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Some help please

  1. Feb 14, 2004 #1
    Hello all,

    I’m evidently not an expert on Mathematics but I still want to question the consistency of this system. How confident can we really be that there aren’t any big flaws? I have done some research and have found the following paradoxes which I can’t explain.


    Assume that
    a = b
    Multiplying both sides by a,
    a² = ab
    Subtracting b² from both sides,
    a² - b² = ab - b²
    Factorizing both sides,
    (a + b)(a - b) = b(a - b)
    Dividing both sides by (a - b),
    a + b = b
    Sinse a = b, we substitute and get
    b + b = b
    So, 2b = b
    Devide by b
    2 = 1

    There is another one...

    Assume A + B = C, and assume A = 3 and B = 2.

    Multiply both sides of the equation A + B = C by (A + B).

    We obtain A² + 2AB + B² = C(A + B)

    Rearranging the terms we have

    A² + AB - AC = - AB - B² + BC

    Factoring out (A + B - C), we have

    A(A + B - C) = - B(A + B - C)

    Dividing both sides by (A + B - C), that is, dividing by zero, we get A = - B, or A + B = 0, which is evidently absurd.
     
  2. jcsd
  3. Feb 14, 2004 #2

    selfAdjoint

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    Assume that
    a = b
    ....
    Dividing both sides by (a - b),


    Quick now, what is wrong with these two statements?
     
  4. Feb 14, 2004 #3
    LOL ....…. I realized afterwards that I’m actually dividing by zero . Which explains everything. Maths is saved !!!
     
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