Full Idea
We write F : A → B to indicate that A maps into B, that is, the domain of relating things is set A, and the things related to are all in B. If we add that F = B, then A maps 'onto' B.
Gist of Idea
We write F:A→B to indicate that A maps into B (the output of F on A is in B)
Source
Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0)
Book Reference
Enderton,Herbert B.: 'A Mathematical Introduction to Logic' [Academic Press 2001], p.5