Remus Toderici Photography: Mathematics

Friday 15 June 2007

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

Friday 15 June 2007