Alright, this is googology world, owned by me, SpongeTechX from googology wiki. I will be showing you guys large numbers, functions, notations, etc. that I have made up.
Operations/Functions
Factorexation
Factorexation is an operation that takes a factorial and exponentiates it by itself. Turn the number that you get into a factorial and exponentiate it by itself, and so on. It's symbol is '''\'''.This is similar to eociration. The pronounciation of''' a \ '''is "A factorexated". The number of \'s signifies how many times you factorexate the number. It is used for hyperoperations.
Examples
· a!^{a!} = b → b!^{b!} = c → c!^{c!} · · · · · a!^{a!} = b → b!^{b!} = a \\ · 2!^{2!} = 2^{2} = 4 → 4!^{4!} = 24^{24} = 1,333,735,776,850,284,124,449,081,472,843,776 = 2 \\ · 3!^{3!} = 6^{6} = 46,656 = 3 \The reason why the operations are notated as "a \" and not "a \ a" is because the "\" signifies how many times you factorexated it, so you don't need to add the other number. It could've been "a \ b", but I decided to use something different. The reason why it isn't "a! \" is because you can't factorexate a number without factorials, so there is really no need for the "!". If you have something like
"a \\\ · · · ", and there are a large number of "\"s, for example, 1000, you would write it as this: "a \^{1000}". Mixed Factorial
Mixed Factorials are a type of factorial where mixed operations are used in the correct order. It is iterated as "n*". An example of a mixed factorial can be represented in the following:
mixed factorial of 4 (or 4*) = 1 + 2 × 3 ↑ 4Whenever you get to 3
^{4}, you take 81 and tetrate it by 5. The number that you get (which is very large, not enough room here) will be pentated by 6. Whatever number you get then, hextate it by 7, and so on. In general, n* = 1 + 2 x 3 ↑ 4 ↑↑ 5 ↑↑↑ 6 . . . (n-2) ↑^{(n-3)} (n-1) ↑^{(n-2) }nWe will now define nested mixed factorials. Let
((( . . . (((n*)*)*)* . . . *)*)*) = n* where there are m *'s. _{m}n* = n*_{1}, (n*)* = n*_{2}, ((n*)*)* = n*_{3}, etc. For farther extension, we can say n*with _{n*n* . . . n*n*n} m n*'s = n*_{(n,m)}. n*, _{n*n} = n*_{(n,2)}n*_{n*n*n} = n*_{(n,3)}, etc.Numbers
Tetrafact
Tetrafact is the mixed factorial of 4, written as
4*.Pentafact
Pentafact is the mixed factorial of 5, written as
5*.Centifact
Centifact is the mixed factorial of 100, written as
100*.Double Centifact
Double Centifact is the 2nd mixed factorial of 100, written as
100** or 100*^{2}Triple Centifact
Triple Centifact is the 3rd mixed factorial of 100, written as
100*** or 100*^{3}Quadruple Centifact
Quadruple Centifact is the 4th mixed factorial of 100, written as
100**** or 100*^{4}^{Quintuple Centifact, Sextuple Centifact, etc.}Hypergraham
Hypergraham is a number equal to
G(G(G(G . . . G(64))) . . . ))), using the same method as G(64), G(G(64)), etc.graham's numberHypercentifact
Hypercentifact is equal to
100* in extended mixed factorials. ^{[100,100]}Duo-hypercentifact would be
100*, trio-hypercentifact would be ^{[100,100:2]}100*, and so on.
^{[100,100:3]}Ultracentifact
Ultracentifact is equal to 100* in extended mixed factorials.^{[100,100:100]} |