How do I use quantifiers to specify a pair of elements?

Question

I'm just learning about quantifiers in class, and my professor has so far only given us examples where he uses quantifiers to specify one element/variable at a time from a set.

So he would write something like: $\forall$ a $\in$ $\mathbb{R}$ ...

Am I limited to only defining one variable at a time? Would it be "legal" for me to write $\forall$ (a, b) $\in$ $\mathbb{R}$?

Answer 1

Formally, you would want to write $$\forall a\in\Bbb R\forall b\in\Bbb R(\ldots)$$

But it is perfectly readable to write $\forall a,b\in\Bbb R\ldots$

Answer 2

You can also write $\forall (a,b)\in\mathbb{R}\times \mathbb{R}$, but this hardly saves over the other answers.