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I'd like to know the syntax for describing a number of elements in a set, and that each of them are distinct. e.g.

{$x,y,z$} $\in A$

I would like to know how I can succinctly express the following, without having to write it out as such:

$ x \neq y \;\;\;\; x \neq z \;\;\;\; y \neq z$

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closed as off topic by Goldstern, Chris Godsil, GH from MO, Todd Trimble, François G. Dorais Feb 3 '13 at 18:29

Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.

"Brevis esse laboro, obscurus fio." (Horace) – François G. Dorais Feb 3 '13 at 18:33
For three elements, $x\neq y\neq z\neq x$ expresses the inequalities in 7 symbols. For four elements, this linear-string approach takes 15. For five, it can be done in 21, and in general, for any odd number $n>1$, it can be done in $n(n-1)+1$ symbols (although I suppose you might run into trouble at $n=27$). Curiously, the OEIS does not (yet) have an entry extending $3,7,15,21$ with both $43$ and $73$ in the proper place. – Barry Cipra Feb 5 '13 at 17:53
up vote 2 down vote accepted

"Let $x,y,z,$ be pairwise distinct", is perfectly fine.

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"Let $x, y, z$ be distinct" is enough.

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Is it? – BCLC Dec 6 '15 at 17:34

"Let $\lbrace x,y,z \rbrace$ be a set with exactly three elements."

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{x,y,z} $\cong3$ or |{x,y,z}| $=3$

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