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Cardinality of Infinite Sets

  1. Dec 4, 2006 #1
    1. The problem statement, all variables and given/known data
    Prove that the union of c sets of cardinality c has cardinality c.

    2. Relevant equations

    3. The attempt at a solution
    Well, I could look for a one-to-one and onto function... maybe mapping the union of c intervaks to the reals, or something? I know how to demonstrate that a countable union of countable sets is countable, by showing how to label them.
    I'm having a hard time with this one, though.
  2. jcsd
  3. Dec 5, 2006 #2


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    [tex]\mathbb{R}^2 = \bigcup _{r \in \mathbb{R}} (\mathbb{R} \times \{ r\} )[/tex]

    This should give you an easy way to associate a c-union of c-sets with R2. Now all you need is a bijection between R and R2.
  4. Dec 5, 2006 #3
    Ohh, I think I finally get it! (after thinking about it for a loong while...) Infinity is hard for me to wrap my head around. Thanks a lot for your help.
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