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Infinite sets, intersection, nested intervals.

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Let [a,b] be an interval and let A be a subset of [a,b]. and Suppose that A is an infinite set.

    Let z be the unique point that belongs to all of the intervals [an, bn]. Show that if I is any interval that contains z, then A intersect I is infinite.

    2. Relevant equations

    I don't know where to start this problem but I think I can use the fact that a set that contains an infinite subset is infinite. Any help would be appreciate.

    3. The attempt at a solution

    I know I is an infinite interval, I think. I also know the set of intervals [an, bn] intersect A is infinite. I believe I can say that [an, bb] is a subset of [a,b] and that [a,b] is infinite.
     
  2. jcsd
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