How do I find the equivalence class of 0? I already wrote the proof.

Question

What is the equivalence class of 0?

Answer 1

Hint:

This relation is nothing else than a and b have the same parity.

Answer 2

The equivalence class of $0$ is given by \begin{align} [0]&=\{a\in\mathbb{Z}:a\sim 0\}\\ &=\{a\in\mathbb{Z}:2|a\}\\ &=\{\dots, -4, -2, 0, 2, 4, \dots\} \end{align}