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Thread: Exists Bijection to a Disjoint Set

  1. #16
    MHF Contributor Matt Westwood's Avatar
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    Quote Originally Posted by MoeBlee View Post
    Note that we could just as well have used domain rather than range.

    dom(E) = {x | exists a y such that <x y> in E}.

    Let z not in dom(E).

    So E is disjoint from {z} X F.

    And F is 1-1 with {z} X F.
    In fact you don't even need to do that. In fact I prefer to use just X or something so as to avoid the misleading language of mapping / relation theory.

    See what I did in:

    Exists Bijection to a Disjoint Set - ProofWiki
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  2. #17
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    I don't know what you think is "misleading" about "mapping/relation theory". For that matter, I don't know what you mean by "mapping/relation theory" that is not just part of basic set theory.
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  3. #18
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    Thread closed.
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