Show that the set of all irrationals is not countable
Proof that the irrational numbers are uncountable
Custom cross-reference formats (e.g. "Equation 1" instead of just "1") How to switch from Resident visa to Tourist visa status in the Schengen area? I have a 1-year residence permit from one Schengen country that is now expiring. Upon its expiration, I would like to get my 90/180 days validity as a tourist to stay, or return here as soon as possible.  I understand that the tourist short-stay scheme is based on the 90/180 days "counter". But what happens if my previous stay was not tourism but residence (as searching year). Wouldn't that mean that I can quickly exit and re-enter the Schengen area to activate my tourist stay?   Also, is there a way to change this purpose of stay without exiting the Schengen area? Is there a way I can see all the versions that are in the archives that I have configured in sources.list. I can see the last version of each archive withapt-get policy, but how can I see them all?  Is there any way that this can also include PPA and anything in sources.list.d? Reattach to lost X11 session I'm using X11 forwarding over ssh to run Linux apps on my Windows box, and when the network drops it loses everything that was running. Is there anything similar to screen for X11? The question of whether P=NP is perhaps the most famous in all of Computer Science. What does it mean? And why is it so interesting?  Oh, and for extra credit, please post a proof of the statement's truth or falsehood. :) Suppose I have an Atwood machine, that is, two different masses connected with an inextensible, massless rope over a pulley. Assuming no friction between the rope and the pulley, the heavier mass will accelerate towards the ground, the lighter mass will accelerate towards the pulley, and the rope will accelerate towards the heavier mass. These three accelerations will be equal in magnitude. But this makes no sense to me. Force causes acceleration. But there is no force acting on the rope. And even if there was, the acceleration of the rope would be infinite because its mass is 0. So why does the rope accelerate? And how can the magnitude of this acceleration be finite? Centos mysql version is 5.5 however PHPmyadmin still says version 5.1 PHP variable variables I want to store courseworks marks of n courseworks into n variables, such as cw1 and cw2 etc. Using variable variables how can I come with cw1, cw2 etc.   How can I dynamically create variables? Is there any work-around if you are somewhere where images are blocked? I'm currently working in a bank, and while about 99.7% of the internet is blocked, Stack Exchange thankfully isn't (yet) however imgur is.  It means I can't view images posted alongside questions. The only workaround I have found is to search Google images for the URL, but you get a  which is a bit useless.  Does anybody know any clever tricks for viewing the images accompanying questions when you are somewhere where imgur is blocked?  Are there any plans to route the images stored on imgur through a Stack Exchange URL? In QGIS I would like to clip a raster precipitation layer using an admin boundary layer that is vector data. However the Geoprocessing tools seem to be usable only for vector data. How can I clip this precipitation layer? How to access a clicked URL in a URL handler application created in Automator I'm currently trying to modify the default URL handling behavior in OS X. I would like, when clicking on any link outside of a web browser, to copy this URL to the pasteboard instead of opening it in the default web browser – for instance, clicking a link in a Skype conversation should copy this URL to the OS X pasteboard instead of opening it in Firefox (which is currently my default web browser).  I have thought about solutions, but I’m currently unable to implement one. If I can create an application that puts URLs into the pasteboard that are sent to it, and can set this application as the default web browser, I would be able to achieve my goal.  I created an application with Automator that executes the shell command pbcopy and have set this application as my default web browser, but I didn’t get the expected result. I did some testing and I can confirm that the application runs on clicking on a link, however, I cannot get the URL passed to the application / shell script. I tried both stdin or a passed argument, but without success.  Is there a way for an application created with Automator to retrieve a clicked URL and send it to pbcopy, when that application is set as a (default) handler for URLs?  Alternatively, is there a better way to create a fake web browser that takes the input and puts it in the pasteboard than Automator? Or is there any other way that I can achieve my goal without a custom application / script? I recently installed an SSD and AFAIK Ubuntu makes a weekly FSTrim on SSD's that support it.  Is there a log file of this trims? The use of "were- should- had” at the beginning of sentences instead of “if” Conditionals in English are usually formed by using if with normal word order; but for the three past (subjunctive) forms were, should, and had, it is also possible to express the conditional through subject–auxiliary inversion alone, with no if in the conditional clause.  Does forming conditionals in this manner differ semantically from if-conditionals? Is some aspect of the conditional statement or the conditionality emphasised more in one version than in the other? Or are there differences in how and when they are used? Or are they simply completely interchangeable?  For example:     If I were you, I would try it again   Were I you, I would try it again      If I had seen it, I would have told you   Had I seen it, I would have told you      If you should drink, don’t get behind the wheel   Should you drink, don’t get behind the wheel Windows 10 high memory usage (unknown reason) Is there a drupal.org API for retrieving the list of available modules, a description of them and available versions? Neutrino project in Tamil-Nadu India In , the Indian government is going to start a neutrino project.  Questions:   Is it harmful for people who stay there?   Will this project affect any living beings? Does it cause any pollution? The preimage of continuous function on a closed set is closed. How do I recursively create a folder inside another non-existent folder? I want to create this folder: $HOME/a/b/c/d while $HOME/a has not yet been created! Is it possible with one line in Terminal? Regular Expression Uppercase Replacement in C# I have the following C# which simply replaces parts of the input string that look like EQUIP:19d005 into URLs, like this:  input = Regex.Replace(input, @"(EQUIP:)(\S+)", @"&lt;a title=""View equipment item $2"" href=""/EquipmentDisplay.asp?eqnum=$2""&gt;$1$2&lt;/a&gt;", RegexOptions.IgnoreCase);   The HTML ends up looking like this.  &lt;a title="View equipment item 19d005" href="/EquipmentDisplay.asp?eqnum=19d005"&gt;EQUIP:19d005&lt;/a&gt;   The only trouble is that the destination page expects the eqnum querystring to be all UPPERCASE so it returns the correct equipment when eqnum=19D005 but fails if it receives eqnum=19d005.  I guess I can modify and correct EquipmentDisplay.asp's errant requirement of uppercase values however, if possible I'd like to make the C# code comply with the existing classic ASP page by uppercasing the $2 in the Regex.Replace statement above.  Ideally, I'd like the HTML returned to look like this:  &lt;a title="View equipment item 19d005" href="/EquipmentDisplay.asp?eqnum=19D005"&gt;EQUIP:19d005&lt;/a&gt;   Notice although the original string was EQUIP:19d005 (lowercase), only the eqnum= value is uppercased.  Can it be done and if so, what's the tidiest way to do it? Say I have a code to draw a flow chart, I want now a arrow from node 3 to node 1, how can I do that?  1&lt;--| |   | 2   | |   | 3----   MWE  \documentclass[class=article,border=0pt]{standalone}  \usepackage{tikz} \usetikzlibrary{shapes,arrows}  % Define block styles \tikzset{     block/.style={rectangle, draw, line width=0.5mm, black, text width=5em, text centered,                   rounded corners, minimum height=2em},     line/.style={draw, -latex} }% &lt;- if you insist in using this in the document add this % here. \begin{document} \begin{tikzpicture}[node distance = 1cm, auto]     % Place nodes     \node [block] (BLOCK1) {a};     \node [block, below of=BLOCK1] (BLOCK2) {b};     \node [block, below of=BLOCK2, node distance=1cm] (BLOCK3) {c};     % Draw edges     \path [line] (BLOCK1) -- (BLOCK2);     \path [line] (BLOCK2) -- (BLOCK3); \end{tikzpicture} \end{document}