# Permutation on infinite set

1. Jun 8, 2009

### guroten

Given a countably infinite set, A, is the set of all permutations of A also countably infinite?

2. Jun 8, 2009

### slider142

Have you learned about Cantor's diagonal slash?

3. Jun 8, 2009

### Dragonfall

No, there are $${\aleph_0}^{\aleph_0}$$ permutations.