A quickie about set theory notation I'm reading the first chapters of my discrete mathematics textbook and I couldn't help but wonder (perhaps I haven't seen enough examples) -- is it more appropriate to write that $a$ is an integer and within a set in the following way:
\begin{align}
a\in\left\{x\in\mathbb{Z}\big|\:b<a<c\right\},\tag{1}
\end{align}
or would it be better to break it up into two statements instead to have something like
\begin{align}
a\in\mathbb{Z},a\in\left(b,c\right)\tag{2}.
\end{align}
And I apologize in advance if some of you feel this is not a good question (perhaps too beginner-ish). I would just like to get all of the formalities down so that in the future I don't make a mistake.
Thanks,

They're both fine. Don't get too hung up on notation, as long as your intent is clear.
My personal preference is to write something like: "let $a$ be an integer, where $b < a < c$." There's nothing wrong with mixing in statements in natural language.
