What is the symbolic form of "there does not exist a largest natural number " Other students in office hour said this is the correct form
$(\forall x)(\exists y)(y>x)$
{ for all x natural number, there exists y such that y is greater than x }
But
"there does not exist a largest natural number "
$\neg(\exists x)(x\text{ largest natural number})$
Am I even close ? 

In English: "there is no natural n, for which all natural k would be smaller than n".
$\lnot \exists n \forall k (k, n) \in \mathbb{N}^2 \land k < n$
