Full Idea
Cantor discovered that the continuum is the powerset of the integers. While adding or multiplying infinities didn't move up a level of complexity, multiplying a number by itself an infinite number of times did.
Gist of Idea
The continuum is the powerset of the integers, which moves up a level
Source
report of George Cantor (works [1880]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.14
Book Reference
Clegg,Brian: 'Infinity' [Robinson 2003], p.185