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June 5th, 2018, 07:01 AM   #1
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Closed set

The set S = {1-(1/n): n belongs to N} is a closed set. True of False. Justify your answer.
Just to be more informative. A set S is called a closed set if it contains all its limit points.
Please help me with the answer.
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June 5th, 2018, 07:07 AM   #2
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Have you any thoughts on the matter? Why might it be a closed set? Why might it not be a closed set? If a set is closed if it contains all its limit points, what are the limit points of your set? Does your set contain them?
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June 5th, 2018, 07:10 AM   #3
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Hint: what's the limit of $1 - \frac{1}{n}$ as $n$ tends to infinity?
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June 6th, 2018, 03:16 AM   #4
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It will be 1. But 1 does not belong to the set. All the very near points to 1 belong to S, but 1 itself does not belong to that. Is this the reason why it is not a closed set? Or is it a closed set as 1 belongs to it?

Last edited by skipjack; June 6th, 2018 at 09:03 AM.
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June 17th, 2018, 11:12 AM   #5
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You say "But 1 does not belong to the set" but then ask "Or is it a closed set as 1 belongs to it?"???
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