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Infinite sigma-algebra

  1. Apr 21, 2005 #1
    I'm supposed to answer the question "Can a sigma-algebra be infinite and countable?"
    I think I can show that if it has a countable number of disjoint subsets, then it can't be countable considering the possible combinations of the subsets.
    Now I need to show that if a sigma-algebra consists of an infinite number of subsets, then it has a countable number of disjoint subsets.
    Any ideas on how I can do this?
  2. jcsd
  3. Apr 21, 2005 #2
  4. Apr 21, 2005 #3


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    No you can't.

    Now, if you instead said countably infinite... :smile:

    (I edited it)

    Proof by contradiction, maybe?
  5. Apr 22, 2005 #4
    That's what I meant. I was sloppy. :redface:
    Thank you both for the help.
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