3D glasses and reflection/polarisation
Viewing computer screen through 3D glasses, why the asymmetry?
Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$ Given $a_1, a_2, a_3, \ldots , a_n$ not all zero, show $\gcd(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$. Also deduce $a_1x_1+a_2x_2+ \ldots +a_nx_n = b$ has solutions $\iff \gcd(a_1, a_2, a_3, \ldots , a_n)|b$.   I know that $ax+by=n$ has integer solutions $\iff \gcd(a,b)|n$. I'll need to use induction to show $a_1x_1+a_2x_2+ \ldots +a_nx_n = \gcd(a_1, a_2, a_3, \ldots , a_n)$ has solutions, and then I will be able to say that as $\gcd(a_1, a_2, a_3, \ldots , a_n) | a_1x_1+a_2x_2+ \ldots +a_nx_n $ for any $x_1,x_2, x_3 \ldots x_n$ then $c \leq \gcd(a_1, a_2, a_3, \ldots , a_n)$ and $c \geq \gcd(a_1, a_2, a_3, \ldots , a_n)$, and thus $c=\gcd(a_1, a_2, a_3, \ldots , a_n)$. Can a deb package contain a PPA dependency and install packages from the PPA? When creating a .deb package I create a file named control that contains some fields:  Package: my-qt-app-name Version: 0.01 Architecture: all Maintainer: my name &lt;my email address&gt; Installed-Size: 2 Depends: some-package-from-ppa Section: extras Priority: optional Homepage: my homepage Description: some description   some-package-from-ppa is not installed on the computer. It can be installed only adding a PPA, running apt-get update and then apt-get install some-package-from-ppa.  Can a control file from a deb package contain a PPA address and install that package when the deb file is installed? I am working on a SQL query that reads from a SQLServer database to produce an extract file. One of the  requirements to remove the leading zeroes from a particular field, which is a simple VARCHAR(10) field. So, for example, if the field contains '00001A', the SELECT statement needs to return the data as '1A'.  Is there a way in SQL to easily remove the leading zeroes in this way? I know there is an RTRIM function, but this seems only to remove spaces. Is a particular sequence required for detailed replicator requests?    To elaborate, is there a reason Captain Picard orders his tea, "Tea. Earl Grey. Hot." aka "Noun. Descriptor. Descriptor." and not "Descriptor. Descriptor. Noun." or "Descriptor. Noun. Descriptor." (in the event he forgot a descriptor)?  Would ordering it as "Hot. Earl Grey. Tea." or even the non-statement "Hot Earl Grey tea." produce a warm (hot), smoky (gray-ish) gas with the odor of tea?  I assume his ordering sequence is an acquired background affectation, but I'd like confirmation.  Note: I'm using "descriptor" instead of "adjective" to avoid minutia/debate about classification. When is a review task "completed" or "invalidated"? I've noticed that the number of reviews required to remove a post from a queue varies. For example, to accept/reject a suggested edit, you need two votes of the same kind. If the votes are conflicting, the number goes higher. This seems to be the case for the other queues as well. (Additionally, I think that a mod-review is binding) So, my question is: what are the criteria for a review to be marked as a &quot;completed&quot; review? Also, when is a review considered invalidated (i.e. &quot;no longer reviewable&quot;)? Formerly When is a post removed from a review queue?. I have seen several times on TV documentaries where the presenter is taken to something like a library archive, and shown a book which they proceed to read an excerpt from.  On a couple of occasions the camera has shown the text they were reading and generally I have thought that I would struggle to read the words because of how the letters were formed (e.g. , or ).  This got me to wondering about how pronunciation and sentence formation may have changed over time as well, and how far back in time could I travel and still be understood while speaking my "modern" English in England (while obviously not talking about modern concepts like mobile phones or space travel)? Pronunciation differences between "finite" and "infinite" In my experience, "finite" is pronounced (IPA) ˈfaɪnaɪt while "infinite" is ˈɪnfɪnɪt.  In general, the prefix "in" negates an adjective, but does not change the pronunciation. Based on this, I would expect ˈɪnfaɪnaɪt.  Is there a reason for this "deviation from the norm"? Are there dialects/regions that actually say ˈɪnfaɪnaɪt (or ˈfɪnɪt, for that matter)? Why have header files and .cpp files? Convert NSDate to NSString How do I convert, NSDate to NSString so that only the year in @"yyyy" format is output to the string? How to setup OpenVPN Client Difference between phrase and idiom What is the difference between a phrase and an idiom? Why do I get "Permission denied (publickey)" when trying to SSH from local Ubuntu to a Amazon EC2 server? Positive integer multiples of an irrational mod 1 are dense I'm not sure how to solve this one. Thank you!  $2.$ For any $\alpha\in \mathbb R$ we define $$\lfloor \alpha \rfloor = \max_{n\in\mathbb Z}\{\,n\mid n\leq \alpha\,\}$$ and $$\alpha\bmod 1 = \alpha - \lfloor \alpha \rfloor$$ Let $\alpha$ be irrational. (a) Given $n\in\mathbb N$ show that $\{\,k\alpha\bmod1\mid k\in\mathbb N\,\}\cap\left[0,\frac{1}{n}\right]\neq\emptyset$ (b) Prove that $\{\,n\alpha\bmod 1\mid n\in\mathbb N\,\}$ is dense in $[0,1]$. How do I install pillow in Ubuntu 16.04 LTS? Label and caption without float I’d like to have an environment that works much like a float, except that it doesn’t float.  That is, in fact, I’d like to be able to define an environment that has a label and a caption.  I explicitly do not want to use a floating environment, though. For one thing, floats do many things fancy which I just don’t need, nor want (such as spacing) and for another, floats have their share of problems (for example consider the problem of ).  Is there a ready-made way to achieve this? Of course, I could always write my own based on the result of the other answer, i.e. harnessing \refstepcounter. But I’m not sure how to use that, documentation is scarce, and I’d prefer an existing solution. The following message keeps appearing on my Samsung Galaxy S4 phone screen about every three seconds  "Unfortunately, Google Play Services has stopped".    Is it actually a virus or it is a problem with the Google Play Service?  I have tried disabling the Google Play Service but the message keeps appearing.  I have Norton Mobile running on my phone to pick up on viruses and to alert me to any possible security issues and also Lookout. They haven't picked up anything.  Does anyone have any suggestions? Difference between "try to do" and "try and do" What is the difference between try to do and try and do?  To me (non-native speaker), asking someone try and do this seems a bit rude. It's like saying you can try all you want but this must be done: try and fail is not an option. However, asking someone try to do this means I am asking you to try: success is bonus, failure is OK. Word for person who looks for flattery What word could be used to describe a person who seeks and seems to depend on constant positive feedback from the people around him. I'm trying to do an incremental backup using cpio but it seems that the busybox version doesn't work the same as the normal one? This is what I've got so far:  find data/Backup -mtime -2 | cpio -cm media/USB_FLASH_2  I origianlly used:  find . -mtime -2 | cpio -cm /media/USB_FLASH_2  However, I've seen people say busybox doesn't like definitive paths while using cpio. Unsure about that though.   It returns an error that basically says I'm using cpio wrong. I can't find anyone using the busybox cpio to do things like this, does that mean i can't do it? I've looked at using rsync as well but again, it doesn't do what i would expect.  For reference I'm using PuTTY to connect through SSH to a ReadyNAS 102.  After using find . -mtime -2 | cpio -o | { cd /media/USB_FLASH_2 &amp;&amp; cpio -imd; }  i get the output:   BusyBox v1.20.2 (Debian 1:1.20.0-7) multi-call binary.  Usage: cpio [-dmvu] [-F FILE] [-H newc] [-tio] [EXTR_FILE]...  Extract or list files from a cpio archive, or create an archive using file list on stdin  Main operation mode:         -t      List         -i      Extract EXTR_FILEs (or all)         -o      Create (requires -H newc)         -d      Make leading directories         -m      Preserve mtime         -v      Verbose         -u      Overwrite         -F FILE Input (-t,-i,-p) or output (-o) file         -H newc Archive format Protons and Neutrons Overshoot Actual Mass? When I add up the mass of 6 protons and 6 neutrons in amu, I get a mass that is greater than the mass of carbon. I thought that it should be the other way around, because I have not including binding energy when I add up the mass of the protons and neutrons.  Proton: 1.007276466812 u  Neutron: 1.00866491600 u  6(1.007276466812)+6(1.00866491600)=12.099  Carbon: 12 u  Why is this so?