\begin{definition}[Definition:Parity of Integer]
Let $z \in \Z$ be an integer.
The '''parity''' of $z$ is whether it is even or odd.
That is:
:an integer of the form $z = 2 n$, where $n$ is an integer, is of '''even parity''';
:an integer of the form $z = 2 n + 1$, where $n$ is an integer, is of '''odd parity'''.
:If $z_1$ and $z_2$ are either both even or both odd, $z_1$ and $z_2$ have '''the same parity'''. 
:If $z_1$ is even and $z_2$ is odd, then $z_1$ and $z_2$ have '''opposite parity'''.
\end{definition}