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Is there any commonly used short notation for the following?

$A_n = \begin{cases} \{a_n\}, & \text{if $n$ is odd} \\ \emptyset, & \text{if $n$ is even} \end{cases} $

I'm looking for something like $A_n = \{a_n\}_{[\text{$n$ is odd}]}$ that will fit on one row.

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  • $\begingroup$ It looks like your sets $A_n$ contain either zero elements or one element, depending on whether $n$ is even or odd. Is that right? $\endgroup$
    – MPW
    Oct 29, 2014 at 15:35
  • $\begingroup$ in this particular case, yes, although it would be interesting to see notation for every $B$, like $A = B_{condition}$ $\endgroup$ Oct 29, 2014 at 15:57

2 Answers 2

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If you use the indicator function (that I note $1_A$) then you can write it $$ a_n 1_{2\nmid n}\ \ \ \ \ \ a_n 1_{ 2\Bbb Z+1}(n) $$

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Maybe use a Kronecker delta/indicator function. But "0" would have to be interpreted set theoretically to be $\{\}$.

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