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Math Help - Proving Cardinality

  1. #1
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    Proving Cardinality

    Hello,
    Urgently need some help with some Mathematical Communication.
    The question is:
    Show that the set of all odd square numbers {1,9,25,49,...} has cardinality ℵ0 [aleph-zero].

    Any ideas?
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by Ellis View Post
    Show that the set of all odd square numbers {1,9,25,49,...} has cardinality ℵ0 [aleph-zero].
    The k-th non-negative odd number is 2k-1...

    Can you use this to find a bijection which maps \mathbb{N} onto \{1,9,25,49\ldots\} ?
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  3. #3
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    Cardinality of R

    What is the largest cardinality, because surely I can start with the cardinality of the set of all Real numbers and then work from there?
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  4. #4
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by Ellis View Post
    What is the largest cardinality
    I don't know.
    because surely I can start with the cardinality of the set of all Real numbers and then work from there?
    I don't think so.
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