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1 = -1... Now Proved!

by Sumit Menon
4 replies
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1 = (1)^(1/2)
= [(-1)(-1)]^(1/2)
= (-1)^(1/2).(-1)^(1/2)
= i.i
= i^2
= -1

Hence Proved.

There's obviously an error.. see if you can figure it out.

Sumit.
  • Profile picture of the author seasoned
    For starters, the proof only basically says that i^2=1. If i=-1 then i^2=1 SO, 1=1! The signs cancel themselves out, and THAT is how you got the first two lines:

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

    If (1)^(1/2)=[(-1)(-1)]^(1/2) then [(-1)(-1)]^(1/2)=(1)^(1/2) which means [(-1)(-1)]=(1) or i.i=1 where i=-1.

    Steve
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    • Profile picture of the author Sumit Menon
      Originally Posted by seasoned View Post

      For starters, the proof only basically says that i^2=1. If i=-1 then i^2=1 SO, 1=1! The signs cancel themselves out, and THAT is how you got the first two lines:

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

      If (1)^(1/2)=[(-1)(-1)]^(1/2) then [(-1)(-1)]^(1/2)=(1)^(1/2) which means [(-1)(-1)]=(1) or i.i=1 where i=-1.

      Steve


      Lol.. But i is not equal to -1. If that were the case, we wouldn't need complex numbers.

      i = (-1)^(1/2)
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  • Profile picture of the author Biggy Fat
    I hate Algebra.
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  • Profile picture of the author KenThompson
    Originally Posted by Sumit Menon View Post

    1 = (1)^(1/2)
    = [(-1)(-1)]^(1/2)
    = (-1)^(1/2).(-1)^(1/2)
    = i.i
    = i^2
    = -1

    Hence Proved.

    There's obviously an error.. see if you can figure it out.

    Sumit.
    (-1)^(1/2).(-1)^(1/2) = -1^[(1/2)+(1/2)]
    (-1)^(1/2).(-1)^(1/2) = -1^(1) = -1

    1 = (1)^(1/2) = -1

    1 DNE -1

    Every positive number has two square roots, +/-


    Ken

    PS - This seriously disturbed the cobwebs. Thanks. The spider
    is now homeless. Happy?
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