Where does rationality break in the Leibniz formula for π?
How can $\pi$ be irrational if it can be calculated using an infinite series of rational numbers?
Setuid bit seems to have no effect on bash Why don't Starfleet vessels have intelligent on-board computers? Problems with booting the system I have yesterday updated packages and today the system cannot boot properly. After seeing the Kubuntu logo there is a black screen which shows repeatedly.     Stopped User Manager for UID 121.      Removed slice User Slice of gdm.      Created slice User Slice of gdm.       Starting User Manager for UID 121...      Started Session c3 of user gdm.       Started User Manager for UID 121.   Please see the screenshot below Does a non-abelian semigroup without identity exist? Is there a 'rule of thumb' that I can use to estimate depth of field while shooting? I can use a DoF calculator, or crunch the heavy math by hand if I really want to know exactly what my DoF is going to be... but most of the time knowing exactly is actually overkill, and taking the time to pull out a DoF calculator is impractical. I'm wondering if anyone knows of a 'rule of thumb' that is common for quickly figuring out a rough estimate of what my DoF will be when I'm in the field... Why do we need to discard one dummy variable? I have learned that, for creating a regression model, we have to take care of categorical variables by converting them into dummy variables. As an example, if, in our data set, there is a variable like location:   Location  ---------- Californian NY Florida   We have to convert them like:  1  0  0 0  1  0 0  0  1   However, it was suggested that we have to discard one dummy variable, no matter how many dummy variables are there.   Why do we need to discard one dummy variable? How to trim whitespace from a Bash variable? I read a book of this series probably around 2000. I think the series was quite new then but not sure.  The main thing I remember about it is that magic is based on words of power. If you knew one word you got some extra ability, knowing two words gave you yet some other ability, and if you knew three words you became a very powerful wizard. Only one person at a time could know each word, and telling someone your word meant you died.  The main protagonist somehow gets hold of one word and then for some reason strives to learn more.  EDIT: I think that I accidentally picked up the second book of the series and never read the first one. From what I remember, the protagonist learned one word of power and got some kind of supernatural ability (cannot remember what though). He then ends up in some kind of challenge where he has to cooperate with another person who knows another word that gives super-strength.  Not very coherent memories, but I hope someone knows what series it is. It has been bugging me for years. (Not even sure if the series is good at all, but still would like to know the name.)  EDIT2:  I remember the world as being medieval-ish. I do not think there were dragons, but there may have been other humanoid races (I have a very weak recollection that there may have been an orc or similar in the story, but this could be completely wrong). The protagonist was male. Can you have multiple Dropbox accounts on one computer? I just discovered an incredibly annoying "feature" of Windows 7 tonight.  If you click on your optical drive in Explorer, and there is no disc in the drive, Windows 7 is kind enough to open the tray for you.  I'm finding it hard to contain my rage over this idiotic design decision.  WTF?  According to , this behavior was apparently introduced in Vista.  The author posted a workaround, but I don't want a workaround.  I want it to stop doing this.  Like he, I have a case with a door that covers the drive bays.  If it's closed, and I accidentally click on that optical drive, it knocks on that door 10 or 12 times before giving up.  Can this behavior be turned off in Windows 7? My directory (in Linux) looks like com/com/{various,files} where com and com are folders of the same name and the second com holds the various files. I want the first com removed, but the second and files in the second kept. I would like to connect a USB Mouse, Keyboard or Storage Device to my Nexus 4. So far I know, for this USB OTG must be supported. Unfortunately I can not find any actual information about this.  Does anybody know whether USB OTG is supported by Ubuntu-Touch? If yes, does anybody know if it would work with a Nexus 4 device? What is a good KPI for software QA? How can you measure the efficiency of the QA team?   What KPIs would you set up? Will Find my iPhone Lost Mode be useful if stolen phone as shows Offline? My phone was stolen last night. I made sure it was in Lost Mode in iCloud and it was immediately in Offline status when I open iCloud. I am positive the thief switched it off. Now I am 100% certain the Find my iPhone option was turned on on my iPhone, but will the "Lost Mode" be of any help if it was not turned on on the iPhone? Would it be showing "Offline" if I did not turn on the option? Do the integral forms of Maxwell's Equations have limited applicability because of retardation? In the usual bookwork treatment, it is easy to show that the differential and integral forms of Maxwell's equations are equivalent using Gauss's and Stokes's theorems. I have always thought that neither version is more fundamental than the other and each has its place in solving problems. (See also  )  But: I have a conceptual problem with applying the integral forms of these equations in cases where there is time-dependence and the "size" of the loop or area means there is a significant light travel time across the regions considered compared with the timescale on which fields vary.  e.g. Suppose there is a time-varying current in a wire $I(t)$ and I wish to find the fields a long way from the wire. My first instinct is that this ought to be solved using the inhomogeneous wave equations to give A- and V-fields that are dependent on the retarded time - hence leading to the E- and B-fields.  But what about using Ampere's law in integral form? What is the limit of its validity? If we write $$ \oint \vec{B}(r,t)\cdot d\vec{l} = \mu_0 I(t) + \mu_0 \int \epsilon_0 \frac{\partial \vec{E}(r,t)}{\partial t} \cdot d\vec{A}$$ then presumably the $t$ that is defined on each side of the equation cannot be the same, since a change in $I$ at time $t$, presumably leads to a change in $B(r)$ at a time $t + r/c$? I suppose one does not care about this so long as the timescale for a current change is $\gg r/c$.  So my question is: Are the integral forms of Maxwell's equations inherently limited by this approximation, or is there a way of formulating them so that they take account of the finite size of a region in cases where the fields are time-variable? Are there any security risks using a single key-pair for both key-exchange and signing?  I'm mainly interested in using Curve25519 for key-exchange and Ed25519 for signing. But similar combinations, such as EC-DH and EC-Schnorr or even EC-DSA with the same key pair would be interesting too.   Curve25519 hashes the output of an x-coordinate only Diffie-Hellman key exchange Ed25519 is a slight variant of EC-Schnorr signatures.   I saw some recommendations to avoid using a single key for multiple purposes, but I couldn't find anything concrete. Get Absolute Position of element within the window in wpf I would like to get the absolute position of an element in relation to the window/root element when it is double clicked. The element's relative position within it's parent is all I can seem to get to, and what I'm trying to get to is the point relative to the window.  I've seen solutions of how to get a the point of an element on the screen, but not in the window. I have a CSV with an address field (no lat/long), so I went to Google My Maps, imported the csv and geocoded of the records.  Now I export the layer as KML and added the KML to QGIS and Google Earth Pro, but in non of them I can see the markers. In fact in QGIS, the KML layer is added as datatable (no geometry).  What's happening? How can I export a geometry layer from google My Maps? Let's say I use a  with a lot of code inside. To improve readability and reusability I'd like to use helper/private methods. However, a Drupal .module file is not a class.  The idea is to split big methods from this file into more readable and reusable smaller methods.  What is the correct way to call helper/private methods from a Drupal .module file? let $a,b,c,d,e$ are positive real numbers,show that $$\dfrac{a-b}{b+c}+\dfrac{b-c}{c+d}+\dfrac{c-d}{d+e}+\dfrac{d-e}{e+a}+\dfrac{e-a}{a+b}\ge 0$$  My try:  I have solved follow Four-variable inequality:  let $a,b,c,d$ are positive real numbers,show that $$\dfrac{a-b}{b+c}+\dfrac{b-c}{c+d}+\dfrac{c-d}{d+a}+\dfrac{d-a}{a+b}\ge 0$$ poof:since \begin{align*} &amp;\dfrac{a-b}{b+c}+\dfrac{b-c}{c+d}+\dfrac{c-d}{d+a}+\dfrac{d-a}{a+b}=\dfrac{a+c}{b+c}+\dfrac{b+d}{c+d}+\dfrac{c+a}{d+a}+\dfrac{d+b}{a+b}-4\\ &amp;=(a+c)\left(\dfrac{1}{b+c}+\dfrac{1}{d+a}\right)+(b+d)\left(\dfrac{1}{c+d}+\dfrac{1}{a+b}\right)-4 \end{align*} By Cauchy-Schwarz inequality we have $$\dfrac{1}{b+c}+\dfrac{1}{d+a}\ge\dfrac{4}{(b+c)+(d+a)},\dfrac{1}{c+d}+\dfrac{1}{a+b}\ge\dfrac{4}{(c+d)+(a+b)}$$ so we get $$\dfrac{a-b}{b+c}+\dfrac{b-c}{c+d}+\dfrac{c-d}{d+a}+\dfrac{d-a}{a+b}\ge\dfrac{4(a+c)}{(b+c)+(d+a)}+\dfrac{4(b+d)}{(c+d)+(a+b)}-4=0$$ Equality holds for $a=c$ and $b=d$  By done!  But for  Five-variable inequality,I can't prove it.Thank you