# Thread: Injective and Surjective sets

1. ## Injective and Surjective sets

The proposition I'm supposed to prove states that let A,B be sets. There exists an injection from A to B if and only if there exists a surjection from B to A. I don't really know where to start , I want to prove it from both directions. And I know the definitions but I keep getting confused with the functions.

2. Originally Posted by nataliemarie
The proposition I'm supposed to prove states that let A,B be sets. There exists an injection from A to B if and only if there exists a surjection from B to A. I don't really know where to start , I want to prove it from both directions.
This is a completely standard theorem.
Any respectable textbook should give you a lead up to its proof.
Please respond with exactly you do not understand.
I hope that you do not expect us to supply the proof.

3. well its not really a published text book its still being revised so i dont know how respectable it is. and i was going to try to use the fact that if its injective it has a left inverse but i dont know if i can just assume that there is an left inverse function g from B to A such that g(b) = a when f(a)=b because then thats assuming that the function f is surjective too isn't it. I just really needed a hint as to where to start thats all. Because my brain is going in circles and confusing itself.