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How would one denote the set of all subsets of $A$ which have size $2$?

Would $$\binom{A}{2}$$

be a good idea?

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    I believe the notation is $[A]^2$. Or atleast, we are using it in our set theory class.2012-02-24
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    With nonstandard notation (at least I believe this is nonstandard notation), I think that being as explicit as possible as helpful. Thus, I would write $$\{X \subset A : |X| = 2\}.$$ Your notation, however, does emphasize the size of such a set which is a great quality in a notation.2012-02-24
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    Dear stefan: It wouldn't be a good idea: it would be a terrific idea!2012-02-24
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    @JavaMan I am not sure whether your notation is First Order Notation I suspect it is Second Order which may be not feasible in some cases. Asaf Karagila had given nice first order definition along with short hand notation. I think $\{x \in 2^{|2|}:|x| =2\}$ might be first order notation but I am not completely sure.2012-02-24
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    I made a mistake in my notation I meant $\{X\in A^{|2|}:|X|=2\}$2012-02-24

2 Answers 2

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$\dbinom A 2$ is standard notation for the set of all size-$2$ subsets of a set $A$, in the usage of combinatorialists.

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    It is a great notation. However, heavily used in inline math it tends to either get cramped or to push the lines apart. So while the mathematician in me approves, my inner typographer does not.2012-02-24
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    @Harald: There is still some effect of you use a smaller version such as $\tbinom A 2$ but I find it quite reasonable.2012-02-24
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    @Henry: I disagree. The letter A is too small. Maybe that is because I am getting a bit old? In the same vein, I dislike text-mode fractions except for simple numerical fractions like $\frac56$.2012-02-24
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    I always thought this was *the number* of unordered pairs from $A$. Which never made real sense in case $A$ was not finite.2012-02-24
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    The _number_ of unordered pairs from $A$ is $\dbinom{|A|}{2}$ (where $|A|$ is the number of members of the set $A$). The _set_ of unordered pairs from $A$ is $\dbinom{A}{2}$.2012-02-25
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In set theory it can be often denoted as $[A]^2=\{\{a,b\}:a,b\in A, a\neq b\}$.

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    Add condition that $a\neq b$.2012-02-24