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Prove that the closure of a bounded set is bounded.

  1. Jan 17, 2013 #1
    1. The problem statement, all variables and given/known data

    Prove that if S is a bounded subset of ℝ^n, then the closure of S is bounded.

    2. Relevant equations

    Definitions of bounded, closure, open balls, etc.

    3. The attempt at a solution

    See attached pdf.
     

    Attached Files:

  2. jcsd
  3. Jan 17, 2013 #2
    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?
     
  4. Jan 17, 2013 #3
    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.
     
  5. Jan 17, 2013 #4

    Dick

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    Homework Helper

    Your original proof looks fine to me. Except when you pick an epsilon, it should be "there exists epsilon" not "for all epsilon".
     
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