Given: a=b. Applying some basic identity transformations, we get:

       a=b
       a^2-ab=a^2-b^2
       a(a-b)=(a+b)(a-b)
       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 (a-b) has been cancelled on both sides.This cancellation is possible only when the term is non-zero finite
quantity.But here a=b.therefore (a-b)=0.
so the cancellation is not allowed & hence
the proof is not valid.

Posted by ananth on 2002-12-21 17:10:22