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

Question

What is the equivalence class of 0?

You haven't proved that your relation is symmetric. On the other hand, a~0 iff $2\mid a+0$. Can you conclude from that? — Xam, Dec 12 '16 at 01:27
Let $a\in\mathbb{Z}$. Clearly, $2|a+a$. Thus, $a\sim a$. Hence, reflexive property holds. — Juniven Acapulco, Dec 12 '16 at 01:31
@ash Please do not deface your question, in courtesy to those who already commented or answered, and also to others who may find it useful in the future. — dxiv, Dec 12 '16 at 02:32

score 0 · Answer 1 · answered Dec 12 '16 at 01:27

0

Hint:

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

answered Dec 12 '16 at 01:27

Bernard

179,256

score 0 · Answer 2 · answered Dec 12 '16 at 01:37

0

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}

answered Dec 12 '16 at 01:37

Juniven Acapulco

9,903

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

2 Answers2