-1 = 1 - how do i prove this wrong?

A little question as usual (and no, this is not homework, its exams time ):
We probably all now this one:

1 = sqrt(1) = sqrt (1*1) = sqrt (-1)^2 = -1

or

1 = -1

I wikid it, but the result of me not being born in an english-speaking country "pawned" me!

 

Meee sqrt(-1) = i

Anyways this step sqrt(1*1) = sqrt(-1) is invalid as far as I know.

 

I know, but how do I prove this?

 

I just thought I might've remembered wrong. Anyway, nonexisting numbers don't count


And the step is sqrt (1*1) = sqrt (-1)^2 which looks legit

 

You can't thats the whole point. The initial proof is invalid, the person who posted it didn't prove it effectively so really all you should have to say is sqrt(1*1) != sqrt(-1)^2 can you give me the wiki link or tell me more about the question?

 

Yeah:http://en.wikipedia.org/wiki/Square_roots look up at "notes". And didnt Einstein say that everything is right until proved wrong?

 

Whoever wrote this "proof" is taking advantage of the +- nature or square roots. The real equation should be: +-1 = +-sqrt(1) = +-sqrt (1*1) = +-sqrt (-1)^2 = +-1 which holds true.

 

My intial thought was along those lines. Until I started reading these notes and the thing stopped making any sense. Well, that's math for you.

I think the proof you're looking for would be:
sqrt(1) = 1 v sqrt(1) = -1

 

yea some one else had it

(-1)^2 implies +-1

and then substitute both back into "sqrt(x)"
one works one doesnt therefore -1 is invalid

 

Wait, you can't take a Sqrt out of a negative number.
What's there to proove?

 

actually the square root of -1 equals i
its an imaginary number, yes, but its still a number

 

No one has answert my question, and it doesnt seem that anybody will so thread closed.