User blog comment:Superman37891/Explain Rayo please/@comment-29915175-20170622003509

Let me see if I can try.

First Order Set Theory is one of those languages you're talking about. It has many symbols and is very strong, and can encode pretty much any Turing machine. So the Rayo function diagonalizes over First Order Set Theory by specifying the largest finite number that can be expressed using that language with at most X symbols. So Rayo (1) would be the biggest number you could express in First Order Set Theory using one 1 symbol, etc. Rayo's number is Rayo(Googol), so the largest number expressed in a Googol symbols. It's very strong because it can exceed any Busy Beaver type function.