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#1 2005-08-07 23:41:47

wcy
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Paradox

i=-1

(-1/1)= (1/-1)
(i/1)= (1/i)
√(i)/√1= (√1)/(√i)
i/1= 1/i
i= 1 (cross-multiplication)

Contradiction!!
How to solve this paradox?
I also don't know the answer.

Last edited by wcy (2005-08-07 23:42:27)

 

#2 2005-08-08 00:02:35

kylekatarn
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Re: Paradox

I've already discussed that on IRC and nobody could explain that too..

 

#3 2005-08-08 00:13:32

wcy
Full Member

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Re: Paradox

i suspect that it is illegal to square root both sides, since square rooting a negative number is not allowed

 

#4 2005-08-08 07:47:29

MathsIsFun
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Re: Paradox

"How wonderful that we have met with a paradox. Now we have some hope of making progress." - Niels Bohr

I suspect it is this curious phenomenon:

(-1) = 1
-1 = 1  ...?

Making:
√(i)/√1= (√1)/(√i)
i/1 = 1/i  ...?

Because:

1/i = (1 x i) / (i x i) =  i/i = i / -1 = -i

* basks in glow of very rare victory, hoping it lasts *


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#5 2005-08-08 14:39:12

ganesh
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Re: Paradox

wcy wrote:

(i/1)= (1/i)
√(i)/√1= (√1)/(√i)

Normally, in such paradoxes, this is where the mistake lies.
Since a = b,
it cannot be inferred that a=b.
Taking square root on both sides of an equation should always have the
'' sign, after the square root is worked out.


Character is who you are when no one is looking.
 

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