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Math Help - Cardinality Question

  1. #1
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    Cardinality Question

    Hi all,

    I have a question that i would love some help with.

    Q: Prove that the set of all integers and the set of all odd integers have the same cardinality.


    So far i really haven't been able to come up with anything. I know that the cardinality of a set is the number of elements in the set. I assume :

    all integers will = n

    and all odd integers will = n+1.

    Obviously both of these sets are infinite, i am just seeming to have trouble formulating a good start to a proof for this.

    Any help would be appreciated.

    Thanks,

    Flea.
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  2. #2
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    Prove the the mapping n\mapsto 2n+1 is a bijection (one-to-one and onto).
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  3. #3
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    I will start there. Thank you very much.

    --Flea.
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