# It seems strange?+x+x .(x times)=x^2 then x=2x(differentiate wrt x)?

1. Jan 23, 2012

### vkash

It seems strange?+x+x.....(x times)=x^2 then x=2x(differentiate wrt x)?

x+x=2x
x+x+x=3x
x+x+x+x=4x
................
x+x+x+x+x+x+...(n times)=nx
x+x+x+x+x+x+...(x times)=x*x=x2
differentiate both sides with respect to x;
1+1+1+1+1+1...(x times)=2x
x=2x(what is it?)
what's wrong????

2. Jan 23, 2012

### micromass

Staff Emeritus
Re: It seems strange?+x+x.....(x times)=x^2 then x=2x(differentiate wrt x)?

Saying x+x+x+x+x+x+...+x (x times) simply makes no sense. It only makes sense if x is a natural number.

What, for example, is

$$\sqrt{2}+\sqrt{2}+...+\sqrt{2}~~(\sqrt{2}~ \text{times})$$

The expression makes no sense.

It only makes sense for natural numbers. And if the domain is only the natural numbers, then we can take no derivative.

3. Jan 23, 2012

### vkash

Re: It seems strange?+x+x.....(x times)=x^2 then x=2x(differentiate wrt x)?

Wow fantastic...
If domain is natural number then the curve will not remain continous and their is nothing like derivative for such function.
thanks....