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.
opposite of disjoint
12
$\begingroup$
elementary-set-theory
terminology
-
5I always say two sets "intersect" or that they "have nonempty intersection". – 2012-07-10
-
7"Non-disjoint". – 2012-07-10
-
10They are joint! – 2012-07-10
2 Answers
7
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.
10
If $A\cap B \not= \emptyset$, I say, "$A$ meets $B$."
-
1I 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
-
3@Norbert: seriously? – 2012-07-16
-
0@Asaf Karagila, Seriously. – 2012-07-16
-
1Is there any notation you can use to indicate this? I recall seeing `$A\uparrow B$` but I cannot find it back – 2015-09-18