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Homework Help: Infinite Sets

  1. Apr 22, 2010 #1
    1. The problem statement, all variables and given/known data

    Using the Schroeder-Bernstein Theorem, prove that any two intervals of real numbers are numerically equivalent.

    2. Relevant equations

    Schroeder-Bernstein Theorem: Let [tex]A[/tex] and [tex]B[/tex] be sets, and suppose that there are injections from A into B and B into A. Then, there exists a bijective correspondence between A and B.

    3. The attempt at a solution
    None. I'm stuck. Can anyone help me with where to go?
  2. jcsd
  3. Apr 22, 2010 #2
    If and only if two intervals are "numerically equivalent", there exists a bijective correspondence between A and B.
  4. Apr 22, 2010 #3
    Picture one of the intervals in the x-axis of the plane and the other in the y-axis. Can't you see the graph of an injective (in fact bijective) function between them?
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