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A function that turns a real number into another real number can be represented like $f : \mathbb{R}\to \mathbb{R}$

What is the analogous way to represent a function that turns an unordered pair of elements of positive integers each in $\{1,...,n\}$ into a real number? I guess it would almost be something like $$f : \{1,...,n\} \times \{1,...,n\} \to \mathbb{R}$$ but is there a better notation that is more concise and that has the unorderedness?

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    I have seen $[n]$ for $\{1,2,3,\ldots n\}$ but it is always defined, not considered standard like $\mathbb{R}$. You could extend your function to be on ordered pairs by symmetry, but maybe that obscures a point you want to make.2011-10-21
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    you may also consider set of unordered pairs as a triangle $X = \{(i,j): 1 \leq i\leq j \leq n\}$ but it maybe also obscuring.2011-10-21
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    If $X$ is any set you may denote the set of unordered pairs of elements of $X$ by ${X\choose2}$. So your function can be described as $f:\ {[n]\choose 2}\to{\mathbb R}$.2011-10-21
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    @Christian: I generally see ${X \choose 2}$ used to denote the set of _subsets_ of $X$ of size $2$, which is very close but not quite the same thing.2011-10-21
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    @Qiaochu Yuan: I don't know whether you can call a singleton $\{a\}$ an "unordered pair". The OP will have to decide what he actually meant.2011-10-22

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