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

[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?

 

[micromass]

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.

 

[vkash]

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.

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