Let S(adsbygoogle = window.adsbygoogle || []).push({}); _{1}be the set that contains the natural number 1. Since S_{1}is finite it has no limit points.

Let S_{k}be the set that contains the natural numbers less than or equal to k. S_{k}is finite and therefore has no limit points. The set S_{k+1}contains only one more element than S_{k}and therefore also contains no limit points.

Therefore the set of natural numbers contains no limit points.

I've been told that the conclusion does not follow. Why is that the case?

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# Problem with Proof

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