The question was to rewrite the statement "The equation $x^2=-1$ has no real solution in $\def\Z{\Bbb Z}\Z$" using only logical quantifiers and the words "such that"
My incorrectly marked answer was $\forall x \in \Z$, $\nexists x \in \Z$ such that $x^2=-1$.
I've looked at it for a while and can't see what I've done wrong, can anyone help me out?
This is how I translate it:
$(\lnot\exists x\in \mathbb{Z})$ such that [sometimes notated as $\ni$] $(x^2=-1)$
In you notation: $\forall x \in \mathbb Z,\lnot \exists x\in \mathbb Z \text{ such that }x^2=-1$ the universal does not make sense. In fact, I am having a hard time interpreting your notation: "For every integer there is no integer?"