Well-defined Sam's Number

Check out the original source of Sam's Number at Googology Wiki.

Member: 1 (this one!)

I define the more well-defined version of the Sam’s number, since the original version of the Sam’s number is completely ill-defined and is not classified as an uncomputable number.

Here the definition of the more well-defined Sam’s number:

1. First, I define Sam(0) to be equal to Oblivion, and Sam(1) to be equal to Utter Oblivion.

2. Sam(n) is defined as "the largest finite number that can be uniquely defined using no more than Sam(n - 1) symbols". For example, Sam(2) is defined as "the largest finite number that can be uniquely defined using no more than Utter Oblivion = Sam(1) symbols"; Sam(3) is defined as "the largest finite number that can be uniquely defined using no more than Sam(2) symbols", and so on.

3. Sam[m+1](n) = Sam[m]^(Sam[m]^(...^Sam[m](n))(n))(n) where there are n Sam's.

4. Sam[A](n) = Sam[A[Sam(n)]](n) where A is a limit ordinal.

My Sam’s number is Sam[ω(ε(ω_1CK×f[ψ(K)×E100#100#100](Rayo(10^100))))CK](Large Number Garden Number)

That’s a salad number!

It is an ill-defined uncomputable number beyond Utter Oblivion. Its ill-definedness is simply Jonathan Bowers' Oblivion and Utter Oblivion are unformalized, although it is intended be larger than Rayo's number and Large Number Garden Number.

Other names

• Sam Number / Sam number

• Dead Sam

• Death Sam

• Sammy Pranker

• Sammy Hoaxer

• Derpy Sam

• Sammy Rayo

• Ultra Sam

• The Dead Jokers

• S.A.M Number / S.A.M number

Other capitalizations

These alternative capitalizations are meant to serve as a joke with stronger irony.

• SAM'S NUMBER

• SAM NUMBER

• SaM'S NuMBeR

• sAm's nUmbEr

• Sam's numbeR

• SAm'S nuMBeR

• SaM's NumbeR

• Sam'S NumbeR