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Math Help - The function "Cardinality"

  1. #1
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    Smile The function "Cardinality"

    hello
    i want to know why the codomain of the function "cardinality" is \left \{ 0 \right \} \cup \mathbb{N},i don't see why we need 0.
    i'm confused,if \mathbb{X} is an empty set : \mathbb{X} = \left \{ \varnothing  \right \}
    we have \left | \mathbb{X} \right | = 1
    am i correct ?
    thanks for helping me
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  2. #2
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    Quote Originally Posted by Raoh View Post
    i want to know why the codomain of the function "cardinality" is \left \{ 0 \right \} \cup \mathbb{N},i don't see why we need 0.
    i'm confused,if \mathbb{X} is an empty set : \mathbb{X} = \left \{ \varnothing  \right \}
    we have \left | \mathbb{X} \right | = 1
    am i correct ?
    I really have no idea how to read this question.
    What do you mean by "codomain of the function cardinality"?

    The cardinality of the empty is \left| \emptyset  \right| = 0
    But the cardinality of its power set \left| {\mathcal{P}(\emptyset )} \right| = 1.

    Does that help?
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  3. #3
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    Smile

    thanks a lot,but i read it in a book
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  4. #4
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    Smile

    and i meant by the codomain,the target domain.
    thanks a lot
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