I'm trying to wrap my mind around the concept of mathematical statements with qualifiers and such, and I am just not seeming to get it.

Check this statement:

$\displaystyle \forall x \exists y \ni y > x $

The book says it's true because there is always a real number y that is greater than x.

$\displaystyle \exists y \ni \forall x, y > x $

This is apparently false "since there is no fixed real number y that is greater than every real number."

At first glance, they appear identical, but the notation is different. What is it that I'm not understanding about the notation that's misleading me?