Simple question, set theory

Question

I'm having quite a bit if trouble finding a straight answer on how one should properly denote the set of all even and all naturals respectively. What is the standard, universally understood way to signify these?

Answer 1

Natural Numbers are denoted $\mathbb{N}$.

Even Numbers are denoted $2\mathbb{N}$.

Answer 2

Usually if $n\in \mathbb N$ , $\space n\mathbb N=\{\alpha\equiv 0\space mod (n) |\alpha \in \mathbb N\}$. So $2\mathbb N$ is the set of all even numbers.(Positive obviously).