[Tex/LaTex] Mapsto vs. rightarrow

Question

This is perhaps half a math question and half a typesetting one. In what circumstances do I use \mapsto and when \rightarrow? I feel like the standard seems to be: when you're specifying the operator you use \rightarrow, but if you're just saying that one domain maps to another you use \mapsto. Is that correct?

e.g. I would say Q\times\Gamma\mapsto Q but \delta:Q\times\Gamma\rightarrow Q.

Answer 1

You use \mapsto to denote the actual function mapping. For example, consider the function $f:\mathbb N\to\mathbb N$ given by $f(n)=5n$. You could write that second part as $n\mapsto5n$.