Surjective function

by Patrick Stevens Jun 14 2016 updated Jun 14 2016

A surjective function is one which "hits everything in the codomain".

A function $~$f:A \to B$~$ is surjective if every $~$b \in B$~$ has some $~$a \in A$~$ such that $~$f(a) = b$~$. That is, its codomain is equal to its image.

This concept is commonly referred to as being "onto", as in "The function $~$f$~$ is onto."