# shortest notation for “set of all maps from $A$ to $B$”?

I usually write the following:

$$\{m| m:A\to B\}$$

Is there a more succint notation?

The standard notation is $B^A$.

• Thank you. Does this notation have a name? – user56834 Apr 29 '18 at 6:49
• Wikipedia doesn't list any name. – Yuval Filmus Apr 29 '18 at 6:52
• @Programmer2134 Although I can't find a name, this notation seems to be derived from cardinal exponentiation and is related to the common notation of $2^B$ for the powerset of $B$. So, if you want to give a name for the notation, something like "function exponentiation notation" or "powerfunction notation" might work. Then again, a lot of notation is generally unnamed and this isn't seen as a problem. – Discrete lizard Apr 29 '18 at 9:36

$A \to B$ is a common notation for the set of functions. For instance

$$\begin{array}{l} f : (A\to B)\times A \to B \\ f(g,x) = g(x) \end{array}$$