Well, basically the electrons contain a charge and flow through the wire. When you wrap a wire around something like an iron nail and hook the wire up to a battery, the electrons flow through and create a magnetic field. You can read more detail about it here...
Regarding your edit, tl;dr we're dumb. We were way over thinking trying to deal with un-integrable functions and somehow got on the topic of Taylor and Maclaurin series without looking into the idea that some functions can't be represented as Taylor Series. We then thought (without properly...
A few non integrable functions I can think of are f(x) = ln(ln(x)), \text{ or } g(x) = e^{e^{x}}, \text{ also } h(x) = \frac{1}{ln(x)} are a few. So for any function, \int{(f(x) + -f(x))dx} = \int{dx} = c. That's a simple way to clear that up!
Oh wow, that's definitely much simpler then the way we were going about it. And yes, I was referring to the typical point-wise addition and multiplication operators...I wasted way more time on this problem then I probably should have, buuut proofs are something I need to definitely strengthen...
I thought as much, but we weren't really sure where to go. The other idea we had was to define the set of integrable functions and work from there. Any idea where I should start looking for a better solution? As you said, I know I am way over-complicating this :/.
This isn't a homework problem, a classmate asked for a challenging proof to try and do and this was the one we were given. We started by trying to derive some rules from un-integratable functions but realized that that would take a long time and a lot of work. After some thinking we came up with...
Finally got around to making one of these hello posts! I have had an account here for a while but I think this is like my second post. Anyway I took physics in high-school, which was Algebra based. Currently I'm a Sophomore Computer Science major, math minor, who over this summer read "Surely...
{\frac{100m}{9.8s}} = {\frac{100m + x(m)}{10.1s}} , so for B to tie A, it can have about a 3.06m lead, or about a 1.133second lead. Now (assuming I did this correctly) any lead B has greater then this will mean that B will overtake A, and any less of a lead for B will mean A will overtake B. You...