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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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"Brevis esse laboro, obscurus fio." (Horace) –  François G. Dorais Feb 3 '13 at 18:33
2  
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
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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

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4 Answers

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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"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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