Is the function $id:X \rightarrow X$ always continuous?
Countinuity of the identity map between different topologies
I'm trying to boot Canonical's Azure 16.04 .vhd file in a VirtualBox VM and it hangs at "non blocking pool is initialized".  It works in Hyper-V, so it may only be a bug in virtual box (5.0.20). For $a,b,c>0$, prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c+\frac{4(a-b)^2}{a+b+c}$ When you attempt to modify a file without having write permissions on it, you get an error:  &gt; touch /tmp/foo &amp;&amp; sudo chown root /tmp/foo &gt; echo test &gt; /tmp/foo zsh: permission denied: /tmp/foo   Sudoing doesn't help, because it runs the command as root, but the shell handles redirecting stdout and opens the file as you anyway:  &gt; sudo echo test &gt; /tmp/foo zsh: permission denied: /tmp/foo   Is there an easy way to redirect stdout to a file you don't have permission to write to, besides opening a shell as root and manipulating the file that way?  &gt; sudo su # echo test &gt; /tmp/foo We know that $2^4 = 4^2$ and $(-2)^{-4} = (-4)^{-2}$. Is there another pair of integers $x, y$ ($x\neq y$) which satisfies the equality $x^y = y^x$? Finding the number of non-negative integral solutions of $x + y + z = 10$ I've tried to render my scene but there's an object that won't show up. I've checked the camera, I've checked the visibility, it isn't hidden and it's showing in the viewport. I feel like I've opened every setting and have achieved nothing. I’m trying to render a book with a cover, flipping pages and stacks of pages. I have no idea how to fix the fact that the book cover doesn’t render. If I create a plane and select both the book cover and the plane and join them with Ctrl+J, the render contains a book cover but it doesn’t turn as it’s rigged to do so because it’s now linked to the plane and loses all the animated properties. As soon as I unjoin them the book cover stops rendering and everything appears as you see it there, a book with binding, pages, but no cover. For the life of me I cannot figure out what’s going on. There's a link to the file here: We are sponsoring a family to visit us in UK as friends from Madagascar for two weeks. They have a 6 year old and a 16 month old.   Do the kids need their own visas, and are they the standard visitor visa or a special child visa?   Also, when I try and apply on the website I can only apply for one person so how do I apply for all the individuals in the family?   I have looked on the Immigration website and can't find the answers I need. How to re-enable tray icons for applications in Ubuntu? Issues Doing a String Comparison in LINQ I'd like to have a horizontal line extending from the end of the text on a line to the right margin. So far I've found \hrulefill and \leaders\hrule\hfill, but these draw a line that's flush with the baseline of my text — how can I get it to be vertically centered? How do tag merge requests work? I had raised a  to merge pre-build-event, and pre-buildevent; and postbuild-event and post-build-event. That was about 11 months ago, and I still see these two tags even now.  How are tag merge requests handled? Is there a better way for tag merge requests other than posting on Meta? Syntax error due to using a reserved word as a table or column name in MySQL Kind of converse of Kolmogorov maximal inequality Let $S_n=\zeta_1+...+\zeta_n$ where $\zeta_i$ are independent with $E\zeta_i=0, E\zeta_i^2=\sigma_i^2&lt;\infty, |\zeta_i|&lt;K$.  Then, $P(\max_{1 \leq m  \leq n}|S_m| \leq x) \leq (x+K)^2/\operatorname{var}(S_n)$.  How do we show this?  The hint says that I should use the fact that $S_n^2-\sum_{m \leq n}\sigma_m^2$ is a martingale. But I am totally clueless....  Any hint would be appreciated! Thanks and regards. How do I install and use the latest version of GNOME? I followed the instructions for compiling GNOME Shell and it did compile with a few errors here and there but it didn't run. I installed GNOME Shell using sudo apt-get install gnome-shell but I got version 2.31.x, while the latest is 2.91.5 or something. So is there a way for me to install the latest build?   Is there some repository available for the latest build? I need to evaluate the limit without using l'Hopital's rule.  $$\lim_{x \to 0}{\frac{\sqrt{1+x\sin{x}}-\sqrt{\cos{2x}}}{\tan^{2}{\frac{x}{2}}}}$$ Live USB for installation does not boot, black error screen followed by visual artifacts on a purple screen I'm trying to install Ubuntu 18.04 desktop with Rufus on a computer with the following specs:  CPU: AMD Ryzen 5 2600 MOBO: ASUS Prime B450M-A/CSM RAM: G-Skill Ripjaws DDR4 F4-2400C15D-16GVB GPU: Nvidia GeForce GTX750 PSU: Apexgaming AG-650M SSHD: Seagate Firecuda Compute mATX: Rosewill SCM-01  Basically it boots from the USB (FAT32) and brings up a black error screen with words and numbers. Then it transitions to the purple splash screen with &quot;ubuntu&quot; and 5 dots, however the screen shows various visual glitches depending on which USB port I plug into. When trying to boot the computer, it boots to a black screen with the following error message: ACPI Error: Needed [Integer/String/Buffer], found [Region]    that shows what I mean. Evaluate the limit : $$\lim_{n \to \infty } {1 \over {\sqrt n }}\left( {1 + {1 \over {\sqrt 2 }} + {1 \over {\sqrt 3 }} + \cdots + {1 \over {\sqrt n }}} \right)$$  I can use the sandwich principle, certain convergence criteria, Cesaro mean theorem, limit arithmetic.. things around this area.  Any help would be greatly appreciated, thanks!  Sorry for not elaborating more at the beginning, rookie first-post mistake I suppose. :) Poiseuille's law states that the rate of flow of water is proportionate to $r^4$ where $r$ is the radius of the pipe. I don't see why.  Intuitively I would expect rate of flow of fluid to vary with $r^2$ as the volume of a cylinder varies with $r^2$ for a constant length. The volume that flows past a point is equal to rate of flow fluid, and thus it should vary with $r^2$.  I cannot understand the mathematical proof completely. Is there an intuitive explanation for this? Firstly my main goal is to try and get FTP files recursively in Centos.  However the actual FTP login contains an @ which ruins the syntax.  Is there some way to place the username in "double quotes" or some such equivalent such that I can use @in the username? Setting knots in natural cubic splines in R I have data with many correlated features, and I want to start by reducing the features with a smooth basis function, before running an LDA. I'm trying to use natural cubic splines in the splines package with the ns function.  How do I go about assigning the knots?  Here's the basic R code:  library(splines) lda.pred &lt;- lda(y ~ ns(x, knots=5))   But I have no idea about how to chose the knots in ns.