Difference between operators and functions Binary operators are maps on a set into itself, for example $* : R \rightarrow R$. There are also unary and trinary operators.
What is the difference between, say a trinary operator of three arguments, and a function of three arguments?

First of all, a binary operator takes two arguments (hence binary), so you want $\ast : R\times R \to R$.
The difference between a ternary operator on $R$ and a function of three arguments on $R$ is the codomain; the former has codomain $R$ (i.e. $R\times R\times R \to R$), whereas the latter could have a codomain other than $R$ (i.e. $R\times R\times R \to S$).
