I know that and is used to join two sentences or phrases. There are some places I've read that have And is used at the beginning of a sentence. What are the occasions when this is done?
Since I first learned English, I have been holding this understanding that "and", as a conj. but unlike "but",  can only connect two clauses, not two sentences ended with periods.  But recently, I have seen so many prints, either in entertainment or in academia, where "And" is popularly used in the beginning of a sentence. It seems like the author is trying to connect the sentence just right before and the sentence following "And" in some intended meaning which I don't quite get.  I was wondering if I have been wrong all the time, or if there is a new trend that I fail to understand and accept? How to understand such usage of "and" in rigorous English grammar? If I am right, why it is used differently from "but" in terms of what I mentioned at the beginning of this post?
Cannot update grub with parameters on live USB I have booted from a live USB ("Try Ubuntu"), that also has a persistent option set (I used  to create one) to do some tests for .  I'm trying to test  (like ) by doing this  sudo nano /etc/default/grub sudo update-grub   The problem is that that last command gives me this:  /usr/sbin/grub-probe: error: failed to get canonical path of /cow.   It looks like /cow is the file-system that is mounted on /, according to:  :~# df Filesystem     1K-blocks    Used Available Use% Mounted on /cow             4056896 2840204   1007284  74% / udev             1525912       4   1525908   1% /dev tmpfs             613768     844    612924   1% /run ....   Is there a way for me to run update-grub? ... but still be required for applications that need admin privilegies?  In order to allow the following:  $ apache2ctl restart httpd not running, trying to start (13)Permission denied: make_sock: could not bind to address 0.0.0.0:80 no listening sockets available, shutting down Unable to open logs  $ sudo !! sudo apache2ctl restart             #no password asked $                                   #works!   For reference I've seen this setup on amazon's e3 instances  Any idea? Is the Eel immortal? In Russian roulette, is it best to go first? Assume that we are playing a game of Russian roulette (6 chambers) and that there is no shuffling after the shot is fired.  I was wondering if you have an advantage in going first?  If so, how big of an advantage?  I was just debating this with friends, and I wouldn't know what probability to use to prove it. I'm thinking binomial distribution or something like that.  If $n=2$, then there's no advantage. Just $50/50$ if the person survives or dies.   If $n=3$, then maybe the other guy has an advantage. The person who goes second should have an advantage.   Or maybe I'm wrong. Delaunay triangulation to generate abstract networks and nodes Is it possible to use Delaunay triangulation to generate an image like the below from a raster or vector of an object (in this case, a human heart)? What software and techniques would be required to make something like this? My intention is to make and use something like this in Inkscape without having to draw all the nodes/lines/effects manually. A little bird told me that if $2^n+1$ is prime, then $n$ is a power of $2$. I tend not to trust talking birds, so I'm trying to verify that statement independently.  Suppose $n$ is not a power of $2$. Then $n = a \cdot 2^m$ for some $a$ not a power of $2$ and some integer $m$. This gives $2^n+1 = 2^{a \cdot 2^m}+1$. Now I suspect there's a way to factor that, but I don't see how. Can someone give me a hint? MWE:  \documentclass{minimal} \usepackage{commath, tikz} \begin{document} \begin{tikzpicture} \node {$:$}; \end{tikzpicture} \end{document}   When I compile this, pdfTeX enters an infinite loop. Why? How to report issues with the mobile SE application Math mode accents In my long document I, sadly, have to use several accents to denote different kinds of symbols. Currently, I use primes ($x'$), hat, tilde, and overline. In addition I use two colored symbols (red colored tilde and blue $\prescript\ulcorner$), as I need further distinguishment.  Now I'd like to have no colors in my document, while I still have at least six different ways to differentiate certain symbols.  Which alternatives could I use that are easy to recognize and 'stand out', while they are different to prime/hat/tilde/overline?  EDIT: The reader should be able to see the kind of accent used even if the symbol in question is in a sub-script (possibly even a sub-sub-script). How to correctly install Minecraft, including setting any needed packages or apps to install it and to troubleshoot the most common problems that Ubuntu users face when trying to use Minecraft.  I am trying to install and run Minecraft without first having to install the Oracle version of Java. I want to use the OpenJDK version that comes with Ubuntu and as a last resort, use the Oracle one.  I also want to know a list of problems related to Minecraft in Ubuntu and the possible solutions to them.  A step by step guide on how to install Minecraft would also help. A lot of people write makefiles that say something like  paper.pdf: paper.tex         pdflatex paper         bibtex paper         pdflatex paper         pdflatex paper   To handle re-running TeX to get new/changed references and so forth. Is there a better way to do this? Why does inertia happen? In  R P Feynman relates a story where his father told him that, even though we know the word "inertia" and what it means, nobody knows why inertia happens. Is that still true? Why None is the smallest in python? How many Marvel Earths (Universes) are there? Starting yesterday, I have a very odd problem on my Windows 10 desktop-- my CPU is constantly running at 100% (according to Task Manager), and it isn't throttling down. Because of this, it's constantly running at 3.3 GHz and the temperatures are rising to the point where the fans kick in at full force. If I go into the Windows power settings screen and manually change the processor power maximum to 50%, then it's capped at 50% frequency (~1.5 GHz), but it never goes below the maximum possible frequency.  The weird thing is, when I look at the process list, there isn't really anything obvious that's triggering it. None of the processes are abnormal, and though the process CPU percentages do add up to 100%, it doesn't make sense to me that each individual process is taking up as much CPU as Task Manager says it is. Everything seems to be "using" a significantly higher amount of CPU resources than it normally does.  As an attempt to diagnose the problem, I've also tried using Process Explorer. The really weird thing is that Process Explorer shows only 1-2% usage when idle, with the System Idle Process taking up the remaining ~98% as I would expect. Again, nothing looks out of the ordinary in the process list, but the processes are showing the levels of activity I would expect in Process Explorer.  I've already run both Windows Defender and Malware Bytes (a virus was my first guess), but nothing has turned up yet.  This same issue also occurs in Safe Mode, so I'm guessing that it's more along the lines of something to do with Windows itself...  So, to recap:   Windows 10 Desktop Intel 970, 3.3 GHz, 6 cores Task manager and resource monitor graphs shows 100% usage total No individual process is taking up significant resources in the resource monitor list CPU is not throttling down automatically based on the dynamic load, causing high temperatures and the fan to kick in Process Explorer is only showing 1-2% CPU usage   Before I go uninstalling everything, how would I figure out what's causing the issue if nothing weird is showing up in Task Manager or Process Explorer? I have close to two hundred images where the subject looks like he just walked out of a sauna. It was 36 degrees with humidex, but he was not that red.   For comparison, attaching another picture, same camera, same lens, auto white balance, next day.       So, two questions, 1) how did that happen?, and 2) how do I fix it? I can bring down the red, but then I have to manually bring back the lip color in 200 pictures.   And next time when I deal with an older guy at 36 degrees C I will be shooting indoors.   *Edit: The camera is Olympus EPM 2. I am now guessing that he may have been THAT red, but my eyes tricked me. The last picture is from the beginning of the shoot before he got very hot and had two glasses of wine AND the background worked better for his skin and clothes. I do not have colour management setup, but I will get on it. I need to implement the following circuit in LTSpice but I don't know if my schematic is ok. Also, I don't know what  values for I should use for Cinf and R2.  The following constraints are imposed:   VCC= 10V VCM = 1.5V Vgis a sine wave with a frequency of 1 kHz. Its amplitude will be chosen so as to ensure minimal distortion of the output signal (i.e. v0 should also be a sine wave) R1= 15kΩ.    I need to choose a value for R2 and Cinf in order to have a (theoretical)gain value Av=1500.   How can I compute the theoretical expressions of the DC collector currents of bipolar transistors Q1–Q8, considering VBE≈ 0.6V and the theoretical expression of the small-signal voltage gain Av= vo/vg?   The first picture is the schematic and the second is the LTSpice implementation.  What I found is that:   ICq5=ICq6=ICq7=ICq8=(Vcc - Vbe)/R2 ICq1=ICq2 = [ICq7 / 2 ] * [Beta/(Beta+1)] ICq4=iCq2-current of Q5 ICq3=ICq1-current of Q3-current of Q4  Beta in my case is 182.1 because I'm using a BC847A transistor. A=Vo/Vg = Gm_q2 * Beta_q5 * R1Gm_q2=ICq2 / Vt that is approx 40*ICq2   How can I find the value of R2? This is what I have now, an sine like wave for Vg Open maps which are not continuous How to set metadata for music files? In windows music files have metadata like artist name, album name associated with them. How is this metadata stored. Is it stored in file system like other file attributes or is it part of MP3 data that Windows Explorer extracts using a MP3 reader plugin?  Is it possible to read/change this information in Linux? Is it possible with commandline?  (I know these attributes can be set using Rhythymbox or some music player but I'm curious if these could also be set directly. Like in Windows the windows itself shows you artist information if you right click the file and open properties dialog) Prove that $x^2 = - 1$ has no solution in $\mathbb{Z}$ I have this proposition to prove: The equation $x^2 = -1$ has no solution in $\mathbb Z$. I was told that this is an opportunity for a proof by contradiction. I have already proven that for $m \in\mathbb Z$, if $m \ne 0$ then $m^2 \in\mathbb N$. I have also proven that 1 is a natural number (hence, -1 isn't one).  Here is my strategy: assume that there is a solution. Hence $x^2$ has 3 options: \begin{align*} x^2 \in\mathbb N\\ -(x^2) \in\mathbb N\\ x^2 = 0 \end{align*}  Option 1 is not possible because -1 is not a natural number. Option 2 doesn't make sense because         -$\mathbb N \in \mathbb N$ and option 3 doesn't make sense either because $0 \ne -1$. What do you think? Thank you!    Here is a simpler strategy based on the comments below.  Proof: Assume that $x^2 = -1$ has a solution in $\mathbb Z$, then $x^2$ will either be $0$ or $\in\mathbb N$. However, $-1 \notin\mathbb N$ and $-1 \ne 0$. Hence, there is a contradiction. Here is how I have proven that $-1 \notin\mathbb N$: Let $m \in\mathbb N$. Hence:  \begin{align*} -m \notin\mathbb N\\ (-1)m \notin\mathbb N \end{align*}  If $-1 \in\mathbb N$, the product of $-1$ and $m$ should $\in\mathbb N$, which is not the case here. Hence, $-1 \notin\mathbb N$.