for all x less than or greater than a number

Question

I need some help with this question, what is the negation of

$\forall x >1$

would it just be,

$\exists x>1$ or $\exists x\le1$

Thanks

Answer 1

"For every $x$ greater than $1$, blah" is falsified by an example of an $x$ greater than $1$ such that blah is false.

So $(\forall x > 1)(P(x))$ is negated to $(\exists x > 1)(\neg P(x))$.