clarification of a logic proof I am a bit confused on what this question is asking me to prove:
Prove $$
\exists z\forall x\in\mathbb{R}^{+}[\exists y(y - x = y/x)\leftrightarrow x \neq z] 
$$
Am I asked to prove that there exists a z where the bi-conditional statement is true? Or is z a given and I should just prove the statement in the brackets for some z?
I put that thought aside and showed that the statement in brackets is true when z = 1, but I just want to be sure that I did what the question I was asked.

It is conventional that quantifiers bind from left to right.  Therefore, to prove this statement, you must first choose a $z$.  Then, your adversary picks an $x$, and regardless of this choice, you must now prove that the biconditional holds.
To do so you must prove that under certain circumstances $y$ exists, and under other circumstances it does not.
