I run 40 hours a week? (or) I run 40 hours per week?
Difference between "per" and "a"
Understanding Group Permissions Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field. I have been having a lot of trouble teaching myself rings, so much so that even "simple" proofs are really difficult for me. I think I am finally starting to get it, but just to be sure could some one please check this proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field. Thank you.  Proof: Notice that $$\langle 1 - i \rangle\\  \Rightarrow 1 = i\\  \Rightarrow 2 = 0.$$ Thus all elements of the form $a+ bi + \langle 1 - i \rangle$ can be rewritten as $a+ b + \langle 1 - i \rangle$. But since $2=0$ this implies that the elements that are left can be written as $1 + \langle 1 - i \rangle$ or $0 + \langle 1 - i \rangle$. Thus  $$ \mathbb Z[i]/ \langle 1 - i \rangle = \{ 0+ \langle 1 - i \rangle , 1 + \langle 1 - i \rangle\}. $$  This is obviously a commutative ring with unity and no zero-divisors, thus it is a finite integral domain, and hence is a field. $\square$ "Nikki's and Alice's X" vs. "Nikki and Alice's X" Which option is grammatical?        There will be readings from Nikki Giovanni’s and Alice Walker’s writings.   There will be readings from Nikki Giovanni and Alice Walker's writings.      Saying it out loud the latter sounds right, but looking at it the former looks better. Why doesn't the Moon fall onto the Earth? A script on AIX which checks the number of parameters passed and complains if they are not correct:-  if [ "$#" -ge 1 ]; then   ... else   echo 'Usage: myscript &lt;a&gt; [b] [c]' fi   The script sets some environment variables so it is sourced. By that I mean I type the following on my command line. There is no second script, I am not sourcing a script from within another script.  . ./myscript.sh   If I pass it no parameters, I expect it to print out the usage statement but instead it runs using the parameters passed to the previous command that was sourced (not necessarily even this script!).  To double check this I added this line at the beginning of my script to prove that this was the case.  echo $# $@   If I pass it no parameters, it prints out the number and the list of parameters from a previously sourced script.  How do I get it to say $# is zero when I pass it zero parameters and source it?  The smallest possible recreate is a script thus:-  myscript.sh  echo $# $@   and then run it thus:-  . ./myscript.sh a b c   which prints out  3 a b c   then run it again without any parameters thus:-  . ./myscript.sh   which prints out the same  3 a b c   when you would expect it to print out  0   If you don't source the script and just run it thus:-  ./myscript.sh   then it works as expected and prints out  0   I hope that clarifies the issue at hand.  Since I seem to be getting lots of answers to explain why the above doesn't work and no answers to tell me what I should do instead, I thought I would have one more attempt at trying to explain what I am trying to do.  Requirement  I need to write a script that expects at least one parameter and complains if it is not invoked with a said parameter (see the first block of code in my question above), and this script needs to set some environment variables. Because of this second requirement I have assumed that I need to source the script so that the environment variables are still set when the script completes. How can you write a script that can tell when it has not been passed parameters that is also able to set an environment variable? Prove that $\mathrm E\left({\max}\left\{X^2 , Y^2\right\} \right) \leq 1 + \sqrt{1 - \rho^2}$ where $\rho$ is their correlation. I have seen only the first three movies, so I don't know whether the other movies/TV series deal with this question or not. My main point is that in the movies, the terminator that travels back furthest in time is of the worst quality, and the quality increases with the time travel (meaning they travelled from a later time). What is a good explanation for this?  Note: I am not interested in the obvious not-in-universe explanation that they wanted something better and bigger for each new movie. Pages documents created on Yosemite cannot be opened by Pages on Yosemite after latest update (5.5.2) Seemingly every single document that I created in the previous version of Pages (I update regularly whenever I see that a new update is available) on this same MacBook Pro with Yosemite will now not open with Pages after the latest update (5.5.2). I am still on Yosemite and nothing has changed aside from updating Pages, Numbers &amp; Keynote.  All of my documents are stored on my internal hard drive. When I attempt to open them I get a message stating the following:     This document can't be opened because it's too old. To open it, save it with Pages '09 first.   As I mentioned above, however, these documents were created in whichever version was right before the current version on the same computer with the same operating system (Yosemite).  Can anybody help? These are time sensitive documents. For now, I may try opening them with my iPad, but wow, if I knew this was going to happen I certainly would not have updated. When does a locational distinction change its suffix and capitialization in a proper name? How do I check the series $\sum_{n=2}^{\infty} \frac{(-1)^n }{n+(-1)^n}$ for absolute convergence/conditional convergence ?  How can I solve this problem? Creating centerline from lines using QGIS How do I create a centerline (vector data) from two parallel polylines (vector data) in QGIS? For example, if the distances between two parallel lines are 14m, then I want to create a centerline at 7m from both lines. In reading through the original GCM specification (), the composition of the 128 bit Initialization Vector as a concatenation of a 96b nonce and a 32b unsigned wrapping counter seems arbitrary and forces the scrambling pattern to repeat every 232 16-byte block.  Is the algorithm expected to be secure for significantly longer stream lengths if for example the IV were a 128b nonce XORed with a 64b or 128b counter, or are there known cryptanalysis issues that begin to arise? Caps-lock remapping stops working Showcase of beautiful typography done in TeX & friends If you were asked to show examples of beautifully typeset documents in TeX &amp; friends, what would you suggest? Preferably documents available online (I'm aware I could go to a bookstore and find many such documents called 'books'). Extra bonus for documents whose LaTeX source is available.  This is not an idle question. Seeing great examples of any craft is both educational and inspiring, let alone explaining why we prefer TeX to Word or other text editors.  For instance, I like how Philipp Lehman's  looks. I don't know enough LaTeX to realize how much customization was done, but the ToC looks polished.  Your nominations, please ... I use Chrome as my main browser.  I also spend a lot of time on a particular webapp that my company uses.  I'd like to keep those two things separate.  I can run the webapp in a separate window - but I'd like to go further than that.  I'd like to have it be identified by a different task in the Win 7 taskbar; ideally a different icon; and ideally a different title in Process Monitor.  How can I run a second, independent instance of Chrome, with a different title and icon, that won't merge with my main Chrome browser. Choice of ECC curve on USB token I would like to get a USB token to secure my keys. My use case is protection of 3 GnuPG keys that I will be using 10 times per day at least. I plan to create a new key ring from scratch. Because ECC seems more future-oriented than RSA, this is what I chose to use. I'm wondering which USB token to choose as well as which curve.  On  it is said that many people think curves recommended by the NIST or defined by Brainpool have a doubtful origin; therefore, they recommend the non-standardized Bernstein’s Curve 25519. On  one poster says that    He is not aware of any profound criticism of Brainpool curves, and Bernstein’s Curve 25519 is hard to protect against side-channel attacks when implemented in embedded devices.   As a result, I'm a bit lost as to which key/curve to choose. Old post apocalyptic cartoon where the main character has red hair and lives with a nomadic group I am looking for an animated TV series which was probably made in the '80s or '90s.  The main character had red hair.  The cartoon is set in a post apocalyptic environment and the character lives with his mother and an old man —his mentor I guess— with a nomadic group.  In one early episode, one of the group is wounded in an ambush, he is taken back to the camp where the mentor performs surgery which is revealed he learned during the war. The wound is caused by a bullet, then the mentor is surprised saying that guns were lost and forgotten.  In another episode the main character is captured and sent to a prison. Then after he escapes with other prisoners, they look outside the gate and see grass and soil which they either didn't see in their lives or were in the prison for a long time.  The main character later finds a sword like Excalibur which can cause some sort of electrical disruptions.  I think his mother was kidnapped in the beginning. How could Thranduil have met a dragon? How to get a list of the filenames of the figures embedded in a document I have a TeX document that is embedding a huge amount of figures from a fig folder that is full of another humongous amount of other figures.  I would like to move the document along with its figures, but I don't want to take the whole fig folder, just the figures in there that are embedded by the document.  Is there a package (or any other way) that allows me to, for example, print out the filenames of all the figures embedded by the document? Something like:  fig/figurename1.eps fig/figurename2.eps ... etc   I could then just copy-paste that list and add some cp's in a plain text file and automate the copy of those files to my desired location by running the file in my shell:  $ cp fig/figurename1.eps wherever/fig/ $ cp fig/figurename2.eps wherever/fig/ ... etc   Of course this is just an idea, if somebody has an alternative to the "file listing and copy-pasting in a shell file" I would be happy to listen =) Android WebView for Facebook Like Button