correct proof for proving 1 + 1 = 3

$-1 \times -1$ = $1 \times 1$

By cross multiplication

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

Taking square root on both sides

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

We know that $i$ = $\sqrt{-1}$

$\frac{i}{\sqrt{1}}$ = $\frac{\sqrt{1}}{i}$

$i \times i$ = $\sqrt{1} \times \sqrt{1}$

$i^{2}$ = $1$

Also we know $i^{2}$ = $-1$

This implies $-1$ = $1$

Taking log on both sides we get $log -1$ = $log 1$

Also $1$ = $-1^{2}$

$log -1^{3}$ = $log -1^{2}$

$3 log -1$ = $2 log -1$

Since $log -1$ is not zero, we can divide by $log -1$ on both sides we get

$3$ = $2$

$3$ = $1$ + $1$

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

See Proof that -1 = 1

Zi Song Yeoh - 8 years, 3 months ago

This question was asked to me by one of my friends and I couldn't answer him and he told me that it was ajoke. But because of you I have come to know the solution. Thanks a lot.

Soham Dibyachintan - 8 years, 3 months ago

just add more problems like this...

Pradeep Ravichandran - 8 years, 3 months ago

Wow .. :D Amazing

Lawrence Regie Rodil - 8 years, 3 months ago

hey,revan check out ur mail (revandon007@gmail.com),a surprise is waiting for u...........

Pradeep Ravichandran - 8 years, 3 months ago

but can we use the idea of log of a negative no. in the proof when it is not defined....???

Rajath Krishna R - 8 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$