possibly a related question on infinite sets is in physics arxiv . org 1208.5424 (s. shelah, etc.) which i think is about whether there are infinite cardinals or sets called p and t (etc.) in between the integers (countable inifnity) and the continuum. the answer there seems to be if there are then there is only one so p=t for all p, t between aleph 0 and the continuum.
i had to look up injective, surjective, recently but I have to look them up again. One means its 1 to 1 (like an isomorphism) , the other is many to 1 (like a homomorphism) if i recall. I like 'self-inverse functions' , and also 'inverse problems' (eg marc kac 'can you tell the shape of a drum by how it sounds')