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-1 = 1

smiles · 2004-02-15 01:26:53

-1 = i^2 = sqrt(-1)*sqrt(-1) = sqrt(-1*-1) = sqrt(1) = 1 Therfore -1 = 1 :) Another of those fun fallacies. << Fio >>

15-02-2004 2:26am

#1

smiles

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-1 = i^2 = sqrt(-1)*sqrt(-1) = sqrt(-1*-1) = sqrt(1) = 1

Therfore -1 = 1

Another of those fun fallacies.

<< Fio >>

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#2 15-02-2004 2:32am

ykt0di9url7bc3

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the universe is doomed i tell ya

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#3 15-02-2004 2:35am

Jonnie_Onion

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sqrt(1) = +/- 1.

Therefore the equation holds for sqrt(1) = -1 and is invalid for sqrt(1) = 1

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#4 15-02-2004 2:10pm

Capt'n Midnight

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sqrt(1) = 0 +/- 1

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#5 20-02-2004 9:37pm

Agent Smith

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thats not wht my calculater says

/me bounces it off wall

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#6 20-02-2004 10:51pm

ecksor

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Originally posted by smiles
sqrt(-1)*sqrt(-1) = sqrt(-1*-1)

Multiplication of reals isn't homomorphic to multiplication of complex numbers?

[EDIT]Under the square root function I should say but I can't think of a function that is a homomorphism between ({R-0},*) and ({C-0},*). Can anyone help me out?[/EDIT]

Never thought about that before, I think that's a correct interpretation ...

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#7 21-02-2004 2:44am

ecksor

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Oh, apart from identity functions.

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#8 23-02-2004 5:54pm

ecksor

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http://mathworld.wolfram.com/ComplexNumberParadox.html

The complex modulus gives us a homomorphism from ({C-0},*) and ({R-0},x), i.e, |a|x|b| = |a*b|

Anyone know of an example of an isomorphism between those groups?

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