## 1 = 2

Post any maths and/or physics related questions here.

Moderators: Darobat, RecursiveS, Dante Shamest, Bugdude, Wizard

"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.

MJOLNIRdragoon

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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?

You can't conquer the game if you can't conquer yourself.

Jetru

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

Square both sides. i^2=-1, -(i^2)=1
If it wasn't for C, we would be using BASI, PASAL and OBOL.

tomcant

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

You can't conquer the game if you can't conquer yourself.

Jetru

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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.
If it wasn't for C, we would be using BASI, PASAL and OBOL.

tomcant

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Location: Colchester, UK

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.

Alvaro
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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.

You can't conquer the game if you can't conquer yourself.

Jetru

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Huh? Correct solution?
Need information on a function I've posted? Chances are it's at the MSDN.
MXP

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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)?

You can't conquer the game if you can't conquer yourself.

Jetru

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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.

Alvaro
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The problem is in a step that is valid for real numbers but not for complex numbers.
Need information on a function I've posted? Chances are it's at the MSDN.
MXP

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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'?

You can't conquer the game if you can't conquer yourself.

Jetru

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Location: Bangalore,India

Maybe it's just me, but I don't see
Code: Select all
`i / 1 = 1 / ii = -i `

Wizard

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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
Need information on a function I've posted? Chances are it's at the MSDN.
MXP

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Joined: Mon Sep 22, 2003 5:27 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...

You can't conquer the game if you can't conquer yourself.

Jetru

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Joined: Sat Oct 18, 2003 11:46 pm
Location: Bangalore,India

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