Does a variable in an expression need to be explicitly bound by a quantifier (or by some other operator), to be bound? Or can it be implicitly bound? For example:
If $x = y^2$ and $y > 0$, then, for any number $z$, $x > -z^2$.
This is sentence is universally satisfied for any x and y adhering to the given restraints, and therefore doesn't depend on x or y. Yet they are not specifically bound by a quantifier. Are x and y free or bound?