2 equals 1

[SheepDog]

See if you can find the flaw in this, which would presume to prove that 2=1:
-----------------------------------------
Let a and b be equal quantities. It follows that:

a = b
a2 = ab
a2 - b2 = ab - b2
(a - b)(a + b) = b(a - b)
a + b = b
b + b = b
2b = b
2 = 1

[mgb]

In this case, doesn't 2 = 1 because you say it does?

I mean if 1 = 1 and 2 = 2 and 1 = 2 then doesn't 2 = 1?

[Johnny]

jimkoppelli already did this one.

[mgb]

Its been a long time since I looked at math.

How does a + b = b if a = b?

I don't get that.

[Werdna]

Its been a long time since I looked at math.

How does a + b = b if a = b?

I don't get that.
If a and b is equal to 0 then a + b = b. And you can't divide by zero like that...
At least I think that's where the flaw is?

[SheepDog]

jimkoppelli already did this one.
well, well...

[mgb]

well, well...

Its ok, we won't judge you, and I am too lazy to try and find it, so keep going...

[SheepDog]

If a and b is equal to 0 then a + b = b. And you can't divide by zero like that...
At least I think that's where the flaw is?
that's the flaw. Divide both sides by (a-b) to go from

(a - b)(a + b) = b(a - b)
to
a+b=b

But since a=b, (a-b) must be zero. And we all know that you can't divide by zero, don't we?
:D

[Werdna]

that's the flaw. Divide both sides by (a-b) to go from

(a - b)(a + b) = b(a - b)
to
a+b=b

But since a=b, (a-b) must be zero. And we all know that you can't divide by zero, don't we?
:D
Yay!
happppy

[jimkopelli]

You see... the cool part is where you make this thingy help prove that Winston Churchhill is a carrot.

[SheepDog]

Yeah, I forgot to mention that part.

[Werdna]

You see... the cool part is where you make this thingy help prove that Winston Churchhill is a carrot.
Never seen it before so I googled it:



Let A=B.
A( A - B )=A2 - AB=A2 - B2 = ( A + B )( A - B ).
Cancelling, A=A+B.
Let B=1.
Then subtracting A from each side, 0=1. Call this equation (*).
Winston Churchill has one head. Therefore, by (*), Winston Churchill has no head.
Winston Churchill has no green leafy top. Therefore Winston Churchill has one green leafy top.
Multiply each side of the equation (*) by two. Then two equals zero. Since Winston Churchill has two arms and two legs, Winston Churchill has no arms and no legs.
Multiply each side of (*) by the waist size of Winston Churchill. Then the waist size of Winston Churchill is zero: Winston Churchill tapers to a point.
Multiply each side of (*) by l, where l is the wavelength in nanometers of any photon reflected off of Winston Churchill. Then l=0 nm. Now multiply each side of (*) by 620 nanometers: 620 nm=0 nm. Therefore, we obtain l=620 nm. Winston Churchill is orange.
Winston Churchill has no head, no arms, no legs, and a green leafy top; he tapers to a point; and he's orange. Therefore Winston Churchill is a carrot.
http://www.koschei.net/blog/archives/000695.html

Cool. You could prove anything with this.