Given:
a=b. Applying some basic identity transformations, we get:
a=b
a^2ab=a^2b^2
a(ab)=(a+b)(ab)
a=a+b
a=a+a
a=2a
1=2
With such a proof, we can show that
1=2, pi=E, 10000000000000=1, etc.... Can you spot the flaw?
In the 4th step ,the factor (ab) has been cancelled on both sides.This cancellation is possible only when the term is nonzero finite
quantity.But here a=b.therefore (ab)=0.
so the cancellation is not allowed & hence
the proof is not valid.

Posted by ananth
on 20021221 17:10:22 