Surgective and bijective functions
A function is said to be onto, or surjective, iff every element of the
codomain is the image of at least one element of the domain.
An injective function is called an injection.
Example (surgection but not an injection):
A function is said to be a bijection, or a one-to-one correspondence,
if it is both injective and surjective.
Example. Let f(x) = x+1. Is f a bijection?
--- No, if the domain is N.
--- Yes, if the domain is Z or R.