Cardinality of Infinite Sets

  • Thread starter mufq15
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  • #1
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Homework Statement


Prove that the union of c sets of cardinality c has cardinality c.


Homework Equations





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.
 

Answers and Replies

  • #2
AKG
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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.
 
  • #3
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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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