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 ?

x+x+x+x+....+x('x' times)= x squared which is the same as saying x*x=x squared.

you then substitute x with 1 in only a portion of the problem when you differentiate. This is mathematically wrong. If you replace x with 1, you must do so with all x's in the problem. It would then become:

1+1+1+1...+1 (1 time)=1²

if you add 1, 1 time, you get 1. so the problem would become:

1=1² which is true. Thank you.

Posted by jonnyw76 on 2003-09-28 20:53:12