Is It Mathematics Or Mathemagic?

Long ago, a mathematician used to cheat people. Once
he borrowed
Rs.4000/- from a rich man. After a few days, he
borrowed Rs.2000/- from the same man.

Many days passed, the mathematician did not return the
money to the rich man. The rich man went to the
mathematician and asked to return the money.

But to his great surprise, the mathematician replied
that there is no
need to pay the debt.

"See here, friend" said the mathematician " the sum of
4000 and 2000 is equal to
zero, so I do not have any balance to pay".

The rich man took the matter to the court. When the
judge came to know
this, he was astonished. He asked the mathematician to
prove that sum of 4000 and 2000 is zero, and not 6000.

The Clever mathematician agreed. He said:

let a == 4000, b == 2000 and c == 6000

a + b == c

Multiply both sides by a + b

(a + b) (a + b ) == c (a + b)

a*a + ab + ba + b*b == ca + cb

a*a + ab - ca == cb - b*b - ba

a( a + b -c) == -b(b + a - c)

so a == - b

a + b == 0

Hence 4000 + 2000 = 0............

interesting huh???