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If a relation is a subset of the Cartesian product of two sets, is there a special term for an individual element of a relation? Might that term be "relationship"?

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  • $\begingroup$ I'd just call it an "element". If you've set things up so that everything is a set, there's no need to invent new words for set-like operations! $\endgroup$ – Billy Feb 27 '18 at 15:53
  • $\begingroup$ Agreed. Each element of a relation is simply an ordered pair of elements of the underlying set. $\endgroup$ – gandalf61 Feb 27 '18 at 16:00
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You might, I suppose, say that the pair $\langle 1, 2\rangle$ is an instance of the 'less than' relation, if you want to say close to informal talk about relations.

(Mind you, call me pernickety, but I'd rather you didn't say the relation is a set of ordered pairs -- the set is the extension of the relation. But that's a sermon for another occasion!)

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  • $\begingroup$ I'm curious about this extension. Do you have a reference to something simple? $\endgroup$ – Jim L. Feb 27 '18 at 16:36
  • $\begingroup$ "Pernickety" is ironic. 😉 $\endgroup$ – Jim L. Feb 27 '18 at 16:39
  • $\begingroup$ What goes here in my remarks about functions math.stackexchange.com/questions/479936/… goes for relations too. $\endgroup$ – Peter Smith Feb 27 '18 at 17:05

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