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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Is my proof correct?

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**