1. Jan 17, 2013 #1

   dustbin

   

   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:

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     Problem.pdf

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   dustbin, Jan 17, 2013
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3. Jan 17, 2013 #2

   clamtrox

   

   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?

    

   clamtrox, Jan 17, 2013
4. Jan 17, 2013 #3

   dustbin

   

   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.

    

   dustbin, Jan 17, 2013
5. Jan 17, 2013 #4

   Dick

   

   Science Advisor

   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".

    

   Dick, Jan 17, 2013

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