##
Is the Rayo of Graham's number larger than the Rayo of TREE(3)? Could we ever know?

I was thinking. Rayo's number, which is meant to be the largest finite number ever concieved, is defined as:

**The smallest number bigger than any number that can be named by an expression in the language of first order set-theory with less than a googol (10^100) symbols.**

Rayo's number must exist somewhere. Presumably we don't have the symbols to express it yet.

But there must be a method to attain a "provisional Rayo" based on the current symbols we have.

The largest numbers we know of are Graham's number, TREE(3) and SSSGC(3).

Graham's number can be written very simply as G_{64}.

Presumably though, we could extend that notation to higher "powers":

G_{G}

_{ 64} etc, a googol times.

Doing so only increases the already small number of digits by one each time.

To do the same to, say, TREE(3) you would have to add five symbols: TREE(TREE(TREE, plus god knows how many closing brackets.

So even though TREE(3) is a much larger number than Graham's number, is Rayo Graham larger than Rayo TREE(3)?

Last edited by parallaxicality; 2021-May-05 at 05:59 PM.

"Occam" is the name of the alien race that will enslave us all eventually. And they've got razors for hands. I don't know if that's true but it seems like the simplest answer."

Stephen Colbert.