Recent content by Arnold1

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    Order of product of elements in a group

    You're welcome. Thank you for the explanation.
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    Order of product of elements in a group

    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...
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    Sequence of continuous functions convergent to an increasing real function

    @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 $$f$$...
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    Prove No Uniformly Convergent Subsequence: Functional Sequence

    Ok, I'll do that. Thanks.
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    Prove No Uniformly Convergent Subsequence: Functional Sequence

    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...
    • Arnold1
    • Thread
    • Convergent Functional Sequence Subsequence
    • Replies: 2
    • Forum: Calculus
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    Sequence of continuous functions convergent to an increasing real function

    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.
    • Arnold1
    • Thread
    • Continuous Continuous functions Convergent Function Functions Increasing Sequence
    • Replies: 9
    • Forum: Topology and Analysis
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    De l'Hospital's theorem - proof

    Thank you very much :)
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    De l'Hospital's theorem - proof

    If you would be so kind. I would really appreciate it :) Thank you a lot :)
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    De l'Hospital's theorem - proof

    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.
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    Graph two colours, no monochromatic path.

    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...
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    Two different circles in the plane with nonempty intersection

    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?
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    Two different circles in the plane with nonempty intersection

    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...
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    Prove there exists a matrix with certain entries and determinant

    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...
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