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Math Help - Denseness of a function

  1. #1
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    Denseness of a function

    If f:\mathbb{R} \to \mathbb{R} is an increasing function and g: \mathbb{R} \to \mathbb{R} is a decreasing function then the set A=\{ x \in \mathbb{R}:  f+g \ \textrm{is continuous at} x\} is dense in (\mathbb{R},d) where d is euclidean metric.
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  2. #2
    Senior Member Shanks's Avatar
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    Hint:for a monotonic function, the set of points at which it is not continous is countable.
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