# Is my proof correct?

1. Sep 12, 2011

Suppose that f is a one-to-one correspondence between two sets X and Y. Prove that if X is finite, then Y is finite too.

my proof: I've already proved that if X is infinite, then Y is infinite too. since f is a one-to-one correspondence, f-1: Y->X exists and by applying the same theorem it can be shown that if f:X->Y and Y is infinite, then X is infinite as well.so, I can claim that if f is a one-to-one correspondence, then X is infinite if and only if Y is infinite. hence, It's possible to say that if f is a one-to-one correspondence between the two sets X and Y, then X is finite if and only if Y is finite.
Is my proof correct?

2. Sep 12, 2011

### micromass

Yes, your proof is correct (once you know that infinite = not-finite). Though, it might not be the shortest proof available. That is, that you proved it by making use of infinite sets is suprising.

3. Sep 12, 2011