Papa Rudin exercise 2.8
Construction of a Borel set with positive but not full measure in each interval
I have forgotten my ID proof and I'm doing an Indian domestic flight. Can I still fly? I am travelling from Delhi to Indore, a domestic flight. I forgot to take ID proof. Can I still fly? System.Exception: Too many SOQL queries: 101 Prevent href="#" link from changing the URL hash headed or heading, started or starting? Consider:  Two units are headed your way. Two units are heading your way. Don't get me started! Don't get me starting!  Is there any difference in meaning? And I don't see why passive voice is used here. I would think they have similar meaning here. Help me to clarify! How to make mesh lights work in Blender Eevee? The closest I can get to making mesh lights affect their environment in Blender Eevee is giving them an Emission material and turning on "Bloom". But this isn't emitting proper light, it just looks like it is, but it doesn't light the surroundings whatsoever.     I would like to be able to light a scene with meshes without having to put point lamps everywhere just to make them emit light. How do I prove that $$ a^3+b^3+c^3−3abc = 1 $$ if   $ a = 1+\frac{x^3}{3!}+\frac{x^6}{6!}......$ , $b=x+\frac{x^4}{4!}+\frac{x^7}{7!}....$ , $c=\frac{x^2}{2!}+\frac{x^5}{5!}+\frac{x^8}{8!}......$ ?  I have tried the following :-  I discovered that $a+b+c=e^x$ and that $a=\frac{d(b)}{dx}$, $b=\frac{d(c)}{dx}$, $c=\frac{d(a)}{dx}$ . But I am unable to proceed further with these information. home socket with DC voltage I'm wondering why, in a standard house, instead of using many low power AC-DC rectifier, there isn't a big (like 12V 20~50A) AC-DC rectifier which supplies some wall socket with a DC voltage? In the long run this should be less expensive, given the fact that AC to DC in one big apparatus is done better than in many low-quality transformers, right?  Also, modern chip DC voltage regulators have efficiency of >90%, so smaller (or even larger) voltages are still efficient and possible.  So we could use a 12V socket to charge a phone, desktop computer, laptop, radio etc... and still have an AC socket to move washing machine engine and other things that work better with an AC supply.  Why isn't this done?  edit: real question is: is it convenient, given a standard family (2 laptop, 1 desktop, 4 smarthpone, 1 big tv and some minor electonic) to do so? Say for a game with irregular hotspots (say Risk, or a strategy game like Paradox's Hearts of Iron or Crusader Kings), how do you   Define a non-rectangular hotspot of irregular shape (much like a territory on a map?), in code? What tool can you use to trace out the hotspot and import into your game? What is the algorithm for detecting if someone has clicked within such a hotspot? Sending & Receiving SMS via WiFi Is there a way to send and receive SMS when a cellular signal is not available, but WiFi is?  I'm often on-site at locations where the building has a strong WiFi (Internet) connection, but a simple cell signal is spotty at best. I'm trying to compute the shadow of 3D objects on the ground. To do this I'm assuming parallel rays from Sun origin.   Let's assume the Sun direction is given by azimuth $\varphi$ and elevation $\theta$ angles. So the direction unit vector is retrieved as:  $$ \hat{\mathbf{s}} = \mathbf{R}_y\left(\theta\right)\mathbf{R}_z\left(\varphi\right)\hat{\boldsymbol{\imath}}$$  where $\mathbf{R}_{x/y/z}$ are the rotation matrices along the $x, y, z$ axes given by, for example, Euler-Rodrigues equation, and $\hat{\boldsymbol{\imath}}$ is the unit vector along $x$-axis.  A point on a ray-line has the equation:  \begin{equation} \mathbf{r} = \mathbf{r}_p + \lambda\hat{\mathbf{s}}  \tag{1} \end{equation}  being $\mathbf{r}_p$ a point on that line.  A point on a general plane is given by the equation:  \begin{equation} \left(\mathbf{r} - \mathbf{r_0}\right)\cdot \hat{\mathbf{n}} = 0 \tag{2} \end{equation}  being $\mathbf{r}_0$ a point on the plane and $\hat{\mathbf{n}}$ the unit vector normal to that plane.   Ensuring the validity of both equations (1) and (2) allows to compute the $\lambda$ multiplier and retrieve the position vector of the projected point (writing $\tilde{\mathbf{r}} = \mathbf{r_p} - \mathbf{r_o}$)  \begin{gather} \lambda = - \left(\frac{\tilde{\mathbf{r}}\cdot \hat{\mathbf{n}}} {\hat{\mathbf{s}}\cdot\hat{\mathbf{n}}}\right) \\ \mathbf{r}_\text{proj} = \mathbf{r}_p - \left(\frac{\tilde{\mathbf{r}}\cdot \hat{\mathbf{n}}} {\hat{\mathbf{s}}\cdot\hat{\mathbf{n}}}\right)\hat{\mathbf{s}} \tag{3} \end{gather}  Applying eq. (3) to all the vertices of a mesh $\left\{\mathbf{r}_{p_i}\right\}$ .   A problem can be noted: $\hat{\mathbf{s}}\cdot \hat{\mathbf{n}}$ can be zero (e.g. Sun is horizontal, i.e. the ray is ortogonal to the normal of plane).   Are there some conceptual mistakes in my reasoning? Is there a way to rewrite the operation as a linear operator applied to the set of vertices position vectors?   $$ \left[\mathbf{A}\right]\left\{\mathbf{r}_{p_i}\right\} = \mathbf{r}_\text{proj}$$ Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis? Is there any software package to solve the linear regression with the objective of minimizing the L-infinity norm. How to disable notifications for a single mailbox in Mail? When managing multiple mailboxes, is it possible to disable the notifications for certain mailboxes? I want to shrink my second (LVM) partition, in order to create a new partition in the newly freed space. I am using the Live CD to do so, because I know I can't resize/move this partition while it is in use. When I opened GParted in the Live CD, I realized that I could not resize the partition, because when I right-click it, the option "resize/move" is disabled.  I tried to unmount it, to "lazy" unmount it (umount -l /dev/sda2) but it didn't work.  A screenshot from GParted: FTPS versus SFTP versus SCP SharePoint People.aspx Page is Visible for All Users The SharePoint People.aspx page is visible for all users by default. Is there any way to restrict this page from certain readers? Is there a way in Java to have a map where the type parameter of a value is tied to the type parameter of a key? What I want to write is something like the following:  public class Foo {     // This declaration won't compile - what should it be?     private static Map&lt;Class&lt;T&gt;, T&gt; defaultValues;      // These two methods are just fine     public static &lt;T&gt; void setDefaultValue(Class&lt;T&gt; clazz, T value) {         defaultValues.put(clazz, value);     }      public static &lt;T&gt; T getDefaultValue(Class&lt;T&gt; clazz) {         return defaultValues.get(clazz);     } }   That is, I can store any default value against a Class object, provided the value's type matches that of the Class object. I don't see why this shouldn't be allowed since I can ensure when setting/getting values that the types are correct.  EDIT: Thanks to cletus for his answer. I don't actually need the type parameters on the map itself since I can ensure consistency in the methods which get/set values, even if it means using some slightly ugly casts. How to find manually installed packages? I installed a plain Ubuntu 10.10 on my computer and installed some software via apt-get. Last week I managed to break everything and just started from scratch, and I need to reinstall my software. Is there some way to create a list with all the packages that I have installed manually?  So that it would give me a list like texlive, ... and not texlive, texlive-dep1, textlive-dep2, ... and all the standard packages removed?  If I could somehow figure out which programs out of the regular install I have removed, that would be awesome too!    Update 2015-05-23: I now use Ansible as configuration management on my systems. There I specify the packages to install. This serves the goal, installing all the programs on a fresh system, even better. So this question might be the entry into some light configuration management. What items are mutually exclusive between worlds? As of 1.2, some features are mutually exclusive between worlds.  In the case of ores at least, .  However, a  gives you the chance for a  (and the upgraded Sweetheart Necklace) which does not seem to have an equivalent version in the Corruption.    What items, if any, are truly mutually exclusive in function between worlds? Why was Gotham City changed from a mostly fictional city to New York City in the Nolan trilogy? In Batman Begins, Gotham City has a futuristic/fictional and run down look: think of Oldtown, the trains built by the Wayne Corporation etc.   In The Dark Knight Rises, Gotham City looks like plain old real world New York City — we don't see the trains anymore. Oldtown is just a standard poor neighborhood. Lots of the locations used in the movie are easily identified as real world NYC locations: the stock exchange or East River bridges for example.   My question is: Why did Nolan change Gotham city from a shady fictional more cartoon-like town to plain old NYC?   Edit: The examples from Batman Begins and The Dark Knight Rises were just for illustration; I didn't intend to limit the question to those two movies.  Edit 2: I specifically want to know why Gotham City was changed from a cartoon-like city in Begins to an almost real-world NYC in The Dark Knight Rises (via not so cartoon-like but not yet real-world like Chicago in The Dark Knight Rises). Why it's NYC or Chicago is not so important for me. But why, e.g., were the trains which featured prominently in Begins gone in The Dark Knight Rises? There was only a very short in-universe time-span between the events of the two movies, yet Gotham changed drastically.