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by **MJOLNIRdragoon** » Thu Oct 20, 2005 7:29 pm

"Supposedly it proves that 1 = 2 but there is a flaw in the steps, can you find it?"

"a(b - a) = (b + a)(b - a)
a = b + a " Doesn't work... the first line would be
1(1-1) = (1+1)(1-1)
which is in turn is
1(0) = (2)(0)
we we all know is totally equal to
0=0
unless you'd like to pull out some old stuff I learned in trig, which would then
= greek to me.

by **Jetru** » Fri Oct 21, 2005 4:50 am

Colin Jeanne wrote:I prefer this:

-1 = -1

-1/1 = 1/-1

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

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

i / 1 = 1 / i

i = -i

1 = -1

How did you get 1=-1 from i=-i?

by **tomcant** » Fri Oct 21, 2005 4:53 am

Jetru wrote:How did you get 1=-1 from i=-i?

Square both sides. i^2=-1, -(i^2)=1

by **Jetru** » Fri Oct 21, 2005 5:14 am

>>>> -(i^2)=1
You can't ignore the factor -1 there. You need to square that too.

by **tomcant** » Fri Oct 21, 2005 5:17 am

Jetru wrote:>>>> -(i^2)=1
You can't ignore the factor -1 there. You need to square that too.

Well then perhaps that is the problem with the proof. What they are saying is that you negate the square of i.

by **Alvaro** » Fri Oct 21, 2005 7:48 am

tomcant wrote:
Jetru wrote:How did you get 1=-1 from i=-i?

Square both sides. i^2=-1, -(i^2)=1

No, that would leave -1=-1 instead. Just divide both sides by i.

by **Jetru** » Fri Oct 21, 2005 10:03 am

Alvaro wrote:
tomcant wrote:
Jetru wrote:How did you get 1=-1 from i=-i?

Square both sides. i^2=-1, -(i^2)=1

No, that would leave -1=-1 instead. Just divide both sides by i.

Aha! Divide one side by i and the other by -i. That's the correct soln.

by **MXP** » Fri Oct 21, 2005 10:36 am

Huh? Correct solution?

by **Jetru** » Fri Oct 21, 2005 11:31 am

Umm well, 1=/ -1, so we dida wrong step somewhere. We replace one of the i's for it's conjugate to get the correct 1=1.
Or am I wrong? Is this a problem inherent to mathematics because of the was i is defined(i^2=-1)?

by **Alvaro** » Fri Oct 21, 2005 11:38 am

Of course the proof is wrong, but the problem is not in the step that you pointed out. After i = -i then the rest of the proof is correct.

by **MXP** » Fri Oct 21, 2005 6:19 pm

The problem is in a step that is valid for real numbers but not for complex numbers.

by **Jetru** » Sat Oct 22, 2005 11:35 am

Oh you mean
sqrt(-1/1) = sqrt(1/-1) to sqrt(-1) / sqrt(1) = sqrt(1) / sqrt(-1)
or do mean assuming sqrt(-1) to mean only 'i'?

by **Wizard** » Sat Oct 22, 2005 12:39 pm

Maybe it's just me, but I don't see

Code: Select all: i / 1 = 1 / i i = -i

by **MXP** » Sat Oct 22, 2005 12:50 pm

Jetru wrote:Oh you mean
sqrt(-1/1) = sqrt(1/-1) to sqrt(-1) / sqrt(1) = sqrt(1) / sqrt(-1)

That's the problem. You can only split up an exponential in this way when using real numbers.

Wizard,

i / 1 = 1 / i

i = (-i / -i) * (1 / i)

i = (-i * 1) / (-i * i)

i = -i / 1

i = -i

by **Jetru** » Sun Oct 23, 2005 12:43 pm

>>That's the problem. You can only split up an exponential in this way when using real numbers.

Why? It seems valid to me...

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