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What's wrong with these equations?

  1. Jan 29, 2009 #1
    1=2? -1=1?

    First:
    Code (Text):
    1-1=0
    2-2=0

    1-1=2-2

    1*(1-1)=2*(1-1)

    [1*(1-1)]/(1-1)=[2*(1-1)]/(1-1)

    [I]1=2[/I]
    Second:
    Code (Text):
    -1=-1

    1/-1=-1/1

    sqrt(1/-1)=sqrt(-1/1)

    sqrt(1)/sqrt(-1)=sqrt(-1)/sqrt(1)

    1/i=i/1 note: i=sqrt(-1) complex number

    i/(i^2)=i note: i/(i^2) equals 1/i as in 3/9 equals 1/3

    i/-1=i note: i^2=-1 complex number

    -i=i

    i*(-i)=i*(i) note: preserved equality of equation

    [I]-1=1[/I]
     
  2. jcsd
  3. Jan 29, 2009 #2
    The error of your first example is that devision by zero is undefined, [tex]1-1=0[/tex].

    The second example fails duo to use of the identity [tex]\sqrt{\frac ab}=\frac{\sqrt a}{\sqrt b}[/tex], since this is only valid for [tex]a,b>0[/tex]. See wikipedia, for more info.

    See more similar "proofs" here.
     
  4. Jan 29, 2009 #3
    Now that was simple, thank you. I saw this around and it was messing with me. Guess math can't be tricked. Never would have guessed something similar was already on wikipedia. Thank you!
     
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