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Is there a shorter notation for

Pairs of all items $\{ x, y, z \}^2$ without $\langle x,x \rangle$, $\langle y,y \rangle$, $\langle z,z \rangle$

i.e. given an arbitrary set of items, construct all possible pairs of those items excluding pairs which have the same item on the left and right side?

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    Hey Ellie! There is no special notation in mathematics known as "concise notation." Rather, the word "concise" is a very general adjective here that roughly means "expressing a lot of information in very few symbols," or "saying a lot with very little." People like notation that's concise because it's easy and looks nice. (You don't have enough reputation points to post a comment, so I'll flag a moderator to turn it into one for you. If you have any more questions feel free to try again here.) Hope that helps,2012-01-27

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I don't think you'll get much more concise than either your own proposal or $\{\, \langle x,y \rangle \in A^2 \mid x \ne y \,\}$ if you want to be understood without spending ink defining your notation first.

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    By the same generalization, $A^{\underline{2}}$ or $(A)_2$ (both borrowed from notations for falling factorials) could work for this. They would certainly need an explicit definition in-text, though.2011-09-03