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    Proof using the Intermediate value theorem

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    Let f : [0,1]-->[0,1] be a continuous function. Show that there exists a real number x in [0,1] such that f(x)=x (apply the intermediate value theorem to the function f(x) -x). This point x is known as a fixed point of f, and this result is a basic example of a fixed point theorem.

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    Solution Summary

    The expert examines proofs using the intermediate value theorems.