad

E100#^(#^#*#^#*#^#*#^#*#^#)100

godgathorquid

E100#^(#^#*#^#*#^#*#^#*#^#*#^#)100

godgathorsid

E100#^#^##7

godgathorseptuce

E100#^#^##8

godgathoroctuce

E100#^#^##100

gralgathor

E100#^#^##100#^#^##100

graltrigathor

E100#^#^##100#^#^##100#^#^##100

graltergathor

E100#^#^##*#^#^##100

deutero-gralgathor

E100#^#^##*#^#^##*#^#^##100

trito-gralgathor

E100#^#^##*#^#^##*#^#^##*#^#^##100

teterto-gralgathor

E100#^(#^##*#^##)100

gralgathordeus

E100#^(#^##*#^##*#^##)100

gralgathortruce

E100#^(#^##*#^##*#^##*#^##)100

gralgathorquad

E100#^#^###5

gralgathorquid

E100#^#^###6

gralgathorsid

E100#^#^###7

gralgathorseptuce

E100#^#^###8

gralgathoroctuce

E100#^#^###100

thraelgathor

E100#^#^###100#^#^###100

thraeltrigathor

E100#^#^###*#^#^###100

deutero-thraelgathor

E100#^#^###*#^#^###*#^#^###100

trito-thraelgathor

E100#^(#^###*#^###)100

thraelgathordeus

E100#^(#^###*#^###*#^###)100

thraelgathortruce

E100#^#^####100

terinngathor

E100#^#^####100#^#^####100

terinntrigathor

E100#^#^####*#^#^####100

deutero-terinngathor

E100#^#^####*#^#^####*#^#^####100

trito-terinngathor

E100#^(#^####*#^####)100

terinngathordeus

E100#^(#^####*#^####*#^####)100

terinngathortruce

E100#^#^#####100

pehaelgathor

E100#^#^######100

hexaelgathor

E100#^#^#######100

heptaelgathor

E100#^#^########100

octaelgathor

Ordinal-Tetration Epoch

E100#^^#4 ~ E100#^^#100

Entries: 48

E100#^#^#^#100

godtothol

E100#^#^#^##100

graltothol

E100#^#^#^###100

thraeltothol

E100#^#^#^####100

terinntothol

E100#^#^#^#####100

pehaeltothol

E100#^#^#^######100

hexaeltothol

E100#^#^#^#######100

heptaeltothol

E100#^#^#^########100

octaeltothol

E100#^#^#^#^#100

godtertathol

E100#^#^#^#^##100

graltertathol

E100#^#^#^#^###100

thraeltertathol

E100#^#^#^#^####100

terinntertathol

E100#^#^#^#^#####100

pehaeltertathol

E100#^#^#^#^######100

hexaeltertathol

E100#^#^#^#^#######100

heptaeltertathol

E100#^#^#^#^########100

octaeltertathol

E100#^#^#^#^#^#100

godpeptathol

E100#^#^#^#^#^##100

gralpeptathol

E100#^#^#^#^#^###100

thraelpeptathol

E100#^#^#^#^#^####100

terinnpeptathol

E100#^#^#^#^#^#####100

pehaelpeptathol

E100#^#^#^#^#^######100

hexaelpeptathol

E100#^#^#^#^#^#######100

heptaelpeptathol

E100#^#^#^#^#^########100

octaelpeptathol

E100#^#^#^#^#^#^#100

godextathol

E100#^#^#^#^#^#^##100

gralextathol

E100#^#^#^#^#^#^###100

thraelextathol

E100#^#^#^#^#^#^####100

terinnextathol

E100#^#^#^#^#^#^#####100

pehaelextathol

E100#^#^#^#^#^#^######100

hexaelextathol

E100#^#^#^#^#^#^#######100

heptaelextathol

E100#^#^#^#^#^#^########100

octaelextathol

E100#^#^#^#^#^#^#^#100

godeptathol

E100#^#^#^#^#^#^#^##100

graleptathol

E100#^#^#^#^#^#^#^###100

thraeleptathol

E100#^#^#^#^#^#^#^####100

terinneptathol

E100#^#^#^#^#^#^#^#####100

pehaeleptathol

E100#^#^#^#^#^#^#^######100

hexaeleptathol

E100#^#^#^#^#^#^#^#######100

heptaeleptathol

E100#^#^#^#^#^#^#^########100

octaeleptathol

E100#^#^#^#^#^#^#^#^#100

godoctathol

E100#^#^#^#^#^#^#^#^##100

graloctathol

E100#^#^#^#^#^#^#^#^###100

thraeloctathol

E100#^#^#^#^#^#^#^#^####100

terinnoctathol

E100#^#^#^#^#^#^#^#^#####100

pehaeloctathol

E100#^#^#^#^#^#^#^#^######100

hexaeloctathol

E100#^#^#^#^#^#^#^#^#######100

heptaeloctathol

E100#^#^#^#^#^#^#^#^########100

octaeloctathol

Epsilon Epoch

e(0) ~ zeta(0)

Entries: 178+

E100#^^#100

tethrathoth

The tethrathoth (or simply thoth) is equal to E100#^#^#^#^ ... ^#^#^#^#100 w/100 #s. It is comparable and slightly smaller than Jonathan Bowers' goppatoth. It is roughly equivalent to an X^^99 array.

E100,000#^^#100,000

tethrathothigong

For old time sake, here is the "gong" version of a tethrathoth, the tethrathothigong. It is equal to E100,000#^#^#^#^...^#^#^#^#100,000 w/100,000 #s. Technically speaking this number is mind-crushingly larger than having a mere hundred cascade levels ... but it's still a very modest improvement compare to how far we're going to take it from here ...

E100#^^#100#2

grand tethrathoth

The grand tethrathoth is equal to E100#^#^#^#^ ... ^#^#^#^#100 w/tethrathoth #s. This is incomparably larger than the tethrathothigong, though from a googologist's perspective just a stone's skip away from the tethrathoth. It is comparable to and slightly smaller than Jonathan Bowers' goppatothplex. It is roughly equivalent to a X^^(tethrathoth-1) array. The next explicitly named googolism after a goppatothplex is a triakulus. This number is much much MUCH larger and it will take us a long time to reach it!

E100,000#^^#100,000#2

grand tethrathothigong

E100#^^#100#3

grand grand tethrathoth

E100#^^#100#4

grand grand grand tethrathoth

E100#^^#100#5

grand grand grand grand tethrathoth

E100#^^#100#6

grand grand grand grand grand tethrathoth

E100#^^#100#7

grand grand grand grand grand grand tethrathoth

E100#^^#100#100

ninety-nine-ex-grand tethrathoth / grantethrathoth

E100#^^#100#101

hundred-ex-grand tethrathoth

E100#^^#100#(1+E100)

googol-ex-grand tethrathoth

E100#^^#100#(1+E100#2)

googolplex-ex-grand tethrathoth

E100#^^#100#(1+E100#100)

grangol-ex-grand tethrathoth

E100#^^#100#(1+E100##100)

gugold-ex-grand tethrathoth

E100#^^#100#(1+E100#^#100)

godgahlah-ex-grand tethrathoth

E100#^^#100#1#2

tethrathoth-minus-one-ex-grand tethrathoth

E100#^^#100#(1+E100#^^#100)

tethrathoth-ex-grand tethrathoth

E100#^^#100#2#2

grand-tethrathoth-minus-one-ex-grand tethrathoth

E100#^^#100#(1+E100#^^#100#2)

grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#3#2

grand-grand-tethrathoth-minus-one-ex-grand tethrathoth

E100#^^#100#(1+E100#^^#100#3)

grand-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#4#2

grand-grand-grand-tethrathoth-minus-one-ex-grand tethrathoth

E100#^^#100#(1+E100#^^#100#4)

grand-grand-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#5#2

grand-grand-grand-grand-tethrathoth-minus-one-ex-grand tethrathoth

E100#^^#100#(1+E100#^^#100#5)

grand-grand-grand-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#1#3

E100#^^#100#(1+E100#^^#100#(1+E100#^^#100))

tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#2#3

E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#2))

grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#3#3

E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#3))

grand-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#1#4

E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100)))

tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#1#5

E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100))))

tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#1#100

E100#^^#100#(1+E100#^^#100#( ... ... (1+E100#^^#100)) ... ... ))

w/100 E100#^^#100s

tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

A modest attempt to extend the tethrathoth using the obvious approach of extending the sequence: tethrathoth, grand tethrathoth, grand grand tethrathoth, three-ex-grand tethrathoth, four-ex-grand tethrathoth, ... etc. This extension however is not as ambitious as it seems! This number is still smaller than a greatethrathoth.

E100#^^#100#100#100

greatethrathoth

E100#^^#100#1#1#2

E100#^^#100#(1+E100#^^#100#( ... ... (1+E100#^^#100)) ... ... ))

w/tethrathoth E100#^^#100s

tethrathoth-ex-grand-tethrathoth-ex-grand- ... ... -tethrathoth-ex-grand tethrathoth

w/tethrathoth "tethrathoth"s

How crazy is that?! This is the sort of number someone might come up with the extend the tethrathoth series given the notation N-ex-grand tethrathoth is the (N+1)th member of the tethrathoth series. Yet it barely taps into the possibilities with Extended Cascading-E Notation (xE^). It's still smaller than a grand greatethrathoth.

E100#^^#100#100#100#2

grand greatethrathoth

E100#^^#100#1#1#3

E100#^^#100#(1+E100#^^#100#( ... ... (1+E100#^^#100)) ... ... ))

w/E100#^^#100#(1+E100#^^#100#(...(1+E100#^^#100))...)) "E100#^^#100"s

w/tethrathoth "E100#^^#100"s

tethrathoth-ex-grand-tethrathoth-ex-grand- ... ... -tethrathoth-ex-grand tethrathoth

w/tethrathoth-ex-grand-...-tethrathoth-ex-grand tethrathoth "tethrathoth"s

w/tethrathoth "tethrathoth"s

This is just insane!!! Yet this is clearly the wrong approach because even torturing language this far doesn't get us as far as a mere grand grand greatethrathoth. This again shows the linguistic approach is vastly inferior to the mathematical approach.

E100#^^#100#100#100#3

grand grand greatethrathoth

E100#^^#100#100#100#100

gigantethrathoth

E100#^^#100#1#1#1#2

tethrathoth-ex- ... ... -ex-grand-tethrathoth-ex-grand tethrathoth

w/tethrathoth-ex- ... ... -ex-grand-tethrathoth-ex-grand tethrathoth "tethrathoth"s

...

w/tethrathoth-ex- ... ... -ex-grand-tethrathoth-ex-grand tethrathoth "tethrathoth"s

w/tethrathoth "tethrathoth"s

where there are a tethrathoth lines

Despite how insane this is, it's still doesn't get one very far. This is still less than a grand gigantethrathoth.

E100#^^#100#100#100#100#2

grand gigantethrathoth

E100#^^#100#100#100#100#100

gorgetethrathoth

E100#^^#100#100#100#100#100#100

gultethrathoth

E100#^^#100#100#100#100#100#100#100

gasptethrathoth

E100#^^#100#100#100#100#100#100#100#100

ginortethrathoth

E100#^^#100##100

E100#^^#100###100

E100#^^#100####100

E100#^^#100#^#100

E100#^^#100#^#100#^#100

E100#^^#100#^#*#100

E100#^^#100#^#*##100

E100#^^#100#^#*###100

E100#^^#100#^#*#^#100

E100#^^#100#^#*#^#*#^#100

E100#^^#100#^##100

E100#^^#100#^###100

E100#^^#100#^#^#100

E100#^^#100#^#^#^#100

E100#^^#100#^^#100

tethratrithoth

E100#^^#100#^^#100#^^#100

tethraterthoth

E100#^^#100#^^#100#^^#100#^^#100

tethrapethoth

E100#^^#100#^^#100#^^#100#^^#100#^^#100

tethra-exthoth

E100#^^#*#7

tethra-epthoth

E100#^^#*#8

tethra-octhoth

E100#^^#*#100

E100#^^#*##100

E100#^^#*###100

E100#^^#*#^#100

E100#^^#*#^##100

E100#^^#*#^###100

E100#^^#*#^####100

E100#^^#*#^#^#100

E100#^^#*#^#^#^#100

E100#^^#*#^^#100

deutero-tethrathoth

E100#^^#*#^^#*#^^#100

trito-tethrathoth

E100#^^#*#^^#*#^^#*#^^#100

teterto-tethrathoth

E100(#^^#)^#100

hecato-tethrathoth

E100(#^^#)^#100#2

grand hecato-tethrathoth

E100(#^^#)^#100(#^^#)^#100

E100(#^^#)^#*(#^^#)^#100

E100(#^^#)^##100

E100(#^^#)^###100

E100(#^^#)^####100

E100(#^^#)^#####100

E100(#^^#)^#^#100

E100(#^^#)^#^#^#100

E100(#^^#)^#^#^#^#100

E100(#^^#)^#^#^#^#^#100

E100(#^^#)^(#^^#)100

E100(#^^#)^(#^^#*#)100

E100(#^^#)^(#^^#*##)100

E100(#^^#)^(#^^#*#^#)100

E100(#^^#)^(#^^#*#^^#)100

E100(#^^#)^(#^^#*#^^#*#^^#)100

E100(#^^#)^(#^^#)^#100

Monster-Giant

E100(#^^#)^(#^^#)^(#^^#)^#100

Super Monster-Giant

E100(#^^#)^^#100

terrible tethrathoth

E100(#^^#)^^#*#100

E100(#^^#)^^#*##100

E100(#^^#)^^#*###100

E100(#^^#)^^#*#^#100

E100(#^^#)^^#*#^#*#^#100

E100(#^^#)^^#*#^^#100

E100(#^^#)^^#*(#^^#)^^#100

deutero-terrible tethrathoth

E100(#^^#)^^#*(#^^#)^^#*(#^^#)^^#100

trito-terrible tethrathoth

E100((#^^#)^^#)^#100

hecato-terrible tethrathoth

E100((#^^#)^^#)^##100

E100((#^^#)^^#)^###100

E100((#^^#)^^#)^#^#100

E100((#^^#)^^#)^#^#^#100

E100((#^^#)^^#)^(#^^#)100

E100((#^^#)^^#)^(#^^#)^(#^^#)100

E100((#^^#)^^#)^(#^^#)^(#^^#)^(#^^#)100

E100((#^^#)^^#)^((#^^#)^^#)100

E100((#^^#)^^#)^((#^^#)^^#)^((#^^#)^^#)100

E100((#^^#)^^#)^((#^^#)^^#)^((#^^#)^^#)^((#^^#)^^#)100

E100((#^^#)^^#)^^#100

terrible terrible tethrathoth

E100(((#^^#)^^#)^^#)^^#100

terrible terrible terrible tethrathoth

E100((((#^^#)^^#)^^#)^^#)^^#100

terrible terrible terrible terrible tethrathoth

E100#^^#>#100

tethriterator

tethrathoth ba'al

ninety-nine-ex-terrible tethrathoth

This number begins to push the limits of LECEN. In xE^ however this can be compactly expressed as E100#^^#>#100, using the new #^^#># delimiter which diagonalizes over LECEN with the fundamental sequence:

#^^#>#[1] = #^^#

#^^#>#[n] = (#^^#>#[n-1])^^#

With this in place it now becomes trivial to move way way beyond LECEN...

E100#^^#>#(1+E100)

googol-ex-terrible tethrathoth

E100#^^#>#(1+E100#100)

grangol-ex-terrible tethrathoth

E100#^^#>#(1+E100#100#100)

greagol-ex-terrible tethrathoth

E100#^^#>#(1+E100#100#100#100)

gigangol-ex-terrible tethrathoth

E100#^^#>#(1+E100#100#100#100#100)

gorgegol-ex-terrible tethrathoth

gulgol-ex-terrible tethrathoth

gaspgol-ex-terrible tethrathoth

ginorgol-ex-terrible tethrathoth

gugold-ex-terrible tethrathoth

gugolthra-ex-terrible tethrathoth

throogol-ex-terrible tethrathoth

teroogol-ex-terrible tethrathoth

godgahlah-ex-terrible tethrathoth

gridgahlah-ex-terrible tethrathoth

kubikahlah-ex-terrible tethrathoth

quarticahlah-ex-terrible tethrathoth

quinticahlah-ex-terrible tethrathoth

sexticahlah-ex-terrible tethrathoth

septicahlah-ex-terrible tethrathoth

octicahlah-ex-terrible tethrathoth

nonicahlah-ex-terrible tethrathoth

decicahlah-ex-terrible tethrathoth

viginticahlah-ex-terrible tethrathoth

nonaginticahlah-ex-terrible tethrathoth

godgathor-ex-terrible tethrathoth

goober bunch-ex-terrible tethrathoth

gralgathor-ex-terrible tethrathoth

thraelgathor-ex-terrible tethrathoth

terinngathor-ex-terrible tethrathoth

godtothol-ex-terrible tethrathoth

graltothol-ex-terrible tethrathoth

thraeltothol-ex-terrible tethrathoth

terinntothol-ex-terrible tethrathoth

godtertathol-ex-terrible tethrathoth

graltertathol-ex-terrible tethrathoth

godpeptathol-ex-terrible tethrathoth

godextathol-ex-terrible tethrathoth

godeptathol-ex-terrible tethrathoth

godoctathol-ex-terrible tethrathoth

tethrathoth-ex-terrible tethrathoth

grand tethrathoth-ex-terrible tethrathoth

Monster-Giant-ex-terrible tethrathoth

Super Monster-Giant-ex-terrible tethrathoth

terrible-tethrathoth-ex-terrible tethrathoth

terrible-terrible-tethrathoth-ex-terrible tethrathoth

terrible-terrible-terrible-tethrathoth-ex-terrible tethrathoth

terrible-terrible-terrible-terrible-tethrathoth-ex-terrible tethrathoth

E100((...((#^^#)^^#)...)^^#)^^#100

w/tethrathoth ba'al "^^#"s

Great and Terrible Tethrathoth

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

tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth

This is as far as I've developed Extended Cascading-E Notation (xE^) at the moment. It's still a VERY VERY VERY VERY ... VERY VERY LONG WAY to pentational arrays. In the next catagory are some unimaginably vast numbers which currently no one quite knows where they should fall on the Fast-growing hierarchy...

Computable Epoch

zeta(0) ~ w_1^CK

Entries: 23

3^^^3 & 3

triakulus

This is the smallest pentational array number Bowers' coins. Currently I'm not entirely certain where it falls on the fast growing hierachy or how much larger it is than the previous entry. All I can say at the moment is that it would have to be much much larger than anything expressible in Limited Extension Cascading-E Notation (LECEN). I believe my Extended Cascading-E Notation (xE^) goes even further than a triakulus, but it remains to be seen how much further. There is currently no consensus on BEAF. There is also no fully formalized definition of "pentational arrays". Although Chris Bird's array notation probably goes much further than this, his system has differences from a hypothetical Bowers' system, and it is not certain what the rules of Bowers' pentational arrays would be like. Solving the problem of Bowers' pentational arrays is an open problem in googology.

10^^^100 & 10

kungulus

A much larger pentational array number.

10^^^kungulus & 10

kungulusplex

The next recursive step for a kungulus!

10^^^^100 & 10

quadrunculus

{10,10,10} & 10

tridecatrix

{10,10,100} & 10

humongulus

This is Jonathan Bowers' humongulus and it is a truly massive value. To define it requires the creation of a general theory for how to apply up-arrow notation to ordinals. I believe that my xE^ notation goes at least this far if not further than {X,X,X}-space. Yet this is just the very beginning...

{10,10,10,10} & 10

tetdecatrix

This is a new googolism created by Bowers' to fill some of the gap between a humongulus and a golapulus. It is much larger than humongulus, though its difficult to describe exactly in what way. This array would have exactly a tetradecal 10s in it's array.

{10,10,10,10,10} & 10

pendecatrix

The next in a sequence of new bowerism's extending from tridecatrix. This number is described by an array with a pentadecal 10s.

{10,10,10,10,10,10} & 10

hexdecatrix

The next logical construction after pendecatrix. This number is an array of {10,10,10,10,10,10} 10s.

7 & 10 & 10

hepdecatrix

Here we have a very early example of nesting the "array of" operator. With just 2 &s , numbers of the form a&b&c already are as strong as SVO (the small veblen ordinal).

8 & 10 & 10

ocdecatrix

The next in a fairly logical and straight forward progression from tridecatrix.

9 & 10 & 10

endecatrix

The last in the logical tridecatrix to endecatrix progression.

10 & 10 & 10

lineatrix

Bowers' breaks with his adaptions of smaller googolism's with his -trix affix. Bowers' doesn't call 10&10 dekadecal either, and instead uses iteral. This suggests iteraltrix, but he doesn't use this either. Instead he names this number lineatrix, from the fact that it's array is formed from "linear" arrays.

(lineatrix) & 10 & 10

lineatrixplex

Bowers' ends his "Lineational Group" with a lineatrixplex. At this point a single recursive step is rather trivial, but it's cool to visualize none the less. It can be imagined as:

{10,10,10,10,10, ... ... ,10,10,10,10,10} & 10 w/lineatrix 10s in the array

Trippy stuff.

The gap to the next Bowerism is huge. He skips LVO, a common benchmark ordinal, entirely. The next bowerism, golapulus, is believed to fall somewhere between LVO and BHO, and may be larger than TREE(3), though due to a lack of a tight upperbound on TREE(3) we can't say for sure this is the case.

TREE(3)

This is a famous large number discovered by Harvey Friedman which at some point supplanted Graham's Number as the largest number ever defined by a professional mathematician. It's value is a consequence of Kruskal's theorem. Take any infinite sequence of labeled trees. There must exist a tree such that it is homeomorphically embeddable in an earlier tree. A consequence of this is that if a sequence of labeled trees has no members homeomorphically embeddable into an earlier tree then the sequence must be finite. Now consider all of these sequences. Friedmann showed that there must be a longest such sequence of trees. Now consider the function TREE(k). It is defined as the length of the longest such sequence of trees using only k-labels. TREE(3) is the length of the longest sequence of trees using only 3 labels. It can be proven that TREE(1) = 1 and TREE(2) = 3 , but TREE(3) is the first non-trivial case and it's such a vast number that even extending the Fast Growing Hierarchy to Gamma(0) or even the Ackermann ordinal is not enough. It has been demonstrated that TREE(k) is at least of order type SVO. A more rigorous bound shows that TREE(k) is at least of order type psi(W^(W^w*w)).

This places it somewhere in the Great Silence between a lineatrix and a golapulus. Whatever TREE(3) turns out to be, it won't collapse like the solution to Graham's problem.

Incredibly this still is not the largest number in professional mathematics ...

*Note: The placement of this number is not precisely known. It has been proven to be larger than lineatrix (under any of the current interpretations), and has a lower bound of phi(w(1)0), but there does not exist any tight upperbound for this number currently, so it is not known for certain to be less than golapulus. Golapulus however is much larger, so it might be unlikely that TREE(3) is larger than it. Perhaps more insight into this will be found in the future. For now I am placing TREE(3) here as it's most likely place in the sequence.

...

THE FIRST GREAT SILENCE

lineatrix ~ golapulus

...

10^100 & 10 & 10

{10,10(100)2} & 10

golapulus

This is a value that just goes way way WAY beyond anything we have yet encountered! It's indescribable with the current techniques I'm employing. It is probably going require the introduction of ordinal collapsing functions.

The gap between this number and lineatrix is just HUGE ... and I don't mean in the usual way. All googolism's are googologically far apart ... but between lineatrix and a golapulus is a great silence. There are no Bowerism's between these numbers. Bowers' makes an increadible leap at this point skipping over a lot of possible inbetween values and jumps straight to this monsterosity! In fact I doubt you'll find many googolism's in the great silence. The systems at this point develop so fast that one can take immediately tremendous leaps into totally new kinds of numbers. A golapulus is just such a "new kind of number". It's not even in the same echelon as lineatrix. It's another breed entirely. An entirely new theory will be needed to reach numbers of this caliber ...

10^100 & 10 & 10 & 10

golapulusplex

golapulusplex takes a leap analogous to the gongulus to the golapulus. Just as golapulus is a gongulus array of 10s (whatever that means), a golapulusplex is a golapulus array of 10s. But make no mistake, this is not a simple recursive step forward like last time. No it's something much much worse. This is the first time that Bowers' uses the plex affix for something other than basic recursion. This could be called a form of ordinal recursion, as it's a way to generate a new much larger ordinal from a smaller ordinal by using an ordinal function. Consequently this number is in a completely different league than a golapulus. We have again made another tremendous leap and skipped ALOT! We have skipped BHO, one of the major milestones, but this is still before the TFB ordinal.

{10&10&10&10&10&10&10&10&10&10}

dekulus

This is a new bowerism. This would already be well beyond a golapulus, or even golapulusplex, though believe it or not, it would still be computable. This is the last of only three entries in the so called "Golapulus Group".

{3,3,3/2}

big boowa

This is Bowers' smallest googolism to utilize the legion bar "/". Bowers' defines {b,p/2} = b&b&...&b w/p bs. So {3,3/2} is {3&3&3} or triakulus. {3,3,2/2} would be {3,triakulus/2}. But this is nothing compare to a big boowa.

{100,100/////.../////2} w/ 100 "/"s

The Big Hoss

Bowers' comes up with a way to apply the legion array trick multiple times and on multiple levels of complexity. This is one example of such a number. We are now way way way beyond the big boowa.

{L100,10}10,10

meameamealokkapoowa

The legions marks can be ranked into a hierarchy of legion marks. This number uses 100th order legion marks. It is the second largest computable googolism of Bowers'.

{{L100,10}10,10&L,10}10,10

meameamealokkapoowa oompa

This is the largest computable number Bowers' has named. It diagonalizes over the strongest version of BEAF that allows for structures of Ls. Despite being frighteningly large, being described as trying to "understand the size of God" in Bowers' own words, there is a good chance it's not the largest known computable number. This honor is probably due to Loader's Number.

D⁵(99)

Loader's Number

Loader's Number is the output of loader.c, a C progam written by Ralph Loader as part of the Big Number Bakeoff and the winning entry. It diagonalizes over the calculus of constructions and is so powerful that it's not even known what level of recursion it employs. It is hailed as the largest known computable number.

Uncomputable Epoch

w_1^CK ~ ????

Entries: 7

Xi(10⁶)

Briefly considered larger than Rayo's Number.

Rayo(10¹⁰⁰)

Rayo's Number

FOOT¹⁰(10¹⁰⁰)

BIG FOOT

????????

croutonillion

????????

Oblivion

????????

Utter Oblivion

Sam's Number

... and so on ...

What's the largest finite number? There isn't one! But that doesn't mean we can just keep going on indefinitely. We can never express ALL the finite numbers, because there is an infinite number of them, so there is a limit to what we can express at any given time. Googology has made incredible progress over the last 200 years. But it really will never be over. As long as there are people interested in large numbers, there will be googology...

... ... ... ...

it never ends ... ... ... ...

and we never reach infinity ... ... ... ...

because it's not a destination ... ... ... ...

it's a direction ... ... ... ...

... ... ... ...

If you really want to skip ahead to infinity go to my FORBIDDEN LIST of Infinite Numbers