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I've come across the term "pairwise distinct" in many research papers. But, I don't understand how it differs from just saying that the elements of a set are unique instead of saying that they are pairwise distinct. Can someone please explain the difference, if any, to me?

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    Well, not a research-level question...But, here's my two cents: They are equivalent, but sometimes saying "pairwise distinct" saves you a few words. For instance, consider this sentence: "for any pairwise distinct $x_1, \ldots , x_n$".2011-02-27
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    migrating to math.SE2011-02-28
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    I guess it is redundant to say "pairwise distinct" for a set since all the elements of a set are unique.2011-02-28
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    There may also be a slight verbal advantage in saying "pairwise distinct" if you intend to use a result of the form "for distinct $a$ and $b$ ..." for each choice of $a=x_i$ and $b=x_j$, $i\neq j$.2011-02-28

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