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In the proof of Stone-Weierstrass theorem provided in Rudin's Principles of Mathematical Analysis, why do we only need to show that there exists a sequence of polynomials $P_n$ that converges uniformly to the continuous complex function on $[0,1]$?

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    Could you please elaborate a little? Maybe give the precise statement of the conclusion and say why you don't see how it follows?2010-11-16
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    Because you can stretch it and so on?2010-11-16

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