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October 24th, 2010, 03:03 PM  #1 
Newbie Joined: Oct 2010 Posts: 25 Thanks: 0  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 don’t 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 doesn’t converge to a specific number. Therefore can’t 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. 
October 24th, 2010, 03:18 PM  #2 
Newbie Joined: Oct 2010 Posts: 17 Thanks: 0  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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