How to make existence proof for Abelian Group condition 3( unit element e), when ($\mathbb{N}. \cdot)$?

How to make existence proof for Abelian Group condition 3( unit element
e), when ($\mathbb{N}. \cdot)$?

How to make existence proof for Abelian Group condition 3( unit element
e), when ($\mathbb{N}. \cdot )$, where $\cdot$ is natural multiplication?
Is it by example? Is it done by constructive proof method?