Difference between two quantifier placements for a single statement

Question

Considering a predicate Q(y,x) stating that x is greater than y, what is the difference between.

$\forall x \exists y$ $Q(y, x)$

and

$\exists y \forall x$ $Q(y, x)$

Thanks,

Answer 1

The first statement says that for every number there is a greater number (true: for any $x$, you can always pick $x + 1$ as a greater number)

The second statement says that there is a number greater than all numbers, which is clearly false! (in fact, 'all numbers' would include itself, so besides $y$ being greater than all other number (which is already false, since there is no greatest number), $y$ would also have to be greater than itself!)

Answer 2

$$\forall x \exists y ~Q(y,x)$$

For every $x$, there's a $y$ such that $Q(x,y)$. but it could be a different $y$ for every $x$.

$$\exists y \forall x ~Q(y,x)$$

For every $x$, there's a $y$ such that $Q(x,y)$. but it is the same $y$ for every $x$.