Recent content by Arnold1

You're welcome. Thank you for the explanation.

Hello. I'm just beginning my course in algebra. I've been reading Milne, Group Theory ( http://www.jmilne.org/math/CourseNotes/GT310.pdf page 29). I've found there a very nice proof of the fact that given two elements in a finite group, we cannot really say very much about their product's...

@chisigma Maybe it'a a stupid question, but I am not sure about one thing. We choose n points, right? From condition 1) we get n+1 points, from 2) we get $$x_{n+1}>x_n$$ and $$x_1>x_0$$. Am I missing something? And could you tell me how to check that $$f_n(x)$$ is pointwise convergent to $$f$$...

Ok, I'll do that. Thanks.

SOLVED Prove that the functional sequence has no uniformly convergent subsequence -check $$n \in \mathbb{R}, \ \ f_n \ : \ \mathbb{R} \rightarrow \mathbb{R}, \ \ f_n(x) =\cos nx$$ We want to prove that $${f_n}$$ has no uniformly convergent subsequence. This is my attempt at proving that...

Hi. Could help me with the following problem? Let f be a real function, increasing on [0,1]. Does there exists a sequence of functions, continuous on [0,1], convergent pointwise to f? If so, how to prove it? I would really appreciate any help. Thank you.

Thank you very much :)

If you would be so kind. I would really appreciate it :) Thank you a lot :)

I was wondering if you know if there is an English version of Tadeusz Wazewski's proof of de l'Hospital's theorem which is available here in French : Biblioteka Wirtualna Nauki But (unfortunately) I don't speak French.

I've just begun studying graph theory and I have some difficulty with this problem. Could you tell me how to go about solving it? I would really appreciate the least formal solution possible. In a graph G all vertices have degrees \le 3. Show that we can color its vertices in two colors so...

So this is it? There are only countably many disjoint circles meeting the above specified conditions nut uncountably many points on x axis. Can we already deduce that at least two circles intersect?

Hi. Here is a problem I've been trying to solve for some time now. Maybe you could help me. We have two sets \mathcal {Q} is a set of those circles in the plane such that for any x \in \mathbb{R} there exists a circle O \in \mathcal {Q} which intersects x axis in (x,0).\mathcal {T} is a set of...

Hi. Here is a problem I found in my algebra book and I don't know how to solve it. Could you please help me? Show that there exists a matrix A \in M(n,n;R), such that m_{ij} \in \{-1,0,1\} and det A=1995 (I think it can be any other number as well, but the book was printed in 1995 :) ) My...