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Sequential compactness

  1. Sep 19, 2007 #1
    1. The problem statement, all variables and given/known data
    http://books.google.com/books?id=th...ts=yfNwPI7lv_&sig=6MWgB7WBS3P8NZ_a_7Dq_um7EvI
    Can someone explain there rational for the statement "for only finitely many indices j" in the second paragraph of the proof?



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 19, 2007 #2

    Hurkyl

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    It means the set of j's such that ______ holds is finite.
     
  4. Sep 19, 2007 #3
    Sorry, I asked the wrong question. I wanted to ask how do they make the conclusion that there "is a grand total of only finitely many positive integers"?
     
  5. Sep 19, 2007 #4

    Hurkyl

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    How many y's are there?
    How many balls are there?
    How many y's per ball?
     
  6. Sep 20, 2007 #5
    Of course! Finite times finite = finite.
     
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