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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?

Parcly Taxel
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MooeSha123
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    For $x=1$ we have e.g. $|1/2| \le |x| \le 1$ and also $|1/3| \le |x| \le 1$; thus : $(1,1/2) \in \mu$ and $(1, 1/3) \in \mu$... – Mauro ALLEGRANZA Oct 19 '16 at 12:47
  • Maybe you first figure out how to do your other relation here: http://math.stackexchange.com/questions/1975509/proving-a-relation-is-function Then this one becomes easy. – Dirk Oct 19 '16 at 12:47

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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.

Mees de Vries
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