# Word for two collections that do not have any elements in common

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:

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.

• 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
Commented Nov 7, 2014 at 12:25
• I might describe them as distinct sets, but as that already appears in your question, you may have already considered that
– Alo
Commented Nov 7, 2014 at 13:41

You want disjoint, as in "disjoint sets".

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
Commented Nov 7, 2014 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.

• 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. Commented Nov 7, 2014 at 17:33
• 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. Commented Nov 7, 2014 at 21:13
• (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. Commented Nov 8, 2014 at 4:09