rewrite in a mathematical format I have many sets containing three values like {1,−2,-5}. I want to write in mathematical form to filter set where there are only elements with same sign and also none of them is zero like {-1,−9,-5} or {4, 6, 2}. I tried this, is it correct?
$$
F = \{ s \in S \mid \forall a \in s, a \neq 0 \land \forall a \in s, a > 0 \vee \forall a \in s, a < 0 \}
$$
EDIT: 
$S$ is collection of all sets (s) and "a" denotes set member. 

What you described is, put into words:

$F$ is the set of all sets which do not contain zero and which have all elements of the same sign.

It is unclear what $S$ is, althoutgh I imagine it should be either $\mathbb R$ or $\mathbb Z$. Without determining what $S$ is, your definition is not clear.
It is also worth noting that sets of different sizes will be in $F$. For example, if $S=\mathbb R$, then $\mathbb N\in S$ and $\emptyset\in S$

Afteer your edit, it seems your notation is correct.
Right now, I understand you already have some selection of sets in $S$, and you just want those that contain elements of the same sign (and do not contain zero). If that is what you tried to achieve, then you did it.
