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?

The step 4  is obtained by dividing both sides of the step 3 by a-b.
However, in tems of the first step, a=b.
So, in reality we are dividing both sides of step 3 by 0 to obtain step 4.
This division by zero is  not permissible and accordingly, this is a contradiction.

Edited on August 20, 2022, 12:34 pm

Posted by K Sengupta on 2007-03-20 12:24:44