\begin{definition}[Definition:Euler Phi Function]
Let $n \in \Z_{>0}$, that is, a strictly positive integer.
The '''Euler $\phi$ (phi) function''' is the arithmetic function $\phi: \Z_{>0} \to \Z_{>0}$ defined as:
:$\map \phi n = $ the number of strictly positive integers less than or equal to $n$ which are prime to $n$
That is:
:$\map \phi n = \card {S_n}: S_n = \set {k: 1 \le k \le n, k \perp n}$
\end{definition}