I have the following proposition in the domain of nonnegative integers:
$$ \forall x \exists y \cdot(2x-y = 0) $$
I translate it as the following: For all $x \in \{0, 1, 2,3,.... \}$, there is always a $y$ to be found, such that $y=2x$. The answer given is True, but I do not understand how this will be true for the case when $x=0$.
Am I correct in assuming that in predicate statements like this, $x$ and $y$ have to be different?