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I am looking for a word to denote an element in a binary relation, which in itself would connote the duality of the relationship. For example, a binary relation is the one between the east and the west half of a sphere so we call each a hemisphere:

From Latin hemisphaerium, from Ancient Greek ἡμισφαίριον (hēmisphaírion), from ἡμι- (hēmi-, “half”) + σφαῖρα (sphaîra, “sphere”); hemi- +‎ sphere

So I am looking for a more abstract/general word (that could be applied to something other than a sphere) that would indicate that the entity in question is one of the two sides in a binary relation and would like that word to unambiguously mean that (and remove the possibility of having more than two sides) and that it's not necessarily half because that implies a 50/50 split, which shouldn't be implied by that word.

Another example could be the word wife meaning (in a traditional sense) one of the two spouses in a marital binary relation: "the wife is a [X] of the marriage"

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  • The best I could do is choice and option, neither of which implies a binary set of options. May 18, 2017 at 21:47
  • I'm sorry, that won't cut it
    – amphibient
    May 18, 2017 at 21:48
  • Yeah, I wanted to exclude those answers explicitly for you. As a side note, wife is not always an example of your desired word. 8^) May 18, 2017 at 22:04
  • The two sides of a binary relation (or any relation) are sets. One side is sometimes called the domain (of the relation); the other is sometimes called the range (of the relation).
    – Drew
    May 18, 2017 at 23:09
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    If you want the math, formal choice, it would be exactly as you have presented it, an element. A relation is an ordered pair on a set, so one side of a the pair is a member of the set, which is called an element. But if you want to fill the slot, "the wife is a member of a marriage" is more natural.
    – Mitch
    May 18, 2017 at 23:15

2 Answers 2

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Specifically in a relationship where there are only two things, both items are each other's complement:

complement

1c: one of two mutually completing parts

In the case of 2 things, it's unambiguous, but the idea can apply to more than 2 items in mathematics. For example, if there are 10 possible items but only 3 exist right now, the complement of those things is 7 items, which is how many would be required to make the whole (ten items).

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  • looks promising...
    – amphibient
    May 18, 2017 at 22:08
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If you want the mathematical, formal choice, it would be exactly as you have presented it, an element. A relation is an ordered pair on a set, so one side of a the pair is a member of the set, which is called an element.

The wife is one element of a pair that forms a marriage

But if you want to fill the slot in normal everyday language there are many possibilities but I find member sounds the most natural and generic

The wife is a member of a marriage.

Other possibilities are 'partner', 'one side', 'spouse' (specific to marriage). I think the best answer will almost always depend on the context.

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  • None of those actually connote duality
    – amphibient
    May 19, 2017 at 13:48
  • @amphibient Can you give another sentence with a slot where that connotation would be appropriate?
    – Mitch
    May 19, 2017 at 15:19

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