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Math Help - Please explain

  1. #1
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    Please explain

    The question:

    What is wrong with the following "proof"? Let x=y. Then

            x^2 = xy
      x^2-y^2= xy-y^2
    (x+y)(x-y)= y(x-y)
             x+y= y
               2y= y
                 2=1

    Solution: I know that 2 does not equal 1 and my answer was an incorrect substitution in step 5 however that makes no sense as x=y. The book says that in step 3 'they' incorrectly divided by (x-y)=0. I do not understand, if (x-y) is a whole number then would it not be valid to perform the division?
    i.e.  \frac {y(x-y)}{(x-y)} = y?

    Now, perhaps this post would be better suited in the set theory/logic section but as the concept under discussion is of elementary character I felt that would be an unnecessary aggrandizement. Also I am unsure as to the formal system of 'proof' being employed, is it deduction?
    Last edited by Foxlion; March 9th 2011 at 06:53 AM. Reason: clarity
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  2. #2
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    Quote Originally Posted by Foxlion View Post
    The question:

    What is wrong with the following "proof"? Let x=y. Then

            x^2 = xy
      x^2-y^2= xy-y^2
    (x+y)(x-y)= y(x-y)
             x+y= y
               2y= y
                 2=1

    Solution: I know that 2 does not equal 1 and my answer was an incorrect substitution in step 5 however that makes no sense as x=y. The book says that in step 3 'they' incorrectly divided by (x-y)=0. I do not understand, if (x-y) is a whole number then would it not be valid to perform the division?
    i.e.  \frac {y(x-y)}{(x-y)} = y?
    since x=y then clearly x-y=o
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  3. #3
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    It is clear isn't it, and yet here I am. Thank you
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  4. #4
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    And it is NOT valid to divide by the whole number 0.
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  5. #5
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    haha no, it isn't, though it is tempting to a layman such as I. It's an English thinker's problem in attempting to reconcile the irreconcilable.
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