Eli5- what exactly is Rayo’s number?

Question

Eli5- what exactly is Rayo’s number?

In: 1

Answer 1

It’s a very large number with no particular significance aside from being very large.

Roughly speaking, it says:

* Given a set of logical tools to make statements about numbers and constants, you can uniquely define a lot of numbers. Now, limit yourself to writing only definitions of at most 10^100 symbols in that language. This is a finite number of statements, so they can only define finitely many numbers. Rayo’s number is one more than the largest number they can define.

This definition turns out to result in an absolutely enormous number.