I'm looking for a word for when you have a collection A and a collection B and they have no overlap.

In mathematical terms: the relation between two sets where the intersection is empty. Like in this Venn diagram:

Empty intersection

The word that keeps popping up in my mind is disparate sets, but I don't feel that completely covers the meaning when I look at the definition, because that doesn't seem to preclude overlapping sets that are different:

disparate 1. distinct in kind; essentially different; dissimilar: disparate ideas.

  • 1
    Disparate is usually applied to a group of items which contain elements which have little in common. The United Nations has a disparate membership. – WS2 Nov 7 '14 at 12:25
  • 1
    I might describe them as distinct sets, but as that already appears in your question, you may have already considered that – Alo Nov 7 '14 at 13:41

You want disjoint, as in "disjoint sets".

From Wolfram Mathworld:

Disjoint Sets

Two sets A1 and A2 are disjoint if their intersection A1 ∩ A2 = ∅, where ∅ is the empty set.

Disjoint sets are also said to be mutually exclusive or independent.

  • This answer includes the words I would use most often. I also hear the word unrelated used for this case. – jxh Nov 7 '14 at 18:26

You might consider orthogonal

Very different or unrelated; sharply divergent: "Radical Islamists are ultimately seeking to create something orthogonal to our model of democracy" (Richard A. Clarke). [American Heritage]

This suggest something very different, not just non-overlapping.

  • 1
    I would use orthogonal when the criteria for one set are disjoint with the criteria for the other; in a sense, when the two sets cannot be meaningfully compared. Not apples vs. oranges but apples vs. a list of dictionary words. – J. C. Salomon Nov 7 '14 at 17:33
  • 2
    It may be worht pointing out that many mathematicians use "orthogonal" as a synonym for "unrelated", often in a tounge-in-cheek manner. (I can't say for the rest of the population). This being said, I would imagine two "orthogonal" things to have as much in common as two random things. Orthogonal lines meet in one point, not zero. – Jakub Konieczny Nov 7 '14 at 21:13
  • 3
    (Following from @Feanor's point) Orthogonal means "right-angled". While for some things this might imply "very different", for others it will imply "completely independent". Most people with a STEM background will assume the latter. In the following examples "x" indicates orthogonality: tall-short x thin-fat x lawful-unlawful x good-evil x capitalist-communist x liberal-conservative. Despite every attribute being orthogonal, short, overweight, lawful-"morally questionable", conservative communists do exist. – DeveloperInDevelopment Nov 8 '14 at 4:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.