\begin{definition}[Definition:Prime Enumeration Function]
Let the function $p: \N \to \N$ be defined as:
:$\map p 0 = 1$
:$\map p n =$ the $n$th prime number
This function is called the '''prime enumeration function'''.
Note, of course, that although $\map p 0 = 1$, there is no suggestion of treating $1$ as prime (it definitely is not).
\end{definition}