Originally Posted by

**Moo** No, it was by email, so I am sure he said it (Worried)

Actually, there exists a *bijection* from the set of even numbers into the natural numbers.

I guess it's even what you call "identity function" :

f : 2N -> N

2n -> n

It may sound weird, but this is a bijection :

- f(n)=f(m) <=> 2m=2n <=> m=n. This is an injection.

- n in N => there exists m in 2N such that f(n)=m, namely m=2n. This is a surjection.

Hence f is a bijection.

This is why I added "injection but not surjection"

urgh ! I forgot it again !