what does this mean? ($ f : A \to B$)

Question

I know that $f : A \to B$ means the function is mapping $A$ to $B$.

My question is that when I say cardinality of $B$ is $x$, then does the x mean total numbers of elements present in $B$ or does it mean that total number of elements getting mapped?

Thank You Any help appreciated.

Answer 1

For finite sets, the carinality of $B$ represents the number of elements which can be potentially but not necessarly reached by $f$.

When all elements of $B$ are reached we say that $f$ is a surjective function.