# Parity ) * Parity is the property of integers, ℤ * Parity determines an integer's inclusion in "even" or "odd" categories * 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.