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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.
Feb
1
comment Properties of sup and lim inf.
@Vinith I think you should not accept such a quick answer. Unless, of course, you've already checked my tip step by step with pencil and paper. Dealing with 'sup' and 'inf' it is necessary familiarity and a good understanding the definition of supremum and the definition of infimum. This familiarity is achieved with practice various exercises.
Jan
31
comment Proof by induction: $(1+x)^n > 1 + nx+nx^2$
@Mufasa Note that if we use approach Taylor (or binomial approximation by Newton) combined with the principle of mathematical induction we get demonstration in which the principle of mathematical induction is superfluous.
Jan
15
comment convergence of $\prod_{n=1}^\infty (1-\frac{z}{n!})$
@corciacandy What do you mean by 'order'? If you are talking about convergence order towards the convergence of the product is uniform or punctually you can use the M test Weiersstrass to achieve uniform convergence.
Jan
4
comment if $x = \sqrt{x+1} + \sqrt{x+2} + \sqrt{x+3}$ then x =?
@user21820 yes. I did not express myself properly. I wanted to say that for each root a new root is added. Thanks for pointing.
Jan
3
comment if $x = \sqrt{x+1} + \sqrt{x+2} + \sqrt{x+3}$ then x =?
What do you think strange is not strange. The truth is that every time you raise squared each algebraic expressions you enter one (1) new root in the equation. Example: $x=1\implies x^2=1\implies x=1 \mbox{or } x=-1$
Jan
3
comment C*-algebras: Literature?
@Freeze_S No problem. Added a more complete list.