I am currently reading Principles of Mathematical Analysis by Walter Rudin. I am a bit confused with theorem 2.41. He is trying to show at one point that if E is a set in ℝ(adsbygoogle = window.adsbygoogle || []).push({}); ^{k}and if every infinite subset of E has a limit point in E, then E is closed and bounded.

The proof starts by assuming that E is not bounded. He then says that if this is the case, then E contains pointsxsuch that |_{n}x| > n for each positive integer n. He then constructs a set S that contains all these points_{n}x. Next he says "The set S ... is infinite and clearly has no limit point in ℝ_{n}^{k}..."

I don't see how it isobviousthat there is no limit point in ℝ^{k}.

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# Rudin Theorem 2.41

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