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For instance for male or female the comparable word would be sex. What is the word that means the state of being either even or odd (referring to numbers)?

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Parity

  1. Mathematics (of a number) the fact of being even or odd.

(Oxford Dictionaries)

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    Also, in computing (from the same reference) : A function whose being even (or odd) provides a check on a set of binary values. – Nigel J Mar 12 '18 at 9:30
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    @Nigel J - That's an important distinction: the computing sense of 'parity' normally refers to whether the number of 1's in the binary representation of the number is even or odd, independently of whether the number itself is even or odd. (e.g. In the computing sense, the number 2 has odd parity.) – Jeremy Mar 12 '18 at 13:59
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    @Jeremy That is indeed the usage of a parity bit, but "parity" in this context refers not to any "parity" of any number represented by those bits, but rather to the parity of the number of bits that are 1. This accords with the sense given by Rupert. Why, the word "parity bit" is used without referring to the collection of bits as representing a number at all. IME the term used for the number of bits that are 1 in a collection of bits is "Hamming weight" or "weight". – Rosie F Mar 13 '18 at 8:04
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    Rosie F's comment sums it up; the other comments indicate that there is often an overloading of the word among certain tech circles but it seems to be more of a contraction that discards the precise context (of being the parity of a Hamming weight). Zebedee's answer that "parity" would not be understood outside of computing circles is thus not the whole situation: plenty of people know the word outside of computing, and it seems plenty of technical specialists are at least slightly ambivalent toward the word's actual definition. – Darren Ringer Mar 13 '18 at 20:02
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What about simply evenness? I think this would require less explanation than parity. If you mentioned parity to a non-mathematical readership, you'd definitely have to explain what was meant.

According to Wiktionary, evenness means:

The quality of being even.

https://en.wiktionary.org/wiki/evenness

and obviously one of those meanings of even is the one you're referring to.

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    This doesn't answer the question. The definition you cite shows that "the evenness of n" means "the quality of n being even". So readers would understand that you were asserting that n is even. The OP wants a word which refers to whether n is odd or even, without asserting which it is. – Rosie F Mar 13 '18 at 7:57
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    @RosieF A lot of words work that way. For example, the Mohs hardness scale is used to describe both hard and soft things, and we can talk about the truth(fulness) of statements even if we expect some of them to be false. – 1006a Mar 13 '18 at 23:02
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    Evenness sounds a lot less odd than oddness. – Andrew Grimm Mar 14 '18 at 3:33

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