Infinite Sets

  • Thread starter nickmai123
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  • #1
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Homework Statement



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

Homework 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.

The Attempt at a Solution


None. I'm stuck. Can anyone help me with where to go?
 

Answers and Replies

  • #2
306
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If and only if two intervals are "numerically equivalent", there exists a bijective correspondence between A and B.
 
  • #3
402
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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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