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Math Help - cardinal numbers! proof

  1. #1
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    cardinal numbers! proof

    1)Prove that binary relation is antisymmetric in the set of the cardinal numbers.

    2)Prove that binary relation is transitive in the set of the cardinal numbers.
    can u guys help me?

    should i prove first one with cantor-bernstein theorem? just prove cantor-bernstein and is that all? or what? (


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  2. #2
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    Re: cardinal numbers! proof

    1) if k ≤ m is defined as "there exists an injection from any set A with |A| = k to any set B with |B| = m" then (1) IS cantor-bernstein.

    2) show that the composition of two injective maps is injective.
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