# 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

$$3$$ = $$2$$

$$3$$ = $$1$$ + $$1$$

Note by Revankumar Gnanavel
5 years, 9 months ago

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

- 5 years, 9 months ago

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

- 5 years, 9 months ago

Wow .. :D Amazing

- 5 years, 9 months ago

- 5 years, 9 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.

- 5 years, 9 months ago

just add more problems like this...

- 5 years, 9 months ago