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Math Help - Continuous functions

  1. #1
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    Continuous functions

    Need some help on the following:

    Suppose f and g are continuous real valued functions defined on I such that I is defined on the closed interval [0,1]. We also know that f(m/(2^n))=g(m/(2^n)) for all rational numbers in I. Prove that f=g.
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  2. #2
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    Quote Originally Posted by PauKelome View Post
    Suppose f and g are continuous real valued functions defined on I such that I is defined on the closed interval [0,1]. We also know that f(m/(2^n))=g(m/(2^n)) for all rational numbers in I. Prove that f=g.
    I am really unsure about my reading of this problem.
    Is it correct that: “each of f and g is a continuous function and f agrees with g in a dense subset of the interval I in the real numbers”? If that is correct then the function f-g is zero on a dense subset. If f-g fails to be zero at some point then f-g fails to be continuous.

    That is a rough outline of a proof based upon my reading of your problem.
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