Friday, 15 June 2007

Mathematics

Proof that

1 = -1 \,


Start with the identity

-1 = -1 \,

Convert both sides of the equation into the vulgar fractions

\frac{1}{-1} = \frac{-1}{1}

Apply square roots on both sides to yield

\sqrt{\frac{1}{-1}} = \sqrt{\frac{-1}{1}}
\frac{\sqrt{1}}{\sqrt{-1}} = \frac{\sqrt{-1}}{\sqrt{1}}

Multiply both sides by \sqrt{-1} to obtain

\sqrt{1}\cdot\sqrt{1} = \sqrt{-1}\cdot \sqrt{-1}

Any number's square root squared gives the original number, so

1 = -1 \,

*see the title link for the solution

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