Describing an equivalence class given a contained number.

Question

I have a question where I am asked to decide whether $∼$ is an equivalence relation on $\Bbb R$ where $x_1∼x_2$ means $x_1-x_2$ is an integer. I have managed to prove it is Reflexive, Symmetric and Transitive but later I am asked to "Describe $[\frac{2}{3}]$, the equivalence class containing $\frac{2}{3}$" if the relation is an equivalence relation (Which is it).I have never come across this phrase, could someone explain this to me?

Answer 1

It's just asking you to say what the set of elements equivalent to ${2\over 3}$ is.

For example, if we looked at the equivalence relation $\approx$ on $\mathbb{Z}$ given by $a\approx b$ iff $a^2=b^2$, we'd have $[2]=\{-2,2\}$. So:

What numbers are $\sim{2\over 3}$?