Re: Contradictory Derivative

Hey vamosromil.

The subtle difference is that 1) this only applies if x is an integer and 2) such a summation assumes that we sum up a known amount of times (i.e. n*x where n is fixed).

If you add up d(x)/dx n times you get n which is what we expect.

The derivative of nx is n and does not depend on x at all.

You can't do what you did because what you are doing (and the way you are doing it) is ill-defined. If you are summing up a fixed amount of times is just (x + x + ... + x) n times and not "x" times (what if x is 1.123123798123978123 or pi)?

You have to be careful with how you specify things.

Re: Contradictory Derivative

Quote:

Originally Posted by

**vamosromil** Now we change the definition of f(x) = x^2 to f(x) = x + x + x... up to x times.

So, $\displaystyle f(\sqrt{2})=\sqrt{2}+\sqrt{2}+\ldots +\sqrt{2}$ up to $\displaystyle \sqrt{2}$ times? :)

Edited: Sorry, I didn't see **chiro**'s post.

Re: Contradictory Derivative

I wonder how can you write down 2.453+2.435+?... exactly 2.435 times?

Re: Contradictory Derivative

Hello everyone, I see there are some typical questions being asked. I posted this problem on another forum too. And the first question of writing a real number other than integer that many number of times has also been addressed. But the core explanation is yet to be found..here is the link for that forum: Contradictory Derivative

Re: Contradictory Derivative

Quote:

Originally Posted by

**vamosromil**

What "core explanation?" Asked and answered.

-Dan