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Jul
7
comment Can there be generalization of Monty Hall Problem?
See arxiv.org/pdf/1208.2638.pdf
Jun
8
comment Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$
@RoryDaulton I do not want to be rude. But if it is not proved the convergence of the sequence $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$ to $f(x)=0.25^x+0.5^x+0.75^x-1$ and $x_0 = 1.5$ converge then your answer is not correct.
Jun
8
comment Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$
@RoryDaulton Another point which I understand is that you are assuming tacitly that if the method of bisection converges then Newton-Raphson method converge. You really mean it?
Jun
8
comment Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$
@RoryDaulton I think that to ensure convergence should use some type of Kantorovich's theorem for Newton methold to ensure the convergence of the sequence obtained by Newton's menthold.
Jun
8
comment Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$
@Rory Daulton It is necessary to prove that the sequence which is obtained from the Newton-Raphson method converges when $x_0 = 1.5$.
May
25
comment Dvoretzky–Kiefer–Wolfowitz inequality holds for discrete distributions?
What is your attempt to deal with the problem? You searched examples or counterexamples?
May
2
comment Number of circuits that surround the square.
see also another related question here.
May
2
comment The problem of the most visited point.
see also another related question here.
Apr
27
comment Why $\int_{\mathbb R^n}e^{-\sum_{i=1}^n x_i^2} \, dx_1\cdots dx_n=\omega_{n-1}\int_0^\infty e^{-r^2}r^{n-1} \, dr$
Did you mean that $\sum_{i=1}^1 x_i^2=1$ rather than $\sum_{i=1}^1 x_i=1$ ?
Apr
27
comment Why $\int_{\mathbb R^n}e^{-\sum_{i=1}^n x_i^2} \, dx_1\cdots dx_n=\omega_{n-1}\int_0^\infty e^{-r^2}r^{n-1} \, dr$
Did you mean that $\omega_{n-1}$ is the area of surface rather than $\omega_{n-1}$ be the surface?
Apr
2
comment Number of circuits that surround the square.
@DavidHolden +1 Yes. That's why we could not solve the problem with this strategy. But at least I can get a lower bound for the number of circuits. And I think with some trick I improve my lower bound.
Mar
27
comment proving gradient of a scalar field is perpendicular to equipotential surface
This question and this answer can give you too a direction:math.stackexchange.com/questions/401845/…
Mar
27
comment Why gradient vector is perpendicular to the plane
See this question and may answer: math.stackexchange.com/questions/401845/…
Mar
18
comment When a function contains a sequence, and how to find the function's limit?
@ElleryLai Do not intend to exhaust all cases to be analyzed. In the case of home work, is not purpose of this site provide full answers.
Mar
18
comment When a function contains a sequence, and how to find the function's limit?
@Ellery If $\lim_{n\to \infty}\frac{n}{x\cdot a_n}=L\neq 0$ and $L\in\mathbb{R}$ then the question is trivial. In your secont coment you are right. I hope helped you.
Mar
12
comment Proof of Banach's homeomorphism theorem without the contraction map principle.
@UmbertoP. Yes. There is. But speaking in terms of mathematics fundamentals I do not believe that such a test would find walking through results that were independent of Banach's fixed point theorem or domain invariance theorem. I think I could proof that uses connectness. I am writing a review about the implicit function theorem. Indeed an alternative proof that does not use the Banach's fixed point theorem.
Mar
6
comment Inverse Function Theorem. On the classical method of proof.
@Siminore No. I had not seen this issue in MathOverflow. The answer ultimately lead me to references I've consulted. Thanks anyway. +1.
Feb
12
comment Pseudo Proofs that are intuitively reasonable
@user4205580 See math.stackexchange.com/questions/239278/puzzle-on-the-triangle
Feb
4
comment The definition of negation
There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.
Feb
2
comment Properties of sup and lim inf.
@Vinith How nice it I've helped. And welcome to Mathstackexchange.