Given the rectangle $Q$, find a subset $S$ of $Q$ whose closure equals $Q$, such that $S$ contains at most one point on each vertical line and at most one point on each horizontal line.  I really don't figure out why there must exists such a set; can you give me an example?
Given a subset $A$ of $\mathbb{R}^{n}$, a point $x \in \mathbb{R}^{n}$ is said to be in the boundary of A if and only if for every open rectangle $B\subseteq\mathbb{R}^{n}$ with $x\in B$, $B$ contains both a point of $A$ and a point of $\mathbb{R}^{n}\setminus A$.  My question is from Spivak's Calculus on Manifolds: Construct a set $A \subseteq [0,1]\times [0,1]$ such that $A$ contains at most one point on each horizontal and vertical line but has boundary equal to $[0,1]\times[0,1]$.
How to design a command inquiring internally required packages? Error 404 : While using flag Recently on Stack Overflow I got privilege to flag a post. So when I try to flag a post as duplicate. The diaglog box is not properly loading.         However I am easily able to use other flag option like "other","spam" or "offensive".   "other"        "spam"        "offensive"        I am using Google Chrome Version 28.0.1500.71 and Win XP Operating System. I have tried in firefox as well but it is showing me same problem. A sphere of radius R is rolling without slipping with a velocity v and collides inelastically with a step of height h &lt; R. What is the minimum velocity for which the sphere will be over the step?    Relevant equations  Total kinetic energy (maybe): $\frac{1}{2}I\omega^{2}+\frac{1}{2}mv^2$  Gravitational potential energy: $mgh$   Moment of inertia about a point a distance d from the CM from de center of mass: $I=I_{cm}+md^{2}$ Rolling without slliping  $v=\omega R$  A discussion of the problem This problem is confusing to me: I know the collision is inelastic so there is no conservation of kinetic energy, there is torque when the sphere pivots the step so the angular momentum is not conserved either, the linear momentum doesn't give a lot information and even though I tried to see what condition needs the torque about the pivot point (to give a net torque in the direction of rotation and thus passing the step), I'm not able to see which torque can overcome the one from gravity which doesn't let the sphere slide up:    The sphere has an angular velocity, but I'm missing something conceptual because I can't figure out how to formally state that the angular momentum changed the right amount so that the sphere made it past the step.  The attempt at a solution  My (almost certainly wrong) attempt was to say that the sphere lost kinetic energy because of the change on potential energy:  $\frac{1}{2}I\omega^{2}+\frac{1}{2}mv^2 +mgR = mg(R+h)\\ v=\sqrt{\frac{10}{7}gh} $  I hope you can help me :) How to derive the standard symplectic form on a 2-sphere in cylindrical polar coordinates? I have already know that at a point $p\in S^2$ with $u,v$ the tangent vectors at $p$. Then the standard symplectic form is $\omega_p(u,v) :=\langle p,\,u\times v\rangle$ where $u\times v$ is the outer product. My question is: How can one deduce from this that the symplectic form is $dz\wedge d\theta$ in the cylindrical polar coordinates $(z,\theta)$ on $S^2$? Here, $z$ is the height and $\theta$ is the angle. Thanks. I installed Ubuntu 17.10. Now I am having trouble with gksu:  $ gksu -dg synaptic No ask_pass set, using default! xauth: /tmp/libgksu-HgUjgQ/.Xauthority STARTUP_ID: gksu/synaptic/8760-0-alex-XPS-15-9530_TIME4974977 cmd[0]: /usr/bin/sudo cmd[1]: -H cmd[2]: -S cmd[3]: -p cmd[4]: GNOME_SUDO_PASS cmd[5]: -u cmd[6]: root cmd[7]: -- cmd[8]: synaptic buffer: -GNOME_SUDO_PASS- brute force GNOME_SUDO_PASS ended... Yeah, we're in... Unable to init server: Could not connect: Connection refused (synaptic:8767): Gtk-WARNING **: cannot open display: :1 xauth: /tmp/libgksu-HgUjgQ/.Xauthority xauth_env: (null) dir: /tmp/libgksu-HgUjgQ   If I don't use -g, the password dialog is disabled. So looks like a problem with creating a tty for root.  Any advice? Let $$ f(x) =    \begin{cases}\begin{align}     1\quad&amp;\text{ if }\; 0\leq x \leq 1 \\     2 \quad&amp;\text{ if }\; 1&lt;x \leq 2 \\   \end{align}\end{cases}$$  Then $\int^2_0 f(x)dx=3$ and an anti derivative of f(x) is $$F(x)=\begin{cases}\begin{align}     x\quad&amp;\text{ if }\; 0\leq x \leq 1 \\     2x \quad&amp;\text{ if }\; 1&lt;x \leq 2 \\   \end{align}\end{cases}$$ But, $F(2)-F(0)=4-0=4 \neq 3.$ Why has this happened?  Find an anti-derivative $G(x)$ of $f(x)$ such that $G(2)-G(0)=3$, the correct answer.  My attempt: $F(2)-F(0)=4 \neq 3$ because we need to break it up into two parts like this: $\int^2_1 2x dx + \int^1_0 x dx = x^2|^2_0 + \frac{1}{2} x^2|^1_0 =4-1+\frac{1}{2}-0=3.5$ but this is not right either. :(  For the "Find an anti-derivative $G(x)$..."I'm completely lost but perhaps if we solve the first part then I'll understand what it's asking for there.  Any help would be appreciated. Clock displays incorrect time I've just installed 64-bit Ubuntu 11.04 and after I updated it, the clock stopped displaying the right time. It's now 8 hours behind my normal time. I've checked the Time and Date settings and the Location field is correct. What's even weirder is that the time displayed in Time and Date Settings adjusts itself after a few seconds and is correct. The time displayed in the task bar remains the same, however.  Any ideas? Creating square buffer around point feature using ArcGIS for Desktop? I would like to create a square buffer from a point feature but I do not understand the code that goes into it.   Similar questions have been asked on the forums.esri website but that was over 10 years ago, and it did not work when I tried the code.  How do I create a square buffer from a point feature? Examples proving why the tensor product does not distribute over direct products. I recently read about the result that the tensor product distributes over direct sums. I was curious if it also distributes over direct products, but google tells me it doesn't.   What are some simple counterexamples to why this property isn't true? I know that there is a natural homomorphism  $$ \left(\prod M_i\right)\otimes N\to \prod (M_i\otimes N) $$ given by $(\prod m_i)\otimes n\mapsto \prod (m_i\otimes n)$ when $M$ and $N$ are modules over some commutative ring $R$. Are there standard examples where this homomorphism is not injective/surjective and hence not an isomorphism? How to parse JSON in iOS App Map of with object references as keys? WI-FI Nic showing 3 different transport id {Device id} There was a problem with my network controller so i opened up cmd and started to check for interfaces. I noticed a strange thing that my Wifi network controller had 3 different Device ID (Transport id's) When i tried to disable the wifi card the different id's went away. On my other computer i tested the same thing and it only shows 1 id? Device\NPF_{4A45A363-6346-48DA-8D28-13DD9C9C1E6A} Device\NPF_{E6994972-C66C-4ABF-BE27-17BAC7C1C971} Device\NPF_{B6394772-H66C-4ABF-HRE27-17JLC0H9C971} I am using snort to check for available interfaces. Can anybody explain why i am seeing this? WLC model: intel dual band wireless-ac 8265 running default settings on the adapter however i have hyper-v open Is "It is you who are mistaken!" correct? Possible Duplicate:          This is a line spoken by the . I always wondered if this is grammatically correct.  Luke says something like "You are mistaken ..." which the Emperor answers with     No, it is you who are mistaken!   Why wouldn't he say     No, it is you who is mistaken!   instead?  I don't know what rules apply here but my stomach tells me the latter is (at least also) correct, although you would say "you are mistaken". It feels as if he should be referring to "you" in the third person.  Could you please shed some light? Are both correct or – if not – which one is correct? And why? We are currently developing a site that currently has 8 million unique pages that will grow to about 20 million right away, and eventually to about 50 million or more.  Before you criticize... Yes, it provides unique, useful content. We continually process raw data from public records and by doing some data scrubbing, entity rollups, and relationship mapping, we've been able to generate quality content, developing a site that's quite useful and also unique, in part due to the breadth of the data.  It's PR is 0 (new domain, no links), and we're getting spidered at a rate of about 500 pages per day, putting us at about 30,000 pages indexed thus far. At this rate, it would take over 400 years to index all of our data.  I have two questions:   Is the rate of the indexing directly correlated to PR, and by that I mean is it correlated enough that by purchasing an old domain with good PR will get us to a workable indexing rate (in the neighborhood of 100,000 pages per day). Are there any SEO consultants who specialize in aiding the indexing process itself. We're otherwise doing very well with SEO, on-page especially, besides, the competition for our "long-tail" keyword phrases is pretty low, so our success hinges mostly on the number of pages indexed.   Our main competitor has achieved approx 20MM pages indexed in just over one year's time, along with an Alexa 2000-ish ranking.  Noteworthy qualities we have in place:   page download speed is pretty good (250-500 ms) no errors (no 404 or 500 errors when getting spidered) we use Google webmaster tools and login daily friendly URLs in place I'm afraid to submit sitemaps. Some SEO community postings suggest a new site with millions of pages and no PR is suspicious. There is a , too, in order to avoid increased scrutiny (at approx 2:30 in the video).      Clickable site links deliver all pages, no more than four pages deep and typically no more than 250(-ish) internal links on a page. Anchor text for internal links is logical and adds relevance hierarchically to the data on the detail pages. We had previously set the crawl rate to the highest on webmaster tools (only about a page every two seconds, max). I recently turned it back to "let Google decide" which is what is advised. Making separate Python installation that can call ArcPy? I see a lot of Q&amp;As asking how you can create a separate Python installation (e.g. the Anaconda or Python XY distribution) that can use arcpy, while not 'breaking' the original ArcGIS python installation.  I had this same problem, and I think I have found a 'universal' solution. So far we have done this on about 8 computers at work and it all works fine.   How to install a separate Python distribution that can use ArcGIS? how to hide files from package explorer Error message says I can't flag... but yes I can When trying to upvote a comment made on a locked post (ordinary lock, not historical lock which remove the vote arrows and flag altoghether) we are greeted with such error message:        Or in words:     This comment is not eligible for voting or flagging   Being the curious type, I went straight away and tried to flag, fully expecting the same message... just to see the flag dialog open up just fine:        I was able to flag as well.  Can the error message please be changed to just "This comment is not eligible for voting"? Or of course, if it's not the intended behavior really disable the option to flag?  The original post on which I experimented is now deleted, but  you can play with. How can PPAs be removed? Beamer to HTML using make4ht \documentclass{beamer} \usetheme{Madrid} \begin{document} \begin{frame} aaa \end{frame} \begin{frame} bbb \end{frame} \end{document}   The above tex file is to be converted into html. I am using the following command   make4ht filename.tex   However it throws error. The basic question is "Is it possible to convert beamer presentation to html using make4ht?" What does "65" mean?