I'm working with injective functions and I'm trying to prove that the cardinality of the domain of a function is equal to the codomain of the same function.
Each input value is mapped to a different output value, so it would be true unless there can be output values that aren't mapped?
Basically my question is, can there be output values that aren't mapped to input values?
Edit: the function I am trying to figure this out for is stated as being just $f: X \to Y$. I then have to prove the theorem that the domain of function f is equal to the codomain of function f.