elementary negation I couldn't be sure about the negation of the statement $\exists x \in N , x < 3$
is it
$$
\lnot(\exists x \in N , x < 3) \equiv (\forall x \in N , x \geq 3)
$$
or
$$
\lnot (\exists x \in N , x < 3) \equiv (\forall x \notin N , x \geq 3)
$$
can someone help me (with an explanation)?

just to be sure, to me your statement reads as "There exists an $x$, element of the positive integers (doesn't matter with or withour $0$), such that $x$ is less than $3$. If this is correct, then the negation is: There is no $x$ element of the positive integers such that $x$ is less than $3$. This means that all $x$ element of the positive integers are greater equal $3$.
