Suppose I want to write, in the context of a proof, say, that $x>0$ for all $x$ in some set $A$. There are several options how to do this:
1) $x>0$ for all $x\in A$
2) $x>0$ for all $x$ in $A$
3) $x>0$ for $\forall x\in A$
4) $x>0$ $\forall x\in A$
In my own writing, I usually opt for the third option based on the fact that it is shortest and uses fewest words (dominance to 1 and 2) but is more readable and 'looks more natural' than 4.
However, an argument can be made that 3 includes 'for' twice, one as a text and one in the $\forall$ symbol. (In fact, a referee recently pointed me to a 'typo' when I used the third formulation.)
Any thoughts/guidelines/preferences/other suggestions on style connected to $\forall$?