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October 24th, 2010, 03:03 PM   #1
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Show set has no limit points

D={set of real numbers consisting of single numbers}
Show set D has no limit points, and show the set of Natural numbers has no limits points.

I know it's a very simple question. I donít know my way of approaching this is appropriate or not. Let me know. Thanks.

A finite set of real numbers consisting of single numbers is not a sequence and doesnít converge to a specific number. Therefore canít have limit points.

I know the fact that the set of Natural numbers are denumerable (infinite countable), and it diverges, therefore natural numbers have no limit point.
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October 24th, 2010, 03:18 PM   #2
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Re: Show set has no limit points

If there is a such that any two points of the set are at least a distance apart, then has no limit points. This is the case for and all finite sets.
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