Prove that if S is a bounded subset of ℝ^n, then the closure of S is bounded.
Homework Equations
Definitions of bounded, closure, open balls, etc.
The Attempt at a Solution
See attached pdf.
Attachments
Problem.pdf
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Answers and Replies
#2
clamtrox
938
9
That looks OK to me apart from a couple of typos.
There is an easier way to prove this too though. Do you know that the closure of S is the intersection of all closed subsets containing S?
#3
dustbin
240
5
Thanks for your input! We have not proved that the closure of S is the intersection of all closed subsets containing S... so I cannot use this result without proof.
Thanks for your input! We have not proved that the closure of S is the intersection of all closed subsets containing S... so I cannot use this result without proof.
Your original proof looks fine to me. Except when you pick an epsilon, it should be "there exists epsilon" not "for all epsilon".