How do commas and brackets affect the meaning of quantifiers?

Question

My logic class didn't introduce us to multiple quantifiers. I've seen a few variations that seem to have distinct meanings:

$$ \forall x, \forall y(...) $$

$$ \forall x \forall y(...) $$

$$ \left( \forall x \forall y \right) (...) $$

$$ \left( \forall x, \forall y \right) (...) $$

$$ \left( \forall x \right)\left( \forall y \right) (...) $$

Do the meanings of those examples differ?

Thank you.

Answer 1

No, they are just typographical variants of the same mathematical meaning.

Answer 2

Just to amplify Henning Makholm's headline answer just a bit ...

1. Some older texts use $(x)$ [without the rotated 'A'] for the universal quantifier, and some use $(\forall x)$ [with the rotated 'A' and brackets]. In those notations multiple universal quantifiers will look like $(x)(y)\varphi$ or $(\forall x)(\forall y)\varphi$.
2. The modern habit is to use the rotated 'A' but then not use the unnecessary brackets: thus $\forall x\forall y\varphi$.
3. In some dialects, we write e.g. instead of $\forall w\forall x\forall y\forall z\varphi$ the simpler $\forall wxyz\varphi$ for brevity.
4. I can't recall having seen the notation $(\forall x\forall y)\varphi$. Nor can I recall any canonical mathematical logic textbook that uses commas. Certainly these uses are non-standard to my eyes.