Definition:Parity of Integer
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Definition
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.
Also see
Sources
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: A Little Number Theory
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): parity