Two sets are isomorphic to each other

[zcdfhn]

I think I had a moment of insight when I was learning about isomorphisms and I just need people to verify what I think I figured out.

So I was thinking if two sets are isomorphic to each other does that mean ANY bijective function from one set to the other is an isomorphism?

Thank you for your help.

 

[Hurkyl]

"Bijection between sets" is synonymous with "isomorphism of sets".