Proving this relation is a function

Question

I want to prove that this relation in $\Bbb R$ is a function. $$(x,y)\in\mu\iff|y|\le|x|\le1$$

I know that for a function that for every $x$ there is only $y$. I also know I can't disprove it, so how can I prove it is a function?

Answer 1

You can't prove it, because it is false. In fact, it is easy to disprove that this is a function: clearly both $(1,0) \in \mu$ and $(1,\tfrac12) \in \mu$, so this is not a function.