Is there a mathematical for "for every fixed element"

Question

I've noticed that "for every fixed element" has come up enough for me to ask is there a mathematical sign for this? If not, why not? I can think of plenty of times when it comes up and such a notation would make reports look smoother.

Answer 1

The notation $\forall x\in S$ means for all elements $x$ in set $S$ (or for every element $x$ of $S$).

Is that symbol what you're looking for? [In latex (Mathjax) it can be done as \forall]

Answer 2

The word "fixed" is used to emphasise the possible dependencies between the variables. But when using formal logic (correctly), there is no need for this because this information is expressed by the ordering of the quantifiers. Therefore, there are only symbols for "for all", $\forall$, and "there exists", $\exists$.