Does 1 equal 2, you tell me? 
Here is the proof (unfiltered by rational arguments):
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- Let a and b be equal non-zero quantities
- a = b
- Multiply through by a
- a2 = ab
- Subtract b2
- a2 − b2 = ab − b2
- Factor both sides
- (a − b)(a + b) = b(a − b)
- Divide out (a − b)
- a + b = b
- Observing that a = b
- b + b = b
- Combine like terms on the left
- 2b = b
- Divide by the non-zero b
- 2 = 1
Well, can you spot the mistake? 
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Webmaster of www.study-habits.com & author of The Study Guide PRO, Abderisak Adam shares study tips, techniques and guides to the student community. As a student of civil engineering at Chalmers University of Technology he focuses on matters relating to engineering, mathematics and physics.
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9 Comments
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You cannot “Divide out (a − b)” because a=b and a-b=0. You cannot divide by 0
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Nice, that’s correct! Or should I say; that’s what makes my proof incorrect ; )
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Hi! How r u?
nice site!
[Reply]
I am doing well, thank you for the positive comment
Take Care!
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nice work a person can learn more n more
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true or false: a^2-b^2=(a-b)^2
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why did you subtract b squared? where did that come from???
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admin Reply:
December 20th, 2009 at 2:31 am
This part of the “proof” was actually valid. Remember, you can always do ‘what ever’ you want to one side of the equation as long as you do the same on the other. x=2 is the same as x-1=2-1
[Reply]
Well,
a + b = b
i.e a = b – b
i.e a = 0
which contradicts the first statement of the proof that a and b are non zero quantities.
Thus, the proof is incorrect.
Another method(which does not make sense, actually):
We know that,
0! = 1
and 1! = 1
This proves that,
0! = 1!
Cancelling factorial sign(!) on both sides, we get,
0 = 1
The blog is pretty good:) I loved all the posts.
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