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    Real Analysis : Intermediate Value Theorem

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    A function is increasing on A if f(x)<=f(y) for all x <y in A. Show that the intermediate value theorem does have a converse if we assume f is increasing on [a,b].

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    Solution Preview

    We'll prove this by contradiction.
    Suppose that f is not continuous and let a<c<b.
    Let e>0 .Since f is ...

    Solution Summary

    The Intermediate Value Theorem is proven not to have a converse over a given interval. The solution is concise.