I recently came across the following expression regarding function composition:
\begin{equation}
g \circ f : A \rightarrow C :: a \mapsto g(f(a))
\end{equation}
I get what this expression is trying to tell me, but I am pretty disturbed by the fact that I don't know what "$::$" means exactly and how to read it. Can anyone tell me what is "$::$"?
Best Answer
In this context it means "defined by", but I've never seen it written like that before. I would have written it "$g \circ f: A \to C$ defined by $a \mapsto g(f(a))$".