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Math Help - cardinality of sets

  1. #1
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    cardinality of sets

    If A\subseteq B then A\le B where \le denotes here that the set A is less than or equinumerous with the set B.
    How to do this? From the hypothesis we know that every element of A belongs to B so A cannot have more elements than B right? or do I understand it wrong?
    Last edited by rayman; May 13th 2013 at 04:58 AM.
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  2. #2
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    Re: cardinality of sets

    Quote Originally Posted by rayman View Post
    If A\subseteq B then A\le B where \le denotes here that the set A is less than or equinumerous with the set B.
    How to do this? From the hypothesis we know that every element of A belongs to B so A cannot have more elements than B right? or do I understand it wrong?
    All proofs depend upon the definitions and axioms one has to work with.

    Usually in this case, show that there is an injection f:A\to B~.

    But check your notes/textbook.
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    Re: cardinality of sets

    yes of course! I totally forgot about the trivial inclusion map thanks
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