# 2 = 1

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### #1jebus

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Posted 04 November 2004 - 06:50 PM

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

### #2Ed Mack

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Posted 04 November 2004 - 06:59 PM

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

### #3-mx5-Kris

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Posted 10 November 2004 - 04:32 AM

wouldn't bb be b^2?

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Posted 10 November 2004 - 04:48 AM

bb is shorter to write
Jesse Coyle

### #5Mihail121

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Posted 10 November 2004 - 05:12 AM

So where exactly was the catch in this question?

### #6Ed Mack

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Posted 10 November 2004 - 04:00 PM

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.

### #7Mihail121

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Posted 10 November 2004 - 04:11 PM

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...

### #8NeZbiE

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Posted 10 November 2004 - 05:00 PM

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 ;)

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Posted 11 November 2004 - 07:36 AM

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 :)

### #10PsiProvider

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Posted 19 November 2004 - 01:05 PM

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 ^^.

### #11tomcant

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Posted 21 January 2005 - 08:52 PM

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

:)

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

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