# Find the mistake 1=-1 ?

1. Jun 14, 2010

### mathlover1

Somebody find the mistake here:

$$1=\sqrt{1}=\sqrt{(-1)(-1)}=\sqrt{(-1)^2}=-1 \Rightarrow 1=-1$$​

2. Jun 14, 2010

### Staff: Mentor

Square root of 1 is not 1, it is either 1 or -1.

3. Jun 14, 2010

### DaveC426913

Since when is the (square root of -1)-squared equal to -1?

-1 squared is 1.
The root of 1 is 1, not -1.

4. Jun 14, 2010

### mathlover1

yes it's -1 because (-1)^2=1 from the definition ;)

5. Jun 14, 2010

### DaveC426913

So do you or do you not see the flaw?

6. Jun 14, 2010

### njama

The error is here
$$\sqrt{(-1)^2} \neq -1$$

$$\sqrt{(-1)^2} = |-1|=1$$

7. Jun 14, 2010

### mathlover1

Well-done Njama, your answer is the correct one.

8. Jun 14, 2010

### DaveC426913

Which is precisely what I said in post 3.

9. Jun 14, 2010

### HallsofIvy

Not true.
Not true.
True! [tex]\sqrt{x}[/itex], as a real valued function, must have only one value for each x and it is defined as "the positive number y such that $y^2= x$"
Then why did you deny it in your post quoted above?

10. Jun 14, 2010

### Redbelly98

Staff Emeritus
Is it just me, or is this the 3rd time in the last month somebody has posted the very same 1=-1 argument?

11. Jun 14, 2010

### DaveC426913

Well, it really belongs in the Riddles section.