1 = -1 ??
 

1 = 1 * 1 = -1 * -1 = sqrt(-1) * sqrt(-1) = i * i = -1

i = complex


any idea :-) ?

How do you figure that -1 = sqrt(-1) ?
(3rd equality you mention)

Because that would mean that -1 * -1 = -1 and that isn't the case....

Disclaimer: I'm only so-so in math, so I could be very wrong.

Re: 1 = -1 ??
 

x*x =! sqrt(x)*sqrt(x)

It's only true for positive values of x

It's not even true for positive values of x other than 1.

What he is doing wrong is he keeps applying transforms to the right hand side without applying it to the left hand side. Bad algebra! bad! No treat for you.

Re: 1 = -1 ??
 

It would surely be

1 = 1 * 1 = -1 * -1 = sqrt(-1) * sqrt(-1) * sqrt(-1) * sqrt(-1) = i * i * i * i = 1

as soon as i saw sqrt(-1) i lost it... i was under the impression that it would produce an imaginary number

Here is a webpage with some more things like this:

http://mcraefamily.com/MathHelp/Jokes.htm

Re: Re: 1 = -1 ??
 

idd that's the spoof :-)


sqrt isn't defined for negative numbers :-)

Re: Re: Re: 1 = -1 ??
 

sqrt is defined for negative numbers

sqrt(-1) = i
sqrt(-2) = 2i
etc.

the spoof is that
-1 * -1 = sqrt(-1) * sqrt(-1)
is false, not just in this instance using negative numbers, but it is false for all numbers except 0 and 1.
e.g.
4 * 4 != sqrt(4) * sqrt(4)

Re: Re: Re: Re: 1 = -1 ??
 

Actually, sqrt(-2) = i * sqrt(2)

Re: Re: Re: Re: Re: 1 = -1 ??
 

errk....you got me! :D