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Sets whose intersection is the empty set are called disjoint. What is the opposite of a disjoint set? For example the sets $\{1,2\}$ and $\{2,3\}$ satisfy this condition. I know that you can just say not-disjoint. But I was wondering if there was a specific term for it. I ask this because someone told me that this term existed but that he could`nt remeber. I have searched extensively but I haven't found it.

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    I always say two sets "intersect" or that they "have nonempty intersection".2012-07-10
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    "Non-disjoint".2012-07-10
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    They are joint!2012-07-10

2 Answers 2

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You seem to be looking for an adjective meaning the opposite of disjoint. Given two sets that aren't disjoint, I would just call them intersecting sets, where intersecting is an adjectival participle derived from the verb to intersect.

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If $A\cap B \not= \emptyset$, I say, "$A$ meets $B$."

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    I don't just say this, Erdos does: http://www.renyi.hu/~p_erdos/1955-14.pdf (Proof of Theorem 2). Pontryagin also uses the term in his topology book. I learned the term from topologists at the University of Texas back in the 80s. It is a descriptive and useful one. I do not understand the downvote.2012-07-10
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    @Norbert: seriously?2012-07-16
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    @Asaf Karagila, Seriously.2012-07-16
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    Is there any notation you can use to indicate this? I recall seeing `$A\uparrow B$` but I cannot find it back2015-09-18