Lebesgue measure of sets with cardinality greater than $ℵ_1$
Let $X\subset \mathbb{R}$ Lebesgue measurable, $|X|<|\mathbb{R}|$, is it true that $X$ is null?
real memory usage Minimum Length Regular Expression "I will appreciate your help" I encounter the phrase "I will appreciate your help" from time to time and it doesn't sound too honest to me. To be more specific, I don't have a problem with this phrase coming from a friend, because he will appreciate my help by "owing me one". But a stranger from the Internet, that's different, methinks.  "How will you appreciate it?" pops in my mind every time I see it, because to me, appreciation equals reward and, well, you can't reward people over the internet much. It is quite possible that I am just wrong and this is a perfectly fine figure of speech. caching JavaScript files Which is the best method to make the browser use cached versions of js files (from the serverside)? Is it possible to write one CSS rule for several prefixed selectors? Why is there free space at the end of NTFS Partitioned Drives? I've been wondering this for a while, why is there free space at the end of a drive that was formatted to NTFS in windows?  You can only see the unallocated space in Linux. So why is it there? Does it serve a purpose? Why do the big nuts always remain at top? The Brazil-nut Effect Can I charge a computer through its USB port? Is there a "do ... while" loop in Ruby? I'm using this code to let the user enter in names while the program stores them in an array until they enter an empty string (they must press enter after each name):  people = [] info = 'a' # must fill variable with something, otherwise loop won't execute  while not info.empty?     info = gets.chomp     people += [Person.new(info)] if not info.empty? end   This code would look much nicer in a do ... while loop:  people = []  do     info = gets.chomp     people += [Person.new(info)] if not info.empty? while not info.empty?   In this code I don't have to assign info to some random string.  Unfortunately this type of loop doesn't seem to exist in Ruby. Can anybody suggest a better way of doing this? Controlling the value of 'this' in a jQuery event I have created a 'control' using jQuery and used jQuery.extend to assist in making it as OO as possible.  During the initialisation of my control I wire up various click events like so  jQuery('#available input',              this.controlDiv).bind('click', this, this.availableCategoryClick);   Notice that I am pasing 'this' as the data argument in the bind method. I do this so that I can get at data attached to the control instance rather from the element that fires the click event.   This works perfectly, however i suspect there is a better way  Having used Prototype in the past, I remember a bind syntax that allowed you to control what the value of 'this' was in the event.  What is the jQuery way? Adjoint pairs, triplets and quadruplets Often we have adjoint pairs $(A, B)$ (meaning $A$ is left adjoint to $B$). Sometimes we have adjoint triplets $(A,B,C)$ (meaning $A$ is left adjoint to $B$ and $B$ is left adjoint to $C$. No adjoint relation between $A$ and $C$ obviously, since they have the same source and target).  So the first question is: can we have quadruplets $(A,B,C,D)$ ? (meaning that $C$ is also left adjoint to $D$).  Second question: It would be then possible that we have $(A,D)$ besides $(A,B)$. But I think not, because I think that it is not possible to have a functor $A$ with two different right adjoints, $B$ and $D$. Is this correct? About Trivariate Normal Distribution I am working on a paper, and have a problem regarding ellipsoid and Trivariate Normal Distribution. Suprisingly I can't find much in literature but I found your in one of your answers:     Because this construction has nothing to do with "confidence" per se,   the objective is to establish some convention for describing the shape   and relative size of the points. Using 1.96 sort of works (for three   variables): it contains about 72% of the probability of the trivariate   normal distribution. But as the number of variables increases this   method produces ellipses that are far too small. For instance, with 10   variables it will contain only 4.6% of the probability; using 4.28   instead of 1.96 in this case will contain 95% of the probability.   How did you get this number 72%? Or do you have some literature to recommend to me in which I can find this. I would appreciate it very much! Desktop link to Eclipse I was tring to install eclipse on ubuntu. What I did: I unzipped the tar archive of eclipse. I tried to start eclipse from the command line - like this - ./eclipse. It works. But then I tried to create a desktop icon with: gnome-desktop-item-edit ~/Desktop --create-new. In a new icon I showed the path to the eclipse executable which I could launch from the command line. But then eclipse does not start stating:  A Java Runtime Environment (JRE) or Java Development Kit (JDK) must be available in order to run Eclipse. No Java virtual machine was found after searching the following locations: /home/artem/eclipse/jre/bin/java java in your current PATH   The same message appears if I try to launch eclipse by double-clicking its original launcher. So it starts from the terminal but not from the desktop (it does not start when double-clicked) And also I get a message in the terminal (at some stage it appeared):  (gnome-desktop-item-edit:8998): Gtk-WARNING **: Attempting to store changes into `/root/.local/share/recently-used.xbel', but failed: Failed to create file '/root/.local/share/recently-used.xbel.DSV8LW': No such file or directory   I am using Ubuntu 12.04 x32 and eclipse Juno.  PS. PATH variable points at jdk/bin and JAVA_HOME - to the jdk folder PSS. I actually set the environment variables through .bashrc file(JAVA_HOME and PATH) Minecraft Vanilla 1.9 crash with problematic frame ig8icd64.dll avoid space after commas used as thousands separator in math mode Is it possible to get the information for a device tree using /sys of a running kernel? Commonly for arm systems, device trees supply hardware information to the kernel (Linux). These device trees exist as dts (device tree source) files that are compiled and loaded to the kernel. Problem is that I do not have access to such a dts file, not even to a dtb file.   I have access to /sys and /proc on the machine and I wanted to ask if that would allow me to "guess the correct values" to be used in a dts?  Also potential answer could highlight additionally the aspect if the answer to this question also depends on whether the device tree interface was used in the first place (i.e. a dtb was created and provided to the kernel) instead of some more hacking "we simply divert from vanilla and patch the kernel so as to solve the device information problem for our kernel only"-solution? Does Thanos' plan apply to higher order beings? We know that Thanos' plan was to       instantly destroy half of all life in the universe    His plan doesn't appear to apply to lower or non sentient life forms      if it did half the trees in the final Wakanda scene would have disintegrated too   Does his plan apply to all beings more powerful than himself? If $|A| > \frac{|G|}{2} $ then $AA = G $ I'v found this proposition.  If $G$ is a finite  group , $ A \subset G $ a subset and $|A| &gt; \frac{|G|}{2} $ then $AA = G $.  Why this is true ? Changing "index.php" Within The Address Solve $y’ = \frac{2-xy^3}{3x^2y^2}$ using Bernoulli form Solve, by bringing the equation to Bernoulli form: $$ y’ = \frac{2-xy^3}{3x^2y^2} $$  Therefore we want to bring it to a form like: $$ y’ + p(x)y = q(x)y^n $$ So working with the equation i get: $$ y’ - \frac{2}{3x^2y^2} = -\frac{xy^3}{3x^2y^2} = -\frac{y}{3x} $$ I don’t see how to get to Bernoulli equation from here...