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Math Help - Sets and Elements

  1. #1
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    Cool Sets and Elements

    Q: Show that the set
    A = {1 2 3 ... 2006}
    contains an even number of elements.



    I have no idea where to start or how to do this
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  2. #2
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    Quote Originally Posted by unstopabl3 View Post
    Q: Show that the set
    A = {1 2 3 ... 2006}
    contains an even number of elements.
    If one adds two even numbers does one get an even number?
    Is the number of elements in \{1,2,3,\cdots,2006\} even?
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  3. #3
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    it doesn't matter whether the number of elements in (1...2006) is even (the answer is yes, because 2006 is an even number). The point is that you have the negative numbers as well. So the number of elements in the set is double the number in (1....2006), so it must be even.


    Step by step
    that is just the positive integers, and the negative integers (up to 2006).

    ie, every positive integer and its negative partner

    ie, every element can be paired with another one

    so there must be an even number


    Edit Posted while plato was typing and not intended to disrespect his answer
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  4. #4
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    Thanks for the replies, but how would I show this in mathematical terms or a simple statement?
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  5. #5
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    Quote Originally Posted by unstopabl3 View Post
    Thanks for the replies, but how would I show this in mathematical terms or a simple statement?
    What is the answer?
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  6. #6
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    Well "Yes" the number of elements are even ...
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  7. #7
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    Quote Originally Posted by unstopabl3 View Post
    Well "Yes" the number of elements are even ...
    That is not what I meant. How many elements are there in the set?
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  8. #8
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    2006 x 2 = 4012 , which is an even number ???
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  9. #9
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    Correct! Now you have done the question.
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  10. #10
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    Thanks, both of you!
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