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  • mathmari's Avatar
    Yesterday, 15:53
    mathmari replied to a thread Open cover in Analysis
    I think that it holds that there is for every $n \in \mathbb{N}$ an $0 < x < 1$ such that $\frac{1}{n} \in \left(\frac{x}{2},\frac{3x}{2}\right)$,...
    3 replies | 33 view(s)
  • MarkFL's Avatar
    Yesterday, 15:42
    Hello and welcome to MHB! :D We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This...
    1 replies | 36 view(s)
  • mathmari's Avatar
    Yesterday, 14:43
    mathmari started a thread Open cover in Analysis
    Hey!! :o Let $\mathbb{R}$ provided with the metric $d(x,y)=|x-y|$. I want to check if the collections of sets $$S_1=\left \{\left (\frac{x}{2},...
    3 replies | 33 view(s)
  • I like Serena's Avatar
    Yesterday, 09:31
    I like Serena replied to a thread Right triangle. in Geometry
    Google translates triangle as sankakkei. And searching for sankakkei shows that this word is also used for a three dimensional puzzle of triangles....
    18 replies | 169 view(s)
  • I like Serena's Avatar
    April 24th, 2018, 06:54
    My own best guess was to look at the differences: $\frac 13, \frac 16, \frac 1{10}$. The next difference might be $\frac 1{15}$, although it does...
    9 replies | 134 view(s)
  • I like Serena's Avatar
    April 23rd, 2018, 15:52
    I like Serena replied to a thread Special Relativity in Physics
    It's the other way around.
    11 replies | 135 view(s)
  • I like Serena's Avatar
    April 23rd, 2018, 15:26
    I like Serena replied to a thread Right triangle. in Geometry
    For the record, something like that is called a sangaku. A drawing that exhibits a proof, without any words, expressions, or symbols. Admittedly my...
    18 replies | 169 view(s)
  • I like Serena's Avatar
    April 23rd, 2018, 15:04
    I like Serena replied to a thread Right triangle. in Geometry
    You mean just drawings? (Wondering) Something like this: \begin{tikzpicture} %preamble \usetikzlibrary{arrows} \def\a{sqrt(17)} ...
    18 replies | 169 view(s)
  • I like Serena's Avatar
    April 23rd, 2018, 13:37
    I like Serena replied to a thread Right triangle. in Geometry
    To be honest, I only used trigonometry because it means I have to use fewer words to explain those ratios! (Rofl)
    18 replies | 169 view(s)
  • I like Serena's Avatar
    April 23rd, 2018, 13:20
    I like Serena replied to a thread Right triangle. in Geometry
    Trigonometry is only used in the first step. We can replace it with non-trigonometry by observing that triangles ABC and ACD are similar, meaning...
    18 replies | 169 view(s)
  • I like Serena's Avatar
    April 23rd, 2018, 12:55
    I like Serena replied to a thread Right triangle. in Geometry
    Let's make a drawing: \begin{tikzpicture} %preamble \usetikzlibrary{arrows} \def\a{sqrt(17)} \def\b{sqrt(68)} \def\c{sqrt(85)} ...
    18 replies | 169 view(s)
  • I like Serena's Avatar
    April 23rd, 2018, 09:13
    I like Serena replied to a thread Special Relativity in Physics
    Indeed, the distance travelled is $v\Delta t' = 240\text{ lightyear}$. So we have $\Delta t' = \frac{240\text{ lightyear}}{v}$ and $\Delta t =...
    11 replies | 135 view(s)
  • mathmari's Avatar
    April 22nd, 2018, 17:50
    mathmari replied to a thread Banach space in Analysis
    I understand!! Thank you very much!! (Smile)
    6 replies | 87 view(s)
  • I like Serena's Avatar
    April 22nd, 2018, 12:30
    Let me throw in another XKCD: I do hope that no one drops our people table! (Worried)
    19 replies | 515 view(s)
  • I like Serena's Avatar
    April 22nd, 2018, 11:32
    I like Serena replied to a thread Optics: Lenses in Physics
    Normally the object and image are at different sides of the lense, meaning their distances add up. However, it is possible that we have a virtual...
    6 replies | 89 view(s)
  • MarkFL's Avatar
    April 22nd, 2018, 10:17
    MarkFL replied to a thread Olinguito in Introductions
    Hello, and welcome to MHB! (Wave)
    8 replies | 105 view(s)
  • I like Serena's Avatar
    April 22nd, 2018, 09:31
    Good! (Happy) We have: $$\epsilon = -\d \Phi t = -\d {(B_i A_i + B_o A_o)} t\approx -A_i\d {B_i} t $$ where $A_i$ is the cross sectional area...
    9 replies | 124 view(s)
  • mathmari's Avatar
    April 22nd, 2018, 09:17
    mathmari replied to a thread Banach space in Analysis
    I got stuck right now. I haven't really understood that part. (Thinking) I thought that the Cauchy sequence should be in $Y$ but its limit...
    6 replies | 87 view(s)
  • I like Serena's Avatar
    April 22nd, 2018, 08:59
    I like Serena replied to a thread Banach space in Analysis
    $C(\mathbb{R})$ means that $\forall t\in \mathbb R: \lim_{h\to 0} f(t+h)=f(t)$. Will that be true if $f$ is the absolute converging limit of a...
    6 replies | 87 view(s)
  • I like Serena's Avatar
    April 22nd, 2018, 08:47
    How about not letting ourselves be stopped by that, but just do the math?
    9 replies | 124 view(s)
  • I like Serena's Avatar
    April 22nd, 2018, 08:45
    I like Serena replied to a thread Optics: Lenses in Physics
    Good! It means that we have the set of equations: \begin{cases} d_o+d_i=2.4 \text{ m} \\ f = 0.55 \text{ m}\\ \frac 1{d_o} + \frac 1 {d_i} = \frac...
    6 replies | 89 view(s)
  • I like Serena's Avatar
    April 22nd, 2018, 08:29
    We have $\varepsilon = -\d \Phi t$. This applies to all of the magnetic field that passes through the loop. And that includes the magnetic field that...
    9 replies | 124 view(s)
  • mathmari's Avatar
    April 22nd, 2018, 08:05
    mathmari replied to a thread Banach space in Analysis
    Great!! (Yes) How could we justify that $C(\mathbb{R})$ is a Banach space? (Wondering) Do we have to show that $\frac{\sin^2\left...
    6 replies | 87 view(s)
  • I like Serena's Avatar
    April 22nd, 2018, 07:58
    I like Serena replied to a thread Banach space in Analysis
    Hey mathmari!! (Wave) What you have is correct. So $X$ is indeed complete and therefore a Banach space. And $Y$ has a Cauchy sequence that shows...
    6 replies | 87 view(s)
  • I like Serena's Avatar
    April 22nd, 2018, 07:32
    Suppose we neglect the contribution of the magnetic field outside the solenoid? So we only consider the magnetic field inside the solenoid to find...
    9 replies | 124 view(s)
  • I like Serena's Avatar
    April 22nd, 2018, 07:30
    Hi Katsa333! Welcome to MHB! (Wave) Properly we have the function $g: \to \mathbb R$ given by $g(x)=\frac{x+3}{2}=\frac 12 x + \frac 32$. The...
    2 replies | 41 view(s)
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    Would it be possible if you helped me on a thread in the Trigonometry Forum? I am still stumped.
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    Thanks so much evinda!
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    Thanks evinda , sorry for late reply. I am busy with exams these days.
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    Thank you very much, evinda!
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    Hey evinda,

    I think if you ask for the proof of FLT for n = 4 in a different thread it would be better as it would be off-topic on the current thread. If you post it as a separate question, I'd be more than willing to answer to it.
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    Thank you very much!!!
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    Thanks, but I would have liked to stay 13.
  8. Ok,thanks!!!!
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    Hello and welcome to MHB, evinda!

    If you have any questions or comments about the forums, please feel free to address them to me or another staff member. We are happy to help, and look forward to your participation here!

    Best Regards,

    Mark.
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