joi, 30 decembrie 2010

Example of wrong proof

Example of wrong proof
Find a mistake in the following chain of arguments, pretending to prove that 2=1
1)
Let a = b
2) Multiply 1) by a
a2 = ab
3) Add a22ab to both parts of 2)
a2 + a22ab = ab + a22ab
4) 3) could be simplified:
2a22ab = a2ab
5) It is the same as
2(a2ab) = 1(a2ab)
6) Reduce 5) by (a2ab).
2=1
Where is a mistake?
Mistake is in the 6th step.
We can not divide by (a2ab) because a2ab = 0.
a = b, so a2ab = 0.

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