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Math Help - finding cardinality

  1. #1
    Junior Member scottie.mcdonald's Avatar
    Joined
    Jan 2009
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    Williamstown, Ontario, Canada
    Posts
    31

    finding cardinality

    I am unable to come up with a correct proof for these questions. I have what I think could be part of it, but I seem to fill in the rest of the proof with wrong steps. help or an explanation would be helpful. thank you.

    Find the cardinal number of the following sets. justify your answer.

    1). the set C of all circles lying in the plane

    C={  C_1 , C_2 , C_3 , ..... } where C is an element of real numbers
     \Rightarrow C \rightarrow to Real numbers  \Rightarrow [circles] \rightarrow [Real numbers x Real numbers]
     \Rightarrow rxr \mapsto Real numbers x Real numbers, where r is the radius of a circle

    i am completely lost and i don't think i'm doing this right. thanks for the help.

    Scott
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  2. #2
    Senior Member
    Joined
    Nov 2008
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    Paris
    Posts
    354
    Hi

    To answer the question, you can find what is necessary and sufficient to determine one circle (two parameters can do that job).
    Then, let A and B be the sets of all possible parameters, A\times B will be equipotent to the set of all circles in the plane, and you will be able to get its cardinality, which is the cardinality of A\times B. I see some interesting words in what you wrote.

    What are the parameters and then what are A and B?
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