Given 'x' not equal to 0, let us consider the follwoing relation:

x + x + x + .... +x (added 'x' times) = x²

Differentiating both sides with respect to x, we get:

1 + 1 + 1 + 1 + .... + 1 ('x' times) = 2x

(Since the derivative of x² with respect to 'x' is 2x).

So we now have:

x = 2x

Cancelling 'x' from both sides, we have:

1 = 2

Now the very obvious question follows:

Where is the flaw ?

The problem lies with your differentiation of both sides. The operation of differentiation is valid only on well defined mathematical functions. "1 + 1 + 1 + ... + 1 ('x' times)" is not a well defined function; it is an algorithm (specifying to add 1 repeatedly), whereas "2x" is a well defined function.

Therefore, the resulting equation is faulty.

Posted by Your buddy on 2003-08-22 08:40:55