Can you spot the mistake in this equation?

[mathlover1]

Somebody find the mistake here:

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

 

[Borek]

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

 

[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.

 

[mathlover1]

The root of 1 is 1, not -1.

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

 

[DaveC426913]

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

So do you or do you not see the flaw?

 

[njama]

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

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

 

[mathlover1]

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

 

[DaveC426913]

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

Which is precisely what I said in post 3.

 

[HallsofIvy]

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

Not true.

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

Not true.

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

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

True! [tex]\sqrt{x}[/itex], as a real valued <b>function</b>, must have only one value for each x and it is defined as "the positive number y such that $y^2= x$"<br /> <blockquote data-attributes="" data-quote="mathlover1" data-source="post: 2761199" cite="https://www.physicsforums.com/goto/post?id=2761199" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> mathlover1 said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Well-done Njama, your answer is the correct one. </div> </div> </blockquote> Then why did you deny it in your post quoted above?[/tex]

 

[Redbelly98]

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

 

[DaveC426913]

Well, it really belongs in the Riddles section.