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More specifically, I have to find a q in A such that q is larger than any p in A. The only thing I can think of is using (2 − p2) somehow, or (p + x)2 <2, but other than that I don't know how to proceed. This exercise is taken from the very first chapter of Walter Rudin's Principles of Mathematical Analysis. Quoting the exercise: To do this, we associate with each rational p> 0 the number: q ...
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