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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- November 11th 2006, 06:09 AMPauKelomeContinuous 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. - November 11th 2006, 07:56 AMPlato
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.