2 = 1

[jebus]

here's an interesting proof. see if you can see where it breaks down:

a = b given
aa = ab multiply both sides by a
aa - bb = ab - bb subtract (b * b) from both sides
(a + b)(a - b) = b(a - b) factor both sides
a + b = b cancel out common factors
b + b = b substitute b for a (from line 1)
2b = b combine the left side
2 = 1 divide both sides by b

the above was taken from Paul Bourke's site (http://astronomy.swin.edu.au/~pbourke/)

[Ed Mack]

(a-b) = 0, therefore you cannot divide both sides by it.

[[mx5]Kris]

wouldn't bb be b^2?

[NomadRock]

bb is shorter to write

[Mihail121]

So where exactly was the catch in this question?

[Ed Mack]

He divided by zero, so answers go out the roof at that point. I think there's some more odd algebra in it, but that's the first I found.

[Mihail121]

Yes, i know what the error in the transformation is but why is he giving it here at DevMaster? I have it in my old 6th grade mathbooks...

[NeZbiE]

Bah, there are a lot more proofs of 2=1 that are actually a *lot* harder to disprove =)
I'll see if I can remember/dig-up a few just for kicks ;)

[ShadowHawk]

It is just for the fun here. Just to keep the gray matter working but if u have better examples that are harder to disprove please go ahead and place them here.
Or other strange things that are not correct but appear to be correct i just love them :)

[PsiProvider]

Another example using complex numbers:

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

So, always be careful with complex numbers and roots in general, or sth like that could happen ^^.
Ah and please forgive me the misuse of the equal-sign ^^.

[tomcant]

Something similiar to the original post, but also flawed by the divide by zero, is this:

2(1-1) = (2-2)
2 = (2-2)/(1-1)
2 = 0

:)

[edit]: woops, sorry to dig up an old topic. :wacko: