# Math Help - Negation of Inequality

1. ## Negation of Inequality

I'm trying to negate the statement

∀ x ∈ ℤ, X^2 > 0

i believe that

∃ x ∈ ℤ, ~(X^2 > 0)

is technically the right answer, but can it be further changed to

∃ x ∈ ℤ, X^2 < 0 ?

2. You are correct. For every number $x$, $\neg(x\ge 0)$ is equivalent to $x<0$.

3. ok, thank you