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# Help! Calculate the closure of a set. Topology questions involving limit points watch

1. Hi

I want to find the closure of the following set:

{ (-1)^n (1- (1/n^2) } n going from 1 to infinity **

So the closure is the union of the set with the limit points

I think the limit points may be +1 and -1

So would the closure be the set ** union with the points +1 and -1 ?

Thanks!
2. (Original post by number23)
Hi

I want to find the closure of the following set:

{ (-1)^n (1- (1/n^2) } n going from 1 to infinity **

So the closure is the union of the set with the limit points

I think the limit points may be +1 and -1

So would the closure be the set ** union with the points +1 and -1 ?

Thanks!
Clearly are limit points of the set, which you can justify by giving an example of a sequence which converge to them.
I've not done a thorough check that they are the only limit points of the set, however, intuitively I agree that this is true - you might want to double check this by supposing another limit say existed and (hopefully) showing that the only two limit points are and .
From there, you are correct that the closure of a set is the set itself plus the limit points of the set.

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Updated: November 14, 2015
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