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UFNL3


ULTIMATE FINITE 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' goppatothplexIt 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-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
or
 tethrathoth ba'al
or
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.


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 THE FIRST GREAT SILENCE
lineatrix ~ golapulus
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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