Prove that the collection of arithmetic progressions $A=A_{a,b}|a,b\in \boldsymbol{Z},$b$\not\equiv 0$ is Basis for topology on $Z$
Arithmetic progression topology
How do I find out the user name and password for an existing account? On Chrome on Android, code blocks on the mobile site have no syntax highlighting, are not a monospaced font, and words are wrapped.  Mobile site on mobile browser:    Desktop site on mobile browser:    Inline code has the same issue, it isn't a monospaced font.  It has been this way for as long as I can remember. Wouldn't be surprised if this is a dupe. Run a command on all subfolders If you have a series of subfolders (like from a to z) and want to run a command on each one of them (like rm *.pdf or ls *.pdf), how do you do that? The "manual" approach would be cd a, rm *.pdf, or ls *.pdf, cd .., cd b, ... That seems too complicated, so I believe there must be an easier approach. When discussing a treaty or international agreement, which is correct?  "There are 100 states party to the treaty." (for example, as used )  Or:  "There are 100 state parties to the treaty." (for example, as used )   Or: "There are 100 states parties to the treaty."  (for example, as used ) I need to group 400 points in 10 groups with 40 points each. The goal is to get the 40 points geographicly together like this:        Any idea how to do this with QGIS? What does \x mean in C/C++? I wish to remove Ubuntu and I'm not quite sure how. I know it has something to do with partitions. I have 3 partitions. 1. OS [683 GB]  2. Recovery [14 GB] 3. Ubuntu 12.04 LTS (E:)  I know it says Ubuntu but when I installed Ubuntu I think I put 14 gigabytes for it so I think its the recovery one but I'm not sure. I could have sworn I put more than 700 megabytes for it.  I have googled this and I can't seem to find an answer. Any help would be nice. How to verify iOS app integrity? If I write an app for iOS and it's accepted by the AppStore, how do I know if the app is actually the app I compiled and has not being substituted/altered by, say, a "Man in the middle" style interception/attack? Is there a way to do a checksum either after the fact or from inside the app itself? Pass php variables to js without drupal behaviour I stand on the following tricky situation:  I have a node with geofield coordinates attached. I am constructing an array of points. Something like:  Array ( [86] =&gt; Array     (         [0] =&gt; Array             (                 [lat] =&gt; 39.1641410477                 [lon] =&gt; -2.633972168             )          [1] =&gt; Array             (                 [lat] =&gt; 41.0420738489                 [lon] =&gt; -2.633972168             )          [2] =&gt; Array             (                 [lat] =&gt; 41.0420738489                 [lon] =&gt; 1.2524414063             )          [3] =&gt; Array             (                 [lat] =&gt; 39.1641410477                 [lon] =&gt; 1.2524414063             )         [4] =&gt; Array             (                 [lat] =&gt; 39.1641410477                 [lon] =&gt; -2.633972168             )     )  [85] =&gt; Array     (         [0] =&gt; Array             (                 [lat] =&gt; 39.1641410477                 [lon] =&gt; -2.633972168             )          [1] =&gt; Array             (                 [lat] =&gt; 41.0420738489                 [lon] =&gt; -2.633972168             )          [2] =&gt; Array             (                 [lat] =&gt; 41.0420738489                 [lon] =&gt; 1.2524414063             )          [3] =&gt; Array             (                 [lat] =&gt; 39.1641410477                 [lon] =&gt; 1.2524414063             )         [4] =&gt; Array             (                 [lat] =&gt; 39.1641410477                 [lon] =&gt; -2.633972168             )     ) )   I want to pass this to my-googlemaps.js in order to be used by google's init map Google map is defined as:  my-map:   header: true js:   js/my-googlemaps.js: { }   https://maps.googleapis.com/maps/api/js?key=my_key&amp;callback=initMap: {type: external, attributes: {defer: true,async: true}} dependencies:   - core/drupal   - core/drupalSettings  my-googlemaps.js:   console.log(Drupal.settings);   function initMap() {}   This way I get Drupal.settings undefined, which makes sense I guess. On the other hanve if I place initMap into a behavior It can not be seen as a callback as defined in googleapis.com before.  Has anyone stumbled with this before? Any idea how to attack the problem? Do I have to move swap partition to the right side? According to  I just expand my sda4 to include unallocated space, my question is after create 2 new partitions sda7, sda8, do I need to move the swap partition to the most right of the disk? (I really don't know this, I saw  which moving the swap partition to the right side)  Thanks. Is $x^3+y^3+z^3-1$ irreducible over a field $k$ of characteristic $\neq 3$? Is $x^3+y^3+z^3-1$ irreducible over a field $k$ of characteristic $\neq 3$?   If I can show that $y^3+z^3-1$ is irreducible, I believe I can use Eisenstein's criterion. But I don't see how to show even this.  The other approach on my mind is to show that $k[x,y,z]/(x^3+y^3+z^3-1)$ is an integral domain, but this doesn't seem particularly promising either. The latest updates (4/1/2018) make my laptop constantly crash the GUI/Unity:  (Intel Pentium su4100 processor)  syslog:  Jan  5 11:38:53 1810 kernel: [ 1850.327738] compiz[11911]: segfault at 0 ip 00007f6c7baf0c16 sp 00007ffd5ec71c60 error 4 in i965_dri.so[7f6c7b513000+82d000]   After login I end up with an empty desktop, just a wallpaper, GUI/Unity are in a crash loop:   No panel.  No dash.  Can't start a program. Launcher disappears. Sidebar disappears. System crash. Windows key not working. The key combination Alt+Tab not working.   Simply, the computer is not usable. Same for guest login. The only thing working: open up a terminal CTRL+ALT+T to examine log files.  I somehow forced  to let me log in and file the bug, but still lots of problems:   Dash not working Alt+Tab not working Sometimes windows all disappear for a few seconds     Any ideas for a solution or workaround?   UPDATE     If you have the same/ very similar problems, follow the link to my    report and mark there that you're affected too. Or file your own. Please leave a comment   if you wish, or upvote - this is a nasty problem - but an answer should   offer a fix or a workaround so users can use their computer again.    Without , Ubuntu can't fix issues. Looking for a book with parallel universes like pages, possibly with "maze" in title, and a black Jewish female character Looking for a book. A series,  actually.  The main characters were a Jewish man and a black woman who was his wife. There was a running gag when she would tell people her last name and they thought it was unusual that a black woman would have a Jewish name.    They went on adventures in parallel dimensions. I believe that each book had a word repeated in the title, maybe "mirror?" Or "maze?" Or "page..."  it seems they jumped into worlds through a tool like a mirror or a book.   The parallel universes were like pages, and the pages closest to you were most similar but the further you got the further they were from your life.  One page over might be that you had something different for breakfast and so now you have a tummy ache, a few more pages over you might have become a prostitute, too far and it was theorized that humans had evolved differently altogether, I didn't get that far in the series.  For adults, and humorous.  I read them about 15 years ago, so they are not new. I would love to find them again. Overview of basic facts about Cauchy functional equation The  asks about functions $f \colon \mathbb R \to \mathbb R$ such that $$f(x+y)=f(x)+f(y).$$ It is a very well-known functional equation, which appears in various areas of mathematics ranging from exercises in freshman classes to constructing useful counterexamples for some advanced questions. Solutions of this equation are often called . Also a few other equations related to this equation are often studied. (Equations which can be easily transformed to Cauchy functional equation or can be solved by using similar methods.) Is there some overview of basic facts about Cauchy equation and related functional equations - preferably available online? How do you change the size of figures drawn with Matplotlib? How do you change the size of figure drawn with Matplotlib? Update query cancelled by user Keyboard macro to change default audio device Windows 7, Logitech G110 keyboard  2 audio devices (headphones and speakers)  I am hoping to find a quick way to macro a key to switch to headphones, and a key to switch to speakers.  Anyone have a good program or anything of that nature?  EDIT:  Using AHK to try and get this task working as hoped is sadly not doing the trick.  I have included a screenshot of my audio set, as well as a screenshot of my script as it sits now.    I have also tried to uncheck "show disabled devices" and modified the script to be Down 1, and Up 1 respectively.  It will work for one device, but it refuses to switch to the secondary. Show that computation of all such expressions will result in the same element of $X$ Time dependent Schrödinger equation with time independent potential and separation of variables suppose we have a potential that's independent of time $V(x,t) = V(x)$ so in Schrödinger equation we get: $$i\hbar \frac{\partial \Psi (x,t)}{\partial t}=-\frac{\hbar^2}{2m}\frac{\partial^2 \Psi (x,t)}{\partial x^2}+V(x)\Psi(x,t)$$ since the LHS involves a variation of $\Psi$ with $x$ and the LHS involves a variation of $\Psi$ with $t$ can we say that a basis for the solutions will be with the form $\Psi(x,t)=\psi(x)T(t)$? How to output string completions to stdout?