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Math Help - Squeeze Theorem

  1. #1
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    Identity at some point

    "Let f:[a,b]->[a,b] be a continuous function. Prove that there exists some point x in [a,b] such that f(x)=x."

    Is it possible to do this WITHOUT using the intermediate value theorem?
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  2. #2
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    Quote Originally Posted by Treadstone 71
    "Let f:[a,b]->[a,b] be a continuous function. Prove that there exists some point x in [a,b] such that f(x)=x."

    Is it possible to do this WITHOUT using the intermediate value theorem?
    This is a good problem. I would go about it using the squeeze theorem. Maybe start that for some x between a and b, f(a)<f(x)<f(b). Post back with any thoughts.
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