Why does $ x\mathcal{R}y \iff |x| >|y| \text{ or } (|x|=|y| \text{ and } x>y) $ not allow a utility function representation?

Question

Suppose we have the preference relation $\mathcal{R}$ defined on the interval $[-1,1]$ by

$$ x\mathcal{R}y \iff |x| >|y| \text{ or } (|x|=|y| \text{ and } x>y) $$

How do you show that this relation does not allow a utility function representation?

Where a utility function representation should satisfy

$$x\mathcal{R}y \iff u(x)\geq u(y). $$

Answer 1

A preference relation that allows a utility function has to be reflexive as $u(x) \ge u(x)$ for all $x \in [-1,1]$. However $1 \mathcal R 1$ doesn't hold.