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# 1=-1

Mon 6 Apr, 2009 08:32 am
Hi all. I found this "proof" and was just wondering if there is an error in it or not, because I couldn't find it. Any ideas?

-1/1=1/-1
sqrt(-1/1)=sqrt(1/-1)
sqrt(-1)/sqrt(1)=sqrt(1)/sqrt(-1)
i/1=1/i
i*i/1=i*1/i
i^2/1=i/i
-1=1 ?
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DrewDad

2
Mon 6 Apr, 2009 08:48 am
The error is that there are two possible values when you take a square root.

sqrt(4)= 2 and sqrt(4) = -2

But 2 ≠ -2
fresco

1
Mon 6 Apr, 2009 11:45 am
@DrewDad,
DrewDad is correct,
The reasoning above used only the postive answer for sqrt(1).
The final line should read
-1=+1 or -1=-1 (where "or" is exclusive).
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