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Math Help - Counting elements

  1. #1
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    Counting elements

    I understand that {1, 2}={1, 2, 1}.
    But do they have the same number of elements??????

    Please help!!! Many thanks!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by acc100jt View Post
    I understand that {1, 2}={1, 2, 1}.
    But do they have the same number of elements??????

    Please help!!! Many thanks!!
    If these are sets yes they have the same elements, and so the
    same number of elements. The elements of {1, 2} are 1 and 2, and
    the elements of {1, 2, 1} are 1 and 2. But we would not normally
    write something like {1, 2, 1} when talking about sets, so maybe
    your question is really about something else?

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    so maybe
    your question is really about something else?
    Perhaps he was told to prove that,
    \{1,2\}=\{1,2\}
    Have the same number of elements?
    ------
    If so then consider the map,
    \phi:\{1,2\}\to \{1,2\}
    defined as, \phi(1)=1 und \phi(2)=2. Then it is a bijective map. And the prove is complete.
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  4. #4
    Senior Member OReilly's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    If these are sets yes they have the same elements, and so the
    same number of elements. The elements of {1, 2} are 1 and 2, and
    the elements of {1, 2, 1} are 1 and 2. But we would not normally
    write something like {1, 2, 1} when talking about sets, so maybe
    your question is really about something else?

    RonL
    They have same elements, but why do they have same number of elements?

    If we are talking about different elements then they have same number of elements. Talking about quantity then we have different number of elements. First set has 2 and second set has 3 elements.
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