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Homework Help: Cardinalities of Sets

  1. May 10, 2014 #1
    1. The problem statement, all variables and given/known data
    Explain why ## (0,1 ) ## and ## (0,2)##

    I have proved that a function ## f: (0,1 ) -> (0,2) ##defined by f(x) =2x is bijective.

    2. Relevant equations

    3. The attempt at a solution
    I could state that due to the sets relationship being bijective they have the same cardinality, but this is only true if both sets are finite. Here, (0,1) and (0,2 ) are infinite.

    Any help?
  2. jcsd
  3. May 10, 2014 #2
    What is your definition of "having the same cardinality"?
  4. May 10, 2014 #3
    Nevermind, you are right. The definition of same cardinality or numerically equivalency doesn't restrict finite from infinite sets.
  5. May 10, 2014 #4
    Right! So you solved the problem correctly. Congratz!
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