How would you show that an infinite set has no cluster points...

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- Feb 14th 2010, 08:36 AMfrenchguy87Infinite Sets and Cluster Points
How would you show that an infinite set has no cluster points...

- Feb 14th 2010, 08:53 AMPlato
- Feb 15th 2010, 07:57 PMDrexel28
A little more generally, any set such that such that for all has no limit points. To see this let be an arbitrary point and consider . It either contains one or zero points of . If the former we're done, if the latter take the open ball of one-half the distance from to that point.