Full Idea
Frege shows that the number of natural numbers is not identical to any natural number. This is because, while no natural number is identical to its successor, the number of natural numbers is.
Gist of Idea
The number of natural numbers is not a natural number
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2
Book Reference
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.41
A Reaction
Frege is notorious for the lack of respect shown in his writings for the great Cantor, and this seems to have blocked him from a more sophisticated account of infinity, but this idea seems a nice one.