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Math Help - empty set question

  1. #1
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    empty set question

    what is the cardinality of this sets:

     a.) \left\{{\varnothing}, \left\{{\varnothing}\right\}, \left\{{\varnothing}, \left\{{\varnothing}\right\}\right\}\right\}
    Last edited by TheRekz; June 25th 2007 at 04:40 PM.
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  2. #2
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    Quote Originally Posted by TheRekz View Post
    what is the cardinality of this sets:

     a.) ({\varnothing, ({\varnothing}), ({\varnothing, ({\varnothing})}}))
    The elements are:
    \varnothing , \{ \varnothing \} , \{\varnothing,\{\varnothing \} \}

    1+1+1=3
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  3. #3
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    Quote Originally Posted by TheRekz View Post
    what is the cardinality of this sets:
     a.) ({\varnothing, ({\varnothing}), ({\varnothing, ({\varnothing})}}))
    First, I must say that I do not think that you are asking the question that you mean to ask.
    Because, I see only one element of the set of triples, 3-tuples.
    Now, I am of course aware that a set of ordered pairs is defined as sets of sets: the pair <br />
\left( {a,b} \right) = \left\{ {\left\{ a \right\},\left\{ {a,b} \right\}} \right\}
    And we define the triple \left( {a,b,c} \right) = \left( {\left( {a,b} \right),c} \right).
    Therefore, have you asked the question you meant to ask?
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  4. #4
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    Quote Originally Posted by Plato View Post
    First, I must say that I do not think that you are asking the question that you mean to ask.
    Because, I see only one element of the set of triples, 3-tuples.
    Now, I am of course aware that a set of ordered pairs is defined as sets of sets: the pair <br />
\left( {a,b} \right) = \left\{ {\left\{ a \right\},\left\{ {a,b} \right\}} \right\}
    And we define the triple \left( {a,b,c} \right) = \left( {\left( {a,b} \right),c} \right).
    Therefore, have you asked the question you meant to ask?

    What the perfect hacker answered is right I guess, it's just a matter of curly braces and ( problem
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  5. #5
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    Because you edited the question to change ( to {, the answer is 3.
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