# Parity

[https://en.wikipedia.org/wiki/Parity\_(mathematics](https://en.wikipedia.org/wiki/Parity_\(mathematics))

* Parity is the property of integers, ℤ
* Parity determines an integer's inclusion in "even" or "odd" categories&#x20;
* An integer is even if it is divisible by 2, else it is odd
* formally, an even integer is the one that can be expressed as `n = 2k`
* formally, an odd integer is the one that can be expressed as `n = 2k + 1`

According to the formal definition, with `k ∈ ℤ`, an even integer is the one that can be expressed in the form `n=2k`. An odd integer is the one that can be expressed either as `n=2k+1` or `n=2k-1`.

To express odd natural numbers, where `k ∈ ℕ`, only the form `2k+1` can be used if 0 ∈ ℕ (otherwise, we'd get -1 for k=0). However, if 0 ∉ ℕ then only the form `2k-1` can be used (otherwise, we couldn't get 1 at all).

In numeral systems with an even base, a number is even if its LSD is even.

In an odd base, the number is even according to the sum of its digits - it is even iff the sum of its digits is even.

[https://en.wikipedia.org/wiki/Parity\_of\_zero](https://en.wikipedia.org/wiki/Parity_of_zero)
