"invertible function" is the same thing as "one to one correspondence" which is the same thing as "bijection"?

Question

It looks like "invertible function" is the same thing as "one to one correspondence" which is the same thing as "bijection" ... so why is there three words for one thing? Seems useless

Answer 1

The indentity map from Q into R is injective (1 to 1 as neophites call it) but it is not invertible (except as that computerist fantansy of a partial function).

Answer 2

• Two predicates ( here " being invertible" and " being bijective") may have the same extension ( apply to exactly the same set of objects) while being intensionally ( conceptually) different.

• It would make no sense to atttempt at showing that all bijective functions are bijective.

But it makes sense to prove that all bijectve functions are invertible, and reciprocally.

The conceptual distinction justifies the existence of 2 distinct terms.