A function  satifying $|f(x)-f(y)|\leq |x-y|^2$ must be constanct.

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfy $$|f(x)-f(y)|\leq |x-y|^2,    \forall   x,y\in \mathbb{R}.$$

Prove that $f$ is constanct.


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Erdos Erdos
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