TITLE: Weak formulations: where should the $\forall$ be placed?
QUESTION [1 upvotes]: Shoud I write (with the appropriate assumptions on $b$ and $l$)

Find $u\in U$ such that $\forall v \in V$, $b(u,v)=l(v)$

or

Find $u\in U$ such that $b(u,v)=l(v)$, $\forall v \in V$

I tend to go for the first formulation but I often see the second version.

REPLY [1 votes]: Unless you're really writing something about logic, you should avoid using so many logic symbols, it looks a bit ugly. I suggest you pick up any math book, and you'll see very rarely a $\forall, \exists, $ etc.
I would just write, in most cases:

Find $u\in B$ such that for every $v\in V$, it holds that $b(u,v)=l(v)$.

Sure, you can vary in style, or be a bit less verbose, but you should reserve logic symbols for shorthand (writing theorems or proofs in some lecture you're giving, so you can write faster(in the cases that you happen to write this symbols, the $\forall$ at the end or in the middle, is perfectly fine (provided you're clear with the order of the quantifiers, etc))).

If you really want to write formulas in a true formal manner, see this.
{"set_name": "stack_exchange", "score": 1, "question_id": 1761599}