off topic - Can $|1-a|<1-|a|$ be solved for $a\in \mathbb{C}$ with $|a|<1$? It is my answer to a question, but I am not sure if I can more explicitly describe the $a$'s.
@Owatch, do this. $\sin^4t \cos^2 t = \frac14\sin^2(2t)(1-\cos(2t))/2 = -\frac18\sin^2 (2t)\cos (2t) + \frac1{16}(1-\cos (4t)$ now all terms should be integrable.
user147690
@TheSubstitute so you mean $|1-z|\lt 1-|z|$? (Which you should draw as circles)
So we are considering the case of a triangle right now @TedShifrin. Our thinking should generalize nicely. Basically we are saying that, away from the corners, the triangle and the square are indistinguishable.
@TedShifrin, we're now thinking that the number of sides determines where the catenary is getting cut off. For a 100-gon, we are gluing together only small neighborhoods around the catenaries' maxima. For a triangle, however, we include a much larger interval centered at the maxima of the catenaries.
Not so bad, @Ted. Lots of long walks. Not as much math as I'd like at the moment, but I'm warming back up to it. It seems I'm a bit more fatigued than I thought, for the time being.
There's a nice bike path that runs by my house, @Ted, where there's a shoulder where you can walk with little interference. It goes decently far, and the foliage lining the path is very pleasant. It's very peaceful.
@Alex Well, I'm actually from a few miles more south, nearish Canton, but basically nowhere. Just Akron for school, and have been living here for the past few years
Oh, I see @pjs36. Cool! I was just curious. I ran cross country in high school, so I crossed paths with a few places in southern Ohio. I've only been to Canton once.
10, raised to the power that it requires to produce a number, will produce that number? I feel my logic is wrong or bad. But since a logarithm represents the power to which a base must be raised to give you a number, then having the base to the log of that number will yield the power required to get that number in the exponent, which means you will just get whatever you are trying to get in the exponent.
Gotcha, @AlexW. Well, it wasn't quite southern Ohio, still NEO (Stark county), just not anywhere in particular :) I take it you're from the greater Cleveland area, then?
Well we will see Others are not like you @Balarka Never comes and brags in front of you saying that he knows more algebraic topology than you Thats the sign of a person who does maths you are just sitting here to gain attention
@Rememberme One more thing, I only do math for passion not for other reasons. Well, to tell it truth, I like very much when any of my proofs are liked by @robjohn. It's a sign I'm on the right track. The opinion of a super professional always matters to me.
I know you mentioned you were wanting to learn some differential stuff and de Rham cohomology, I am in a sort of similiar boat and I found it and it looks like just what I have been looking for. You should take a look at it @BalarkaSen
Thats shows the difference between you and robjohn He never forces anyone to just do analysis he appreciates every bit of math Not like you @Chris'ssis
@Rememberme If robjohn and r9m weren't here you would never see me here. When you don't see them coming here be sure I won't return for gaining attention.
@Rememberme I don't force anyone to consider any of the sentences I write here. I mean you can consider that I have no question created by me (although there are many thousands I created so far - only a profound passion pushed you in this direction)
I will never compare myself with robjohn coz i am not that much knowledgeable as him but i am sure of this much that the way you think (sorry to say) is nonsense
@Rememberme No, no, no. This is just what you like to believe. It's simple: when talking abut non-mathematical stuff, of course I can say all kind of things because I'm not interested in saying things about personal life, as regards mathematics, all is serious.
Besides that, I'm not here to be criticized by you. Who are you? Why don't you attend some mathematics instead? You talk far more about non-mathematical subject (like @BalarkaSen) , and not only that you do that, you want to put me into a certain kind of light. This is just a lose of time. You'd better learn something instead.
@Rememberme Of course, I'm preparing to publish more papers in this area, I also prepare a book. Be sure I'll still be here for some time. Well, I think I can do the math I like without reciving permissions from you.
I'm busy now, and it's also interesting such discussions appear almost all the time when I'm in the middle of some amazing research. I prefer to do research instead.
You dont need permissions from me its just that dont say facts like analysis is the world until you havent learnt everything in maths (which you can never)(well no one can)
@Rememberme I never said that. Related to discussion yesterday I said those thiongs to @teadawg1337 because he seemed to me very passionate about analysis. Well, sometimes people get discouraged in front of some topics, I just wanted to help him (but it was a mistake from my side - I admite that).
e.g. the units mod 3 and the cyclic group of order 2 are different groups in a technical sense, but they are both the same type of group. similarly, two different sets can be well-ordered, but they can have the same type of well-order
Is there a general formula for the following
$$\sum_{n\geq 1}\frac{\left(1-\frac{1}{2}+\frac{1}{3}-\cdots \pm \frac{1}{n}\right)}{n^p}\,\, p\geq 1$$
What about some restrictions on $p$ , like integers or anything helpful ?
Let V be a finite dimensional vector space over $\mathbb{F}$ , and let $T,S:V\to V$ be linear transformations and $B,C$ ordered bases for $V$. Assume that $$\left[T\right]_{B}^{B}=\left[S^{2}\right]_{C}^{C}$$
(Where $[T]^B_B$ is the matrix of the linear transformation $T$ with respect to bas...
Hello @DanielFischer :) Are you familiar with the algorithm of FastFourierTransform ? I want to write a version of FastFourierTransform(fft) for the case that N is a power of 3, in which we seperate the input-vector into three subvectors, solve the problem recursively at them and combine the solutions of the subproblems.
Let V be a finite dimensional vector space over $\mathbb{F}$ , and let $T,S:V\to V$ be linear transformations and $B,C$ ordered bases for $V$. Assume that $$\left[T\right]_{B}^{B}=\left[S^{2}\right]_{C}^{C}$$
(Where $[T]^B_B$ is the matrix of the linear transformation $T$ with respect to bas...
