# What's wrong with these equations?

1. Jan 29, 2009

### kacete

1=2? -1=1?

First:
Code (Text):
1-1=0
2-2=0

1-1=2-2

1*(1-1)=2*(1-1)

[1*(1-1)]/(1-1)=[2*(1-1)]/(1-1)

[I]1=2[/I]
Second:
Code (Text):
-1=-1

1/-1=-1/1

sqrt(1/-1)=sqrt(-1/1)

sqrt(1)/sqrt(-1)=sqrt(-1)/sqrt(1)

1/i=i/1 note: i=sqrt(-1) complex number

i/(i^2)=i note: i/(i^2) equals 1/i as in 3/9 equals 1/3

i/-1=i note: i^2=-1 complex number

-i=i

i*(-i)=i*(i) note: preserved equality of equation

[I]-1=1[/I]

2. Jan 29, 2009

### element4

The error of your first example is that devision by zero is undefined, $$1-1=0$$.

The second example fails duo to use of the identity $$\sqrt{\frac ab}=\frac{\sqrt a}{\sqrt b}$$, since this is only valid for $$a,b>0$$. See http://en.wikipedia.org/wiki/Exponentiation#Failure_of_power_and_logarithm_identities", for more info.

See more similar "proofs" http://en.wikipedia.org/wiki/Invalid_proof" [Broken].

Last edited by a moderator: May 3, 2017
3. Jan 29, 2009

### kacete

Now that was simple, thank you. I saw this around and it was messing with me. Guess math can't be tricked. Never would have guessed something similar was already on wikipedia. Thank you!