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Counting infinite sequence of sets

  1. Mar 11, 2010 #1
    Let K1, K2, K3, . . . be an infnite sequence of sets, where each set Kn is countable.
    Prove that the union of all of these sets K = Union from n=1 to infinity, Kn is countable.

    I tried to start, but I don't even understand the question

    Need some idea on how to start
     
    Last edited: Mar 11, 2010
  2. jcsd
  3. Mar 11, 2010 #2

    Dick

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    Not understanding the question is not a good start. What does 'countable' mean?
     
  4. Mar 11, 2010 #3
    Denumerable?

    The set K would be denumberable if there is a bijection ZZ+->K

    by the way, can you teach me how to read "Bijection ZZ+->K?" ZZ+ is the symbol for all positive integer, -> is the arrow pointing to the set K.
    and I have trouble understanding what F: NN -> A mean intuitively
     
    Last edited: Mar 11, 2010
  5. Mar 11, 2010 #4

    Dick

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    I don't know what you are talking about. What does ZZ+->X mean? Countable means there is a bijection with N, the natural numbers. This is basically the same proof as showing NxN is countable. How do you do that?
     
  6. Mar 11, 2010 #5
    I'm sorry, >.< but what does NxN mean? is it the symbol for natural number?
     
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