How to show that the following relation is not an equivalence relation?

Question

We have the relation $\sim$ in $\mathbb{R}^n$: $x\sim y \leftrightarrow d(x,y)\in \mathbb{Q}$, where $d(x,y)=\sqrt{\sum^n_{i=1}(x_i-y_i)^2}$. How do you prove that this isn't an equivalence relation for $n>1$? I know for sure that it's reflexive, so it must either not be symmetric or not transitive.

Answer 1

$d(0,e_1)\in\mathbb{Q}$, $d(0,e_2)\in\mathbb{Q}$, yet $d(e_1,e_2)\notin\mathbb{Q}$.