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I'm trying to show that a monotone function on a closed interval can only contain jump discontinuities. Could someone give me a hint as to how I should begin? I am not sure how to start this problem.

Edit: Let $f$ be a increasing function. Then if $x \leq y, f(x) \leq f(y)$.

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    Firstly reduce your case to proving only for increasing functions. How do you do this? And, the one-sided limits exist for a monotonic function, what does this tell you?2012-05-01
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    Huh? **Re to your edit**: Monotonic functions are not necessarily increasing.2012-05-01
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    @KannappanSampath: Would it be a bad idea to negate the $\epsilon - \delta$ definition of continuity?2012-05-01

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