My Math Forum Show set has no limit points

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 October 24th, 2010, 02:03 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, 02:18 PM #2 Newbie   Joined: Oct 2010 Posts: 17 Thanks: 0 Re: Show set has no limit points If there is a $c>0$ such that any two points of the set $A \subseteq \mathbb{R}$ are at least a distance $c$ apart, then $A$ has no limit points. This is the case for $\mathbb{N}$ and all finite sets.

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# Limit point of the set of natural number

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