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?

First of all a*a - a*b is zero though not a flaw. But the removing of (a - b) on both sides in 3rd statement is not valid as (a - b) = 0. This is the flaw.

Posted by Gautam Joshi on 2002-12-23 14:18:27