[pwdisswordfish]

> Let X be infinite.

That assumption is unnecessary. Cantor's theorem works just as well for finite sets: it's simply the statement that 2ⁿ > n.

[Smaug123]

True, thanks. I thought the proof I knew of Cantor only worked for infinite sets, and that a separate proof was required for the finite case; but actually the same proof works for both.