"Let r be a rational number greater than 1. Let f:R->R be a function that satisfies the condition that for all real numbers x and y,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]|f(x)-f(y)|\leq (x-y)^r[/tex]

Prove that f is a constant."

Perhaps there's some subtlety which I misunderstood, but even a constant function fails to satisfy the conditions for some choice of r. For instance, let r=3 and f be a constant. Let x<y, and the inequality fails, i.e.,

[tex]|f(x)-f(y)|=0\leq (x-y)^3 <0[/tex]

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# Homework Help: Constant Function

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