# Notation for a “conditional” set

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.

• 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? – MPW Oct 29 '14 at 15:35
• in this particular case, yes, although it would be interesting to see notation for every $B$, like $A = B_{condition}$ – Hrant Khachatrian Oct 29 '14 at 15:57

If you use the indicator function (that I note $1_A$) then you can write it $$a_n 1_{2\nmid n}\ \ \ \ \ \ a_n 1_{ 2\Bbb Z+1}(n)$$
Maybe use a Kronecker delta/indicator function. But "0" would have to be interpreted set theoretically to be $\{\}$.