Lipschitz function and uniform continuity

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SUMMARY

A Lipschitz function f:D→R is defined by the condition |f(u) - f(v)| ≤ C|u - v| for all u, v in D, where C is a nonnegative constant. The discussion confirms that if f is Lipschitz, it is uniformly continuous. This conclusion is established through a direct proof, demonstrating that the Lipschitz condition inherently satisfies the criteria for uniform continuity.

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A function f:D\rightarrowR is called a Lipschitz function if there is some
nonnegative number C such that

absolute value(f(u)-f(v)) is less than or equal to C*absolute value(u-v) for all points u and v in D.

Prove that if f:D\rightarrowR is a Lipschitz function, then it is uniformly continuous.

I am having trouble proving this, I am not sure if I should suppose not or go about it by some other method?
 
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try a direct proof.
 

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