Can you help me proving this equality? $$|x|-|y|\leq |x-y|$$  I think that it's possible to give a too short proof if the things are written correctly.
Is there a clever way to show that  $$|x| - |y| \leq |x-y|$$  I believe I can think of a way to solve this using cases, but the book I'm working out of said that "A very short proof is possible if you write things in the right way" which has motivated me to figure out this quick way, but I've failed thus far and any help would be appreciated
Does OpenSSH support multihop login? Ansible uses OpenSSH as the bottomed network communicative implementation, but does it support multi-hop login?   I mean, if Ansible can login a server directly, but can it log in server_a then from server_a login server_b for config the server_b? What would be a good way to go about attacking a Quagmire 3 cipher?  I understand that it is polyalphabetic with a key and an indicator. I have started by taking the cipher text, taking every n-th letter and putting that in a string, computing the index of coincidence for the n strings I get and then averaging that. I would assume that whatever n value corresponds with the closest average index of coincident to English (0.066) would be the number of alphabets, i.e. the length of the indicator.  Where do I go from there? Or is my approach incorrect? I'm trying to create a command, which calls on an environment, which defines a custom column definition with one argument using \newcolumntype, and defines a second command, containing parameters for a table column.  Then, still within the first command, I begin the tabular environment and call the custom column, with the second command as its argument. I always get an undefined control sequence error, though. Any thoughts on why that might be?  I'm sure that was clear as mud, but I've cut it down to a minimal example, which follows:  \documentclass{article} \usepackage{array} \usepackage[table,dvipsnames]{xcolor} \usepackage{colortbl}  \newenvironment{tablecolor}{     \newcommand{\tlight}{\columncolor{SkyBlue!30}\color{black}}     \newcolumntype{C}[1]{&gt;{##1}c} }{}  \newcommand{\tablegoals}{ \begin{tablecolor} \begin{tabular}{l|C{\tlight}} Goal 7  &amp; \\ \end{tabular} \end{tablecolor} }  \begin{document}     \tablegoals \end{document}     Here's my second attempt. Different approach, same undefined control sequence error with \columncolor.  \documentclass{article} \usepackage{array} \usepackage[table,dvipsnames]{xcolor} \usepackage{colortbl} \usepackage{ifthen}  \newenvironment{tablecolor}{     \newcolumntype{C}[1]{&gt;{         \ifthenelse{\equal{dark}{##1}}{             \columncolor{Cyan}\color{white}             }{             \columncolor{SkyBlue!30}\color{black}         }     }c} }{ }  \newcommand{\tablegoals}[1]{     \begin{tablecolor}         \begin{tabular}{l|C{dark}}             Goal 7  &amp;   #1         \end{tabular}     \end{tablecolor} }  \begin{document}     \tablegoals{Check mark} \end{document} I dual booted ubuntu 11.04/11.10 a while ago with a USB stick and i want to uninstall it.   I would like to completely uninstall the old version and get 12.04.  I have a 64 bit laptop. Please help! Regionalism or just bad English? I've encountered a particular type of writing occasionally and it being, derp, in writing, it's hard to tell whether there's an accent behind it. The English used seems to me to be simply incorrect, but I can't help but feel that the following features are part of a dialect or a regional style of English. One of the most glaring (and grating) features is the substitution of &quot;saw&quot; with &quot;seen&quot;.  He seen him at the shop the other day. I seen that you were looking for... etc.  The use of &quot;away (to)&quot; is also peculiar, if not incorrect.  He was away to open the door when... He was away to get what he had asked for. etc.  I haven't come across these forms very often, and even then it was accompanied by otherwise mostly correct English, which is what makes me wonder what the hell. This is more intellectual curiosity than anything else. Trying to identify a science fiction short story from an anthology likely published before 1991.  Aliens invade during a nuclear war (which would be World War III, WWIII, WW3). The warring nations then turn their nukes on the landing sites, but the invasion succeeds.  Believe the setting is in the U.S., possibly Pacific Northwest, but definitely a mountainous region.  Based on negative inference from the aliens' description of humans as fur-less, no-tail, bipeds (or similar), the aliens are apes or monkeys.  The aliens describe Earth as worse than the Hell planet they previously conquered. They see our tanks and think that we can't have more than a few of those to fight with.  Yet the aliens are somewhat benign, as they take some children back to their parents for a stern talking-to after the children run an alien convoy off the road into a chasm by stringing a rope across the road. Setting up LVM Snapshot as a backup/restore point in ubuntu Setting up LVM Snapshot as a backup/restore point in ubuntu. Why? Well, as I see it, with all the great usefulness of Linux, its biggest drawback is with its mixed up way of installing apps. All the dlls go to one directory. All the configuration files to another. And the binaries are also put in a bunch. Yes, Windows works the same way more or less, but with the nature of system/server software installed on Linux, being that most of the software installed is only about 95% mature at any given time, messing up your system twice a month is very probable.. Of course, we can backup the system before and after each installation, but that takes a million years. System backups (as oppose to just data/files backup) requires you to turn off you computer and use some form of bootable live CD and a backup media. And, if the drive is more than 15% full, it might take a long time to do the backup, even with modern hardware. So, how can this be done? MySQL Insert query doesn't work with WHERE clause a / an - adjective - noun The article a becomes to an when the following noun starts with a vowel.     Not a adventure but an adventure.   But how is it, when there's an adjective before the noun?     Not a thrilling adventure or not an thrilling Adventure?   And how is it, when the adjective starts with a vowel but the noun does not?     Not a exciting tournament or not an exciting tournament? Linux/Bash: Create relative soft links to files in directory tree? Quick easy way to migrate SQLite3 to MySQL? How to remove indentation in footnote? Can you travel to the US prior 1 months of tourist visa expiry? I've heard that i can travel to the US any time before my tourist visa expiry.  Is that true?  (please advise) Let $u$ be an integer of the form $4n+3$, where $n$ is a positive integer. Can we find integers $a$ and $b$ such that $u = a^2 + b^2$? If not, how to establish this for a fact? i install ubuntu and followed a guide to put 20gb in '/' and the rest (150gb) in '/home'. Now i just found out that a lot of the things installed in ubuntu usually goes to '/' instead of '/home'. I have a lot more things to install.  So what is the point of '/home' ? How do I fix this ? Should I transfer 150gb from '/home' to / ?  Filesystem      Size  Used Avail Use% Mounted on udev            7.8G     0  7.8G   0% /dev tmpfs           1.6G  9.5M  1.6G   1% /run /dev/sda6        19G   16G  1.8G  91% / tmpfs           7.8G  676K  7.8G   1% /dev/shm tmpfs           5.0M  4.0K  5.0M   1% /run/lock tmpfs           7.8G     0  7.8G   0% /sys/fs/cgroup /dev/sda2        96M   29M   68M  31% /boot/efi /dev/sda8       159G  1.1G  150G   1% /home tmpfs           1.6G   56K  1.6G   1% /run/user/1000   what is /boot ? Its not '/' or '/home' How can I reproduce the error "package... needs to be reinstalled, but I can't find an archive for it" for testing? From time to time, Ubuntu users encounter errors from  or , of the form:  The package some-package needs to be reinstalled, but I can't find an archive for it.  I want to know what causes this error so that I can reproduce it and try to find safe ways of fixing it, even when the broken package is important and has many dependencies.  of the  might give a bit of a clue, but I don't know how packages get the status that causes the error.  How can I produce this error for testing on my (Ubuntu MATE 17.10) system?  This is prompted by  and my long-standing discomfort with closing questions about this error against , whose answer uses dpkg --force-all to remove the offending package.  suggests this solution has worked for many users, but I am not confident that using --force-all won't cause later problems, or that it's a good idea to use this method to remove important packages like APT. Working with a huge file. Illustrator is super slow. What can I do to ease the load? Combining Multiple Lists How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? Weird Integer boxing in Java