Re: Ok so I just proved 1 = -1. Someone help me find my error.
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Hi guys. First post in this forum.
Working on a problem set recently, a few friends and I accidentally discovered a proof of -1=1, and for the life of us we can't find out what we did wrong. And it's not like we're math slouches either; we're all graduate students in physical/theoretical chemistry.
From what I understand posting TeX doesn't work on 2+2, so you'll have to follow my algebra.
Start with the identity
(E-V)^(1/2) = (E-V)^(1/2)
Now multiply each side by -1, except on the RHS substitute i^2 for -1 (where i of course is the imaginary number).
(-1)(E-V)^(1/2) = (i^2)(E-V)^(1/2)
Now divide through by i
(-1/i)(E-V)^(1/2) = i*(E-V)^(1/2)
But since i is just the square root of -1, we can subsume it into the square root of E-V
(-1)[(E-V)/-1]^(1/2) = [(-1)(E-V)]^(1/2)
and then rearrange the interior of the square root to find
(-1)(V-E)^(1/2) = (V-E)^(1/2)
or
-1 = 1.
No dividing by zero in this proof either. Where did I make a mistake?
The Doc
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(-1/i)(E-V)^(1/2) = i*(E-V)^(1/2)
for the (-1/i), times top and bottom by i
you get -i/i^2 = -i/-1 = i
so u have i*(E-V)^(1/2) = i*(E-V)^(1/2)
...pretty obvious mistake u made having root(-1) = -i
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