User:Alemagno12/B Function

The B function is a function that uses numbers as an input, and ordinals as an output, via the X hierarchy. Here, I explain it.

Definition of the B Function
In X hierarchy, we apply operators to X to increase it's value.

Here, in the B function, we can replace X with n, and it will give us the ordinal value of the X hierarchy equivalent.

Up to w
This is easy.
 * n=n

Up to w^2
WIP!
 * 1) X=sup(0,1,2,...)=w
 * 2) X*(n+1)=sup(X*n,X*n+1,X*n+2,...)