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Math Help - denumerable sets

  1. #1
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    denumerable sets

    Code:
    Prove the following statement using induction on n: if A1, . . . ,An are 
    denumerable sets, then the set of all n-tuples 
    
    {(a1, . . . , an} | ai belongs to Ai for i=1, . . . , n} is denumerable
    Last edited by anncar; January 24th 2008 at 11:10 AM.
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  2. #2
    Super Member Rebesques's Avatar
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    It would suffice if you just proved it for two sets, as then A_1\times A_2\times\ldots\times A_n=(\ldots(A_1\times A_2)\times \ldots)\times A_n).

    So, you need to show that the Cartesian product of two denumerable sets (infinite, in the interesting case) has the cardinality of \mathbb{N}. This is equivalent to finding a 1-1 mapping f:\mathbb{N}^2\rightarrow \mathbb{N}.

    There's plenty of those. You try!
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