Some googologisms here might be ill-defined or not even defined at all. As i said, this is pointless.
Himself = 1
nHimself = n
Himself<n> = Himself<n-1>Himself
Himself<0,1> = Himself<Himself>
Rest of rules apply like TaN, but replacing f(n) with nHimself and n with Himself.
Failed attempts at googological cheating
The smallest positive integer not definable in the smallest positive integer not definable using ASCII characters
The smallest positive number that cannot be computed by any means
The smallest positive number that cannot be defined by any means
The largest positive number (excluding this one) + 1
N = M, M = N
N = N+1
Everyone else's number + 1
N changing over time
A bunch of complicated messup
N = M+1 for some large M
Something that contains infinity
More common fails
Sumbitted by a wikia contributor
Freakingly big number.
Ten to the tenth tesseract.
The number so that ball is true and orange is false.
Eleven plus something.
The last number used by humanity until now.
Inverse of factorial divided by two.
First number which doesn't fit in entire Universe. Multiplied by the number of Multiverse.
Seventeen. Just seventeen. Eat it.
The most undefined number ever spoken by human being.
The largest number which can be named by English language with a billion symbols.
The last number used by humanity until now. Now is now equal to three.
Number which equals to a result of stupendously fast-growing function.
The smallest number which is not small.
The number with the most sensible definition ever. It also must be sensible in all its definitions.
The smallest number about which people will never know.
Number which is neither small nor big. Also nobody should care whether this number is small or big.
The largest number about which nobody cares.
Size of the smallest mountain on Earth.
Define tree to be high rooted structure. Take the factorial of three and multiply it by tree.
The first number about which we can talk seriously in this list.
Number of busy beavers with three states.
Number of words in this sentence.
Hundredth term of sequence: one, five, zero, two, nine, eight, etc.
One divided by the smallest number which everyone ever had in mind.
H(1) = infinity
H(n) = infinityn
H(n,1) = H(n)
H(1,m) = H(H(...(H(m,m-1),m-1)...),m-1) with n levels of nesting
H(n,m) = H(1,m)n
# = rest of expression
0 --> End of game
#0 --> #
#1 --> #00
#(#) --> ##
#~ = The number of steps it takes to decompose #
Extended Binary Hydra
#2 --> #11
#3 --> #22
#4 --> #33
#5 --> #44
#6 --> #55
#7 --> #66
#8 --> #77
#9 --> #88
Unet = 0~
Biet = 1~
Triet = 2~
Tetraet = 3~
Pentaet = 4~
Hexaet = 5~
Heptaet = 6~
Octaet = 7~
Enneaet = 8~
Decaet = 9~
Sebros Sah = 0123456789~
Cyblorgly Sebros Sah = 0123456789876543210~
Sebros Ah = 123456789~
Cyblorgly Sebros Ah = 12345678987654321~
Retollieseauts = 40823095213834643096489350435~
Retollieseautser = 4082309521383464309648935043534590439503492308213032853405934028394023490582430589304823058~
Retollieseautserest = 4082309521383464309648935043534590439503492308213032853405934028394023490582430589304823058248398394893489234892348039248309482340982340823048230948230948230948023579324893248932580932580235804386950438504395804395809435809347534096823094732095750436804823402325836809473523048045684068046803458034585894589435834058320482~
Mom = 01010101010101010101~
Dad = 10101010101010101010~