Rendering issue where code snippet joins with info section under question
The case of the bleeding monospace font!
Let V denote the Klein 4-group. Show that $\text{Aut} (V)$ is isomorphic to $S_3$ After a week in my Abstract Algebra class, the professor proposed this as a problem. I'm not entirely sure where to begin. $ V = \{ e, \tau, \tau_1, \tau_2 \}$, so I'm not sure exactly what is meant by $\text{Aut} (V)$. Is it simply saying that the only way to have an automorphism on $V$ is to rearrange the order of the elements of $V$ and therefore $\text{Aut} (V) \cong S_3$? Is Dishonored an open-world game? I was considering whether or not to buy Dishonored, and watching gameplay of it on Youtube, when a thought popped into my head: is Dishonored free-roam? Can you go anywhere you want, similarly to Fallout or The Elder Scrolls? Which close reason should I use for questions that do not demonstrate research effort? I regularily encounter questions on StackOverflow which are asked only because of the sole fact that the poster haven't made the effort to google for and the docs of a particular function/class/framework/whatever. My question is, to which category of the five proposed one should I vote when I vote to close the question? Is it: off-topic, not constructive, not a real question, exact dupe or too localized? I tend to be all for 'not a real question' - am I quite right? How to use Launchctl for schedule application I try to work with Launchctl and have a question:  How can I set up an application to run in a few minutes using Launchctl? (for example, open the program MyApp.app with arguments "hello" "world" Every 10 minutes)  I know that it can easily be done by creating Launch Agent, I looking for a way to do it using Launchctl directly to programmatically. So, I thought I had a good understanding of this, but just ran a test (in response to a conversation where I disagreed with someone) and found that my understanding is flawed...  In as much detail as possible what exactly happens when I execute a file in my shell? What I mean is, if I type: ./somefile some arguments into my shell and press return (and somefile exists in the cwd, and I have read+execute permissions on somefile) then what happens under the hood?  I thought the answer was:   The shell make a syscall to exec, passing the path to somefile The kernel examines somefile and looks at  of the file to determine if it is a format the processor can handle If the magic number indicates that the file is in a format the processor can execute, then   a new process is created (with an entry in the process table) somefile is read/mapped to memory. A stack is created and execution jumps to the entry point of the code of somefile, with ARGV initialized to an array of the parameters (a char**, ["some","arguments"])  If the magic number is a  then exec() spawns a new process as above, but the executable used is the interpreter referenced by the shebang (e.g. /bin/bash or /bin/perl) and somefile is passed to STDIN If the file doesn't have a valid magic number, then an error like "invalid file (bad magic number): Exec format error" occurs   However someone told me that if the file is plain text, then the shell tries to execute the commands (as if I had typed bash somefile). I didn't believe this, but I just tried it, and it was correct. So I clearly have some misconceptions about what actually happens here, and would like to understand the mechanics.  What exactly happens when I execute a file in my shell? (in as much detail is reasonable...) $A_n$ is the only subgroup of $S_n$ of index $2$. Option to hide rep/badges on the avatar block displayed of you This question has bugged me for a while. I want to write a nested function, f(g(x)). If I naively enter it:  \begin{align}     f(g(x))=y \end{align}     The problem is that each and every parenthesis is the same size as all of the others. Shouldn't the outer parentheses be larger? But if I do this:  \begin{align}     f\left(g(x)\right)=y \end{align}     Now it looks even less like the functions are nested. What's the proper way to do this? How to use my aliases in my crontab? Pullback of locally free sheaves is locally free states that if $f:X \rightarrow Y$ is a morphism of ringed space, $G$ is a locally free $O_Y$-module, then $f^*G$ is a locally free $O_X$ module.     Suppose that $G$ is a locally free $O_Y$ module, hence it is a free $O_Y|_U=O_U$ module. We have an induced map  $$f^{-1}(U) \rightarrow U$$ given by restriction of morphism of ringed spaces.   Hence, as $\bigoplus O_U \simeq G|_U$, $f^*:Mod(O_U) \rightarrow Mod(O_{f^{-1}(U)})$ is functorial, $f^*(G|_U) = (f^*G)|_{f^{-1}(U)}$, we have isomoprhism,  $$ \bigoplus O_{f^{-1}(U)} \simeq (f^*G)|_{f^{-1}(U)} $$ Why are my quotation marks causing an “unexpected token” error with this command? On finding polynomials that approximate a function and its derivative (extensions of Stone-Weierstrass?) Suppose $K/F$ is an extension field, and $E_1$ and $E_2$ are two intermediate subfields of finite degree. Let $E$ be the subfields of $K$ generated by $E_1$ and $E_2$. I'm trying to prove that $$ [E:F]\leq[E_1:F][E_2:F].$$  Since $E_1$ and $E_2$ are finite extensions, I suppose they have bases $\{a_1,\dots,a_n\}$ and $\{b_1,\dots,b_m\}$, respectively. If $E_1=F$ or $E_2=F$, then the inequality is actually equality, so I suppose both are proper extension fields. I think $E=F(a_1,\dots,a_n,b_1,\dots,b_m)$. Since $\{a_1,\dots,a_n,b_1,\dots,b_m\}$ is a spanning set for $E$ over $F$,  $$[E:F]\leq n+m\leq nm=[E_1:F][E_2:F]$$ since $m,n&gt;1$.  Is this sufficient? I'm weirded out since the problem did not ask to show $[E:F]\leq [E_1:F]+[E_2:F]$ which I feel will generally be a better upper bound. Outcast boy meets girl underwater Expression Functions for Lightning Web Components How can expression functions similar to Visualforce and Lightning Aura Components be achieved within lightning web components?   For example, &lt;template if:true={index % 5 == 0}&gt;&lt;br&gt;&lt;/template&gt; expression index % 5 == 0 is not compyling at all.  accountList.html  &lt;template&gt;     &lt;template if:true={accounts.data}&gt;         &lt;template for:each={accounts.data} for:item='item' for:index='index'&gt;             &lt;!--LWC DOES NOT SUPPORT EXPRESSION FUNCTIONS--&gt;             &lt;!--&lt;template if:true={index % 5 == 0}&gt;&lt;br&gt;&lt;/template&gt;--&gt;             {item}         &lt;/template&gt;     &lt;/template&gt; &lt;/template&gt;   accountList.js  import {LightningElement, wire} from 'lwc'; import getAccounts from '@salesforce/apex/TestController.getAccounts';  export default class AccountList extends LightningElement {      @wire(getAccounts) accounts;  }   Since LWC doesn't support Expression Functions, I'd like to know how to implement them. Space between 2 paths in Illustrator What are C++ functors and their uses? I keep hearing a lot about functors in C++. Can someone give me an overview as to what they are and in what cases they would be useful? Negative values for AICc (corrected Akaike Information Criterion) I have calculated AIC and AICc to compare two general linear mixed models; The AICs are positive with model 1 having a lower AIC than model 2.  However, the values for AICc are both negative (model 1 is still &lt; model 2).  Is it valid to use and compare negative AICc values? I have my A* pathfinding algorithm right now working such that given a graph it can find the route from one starting node to one goal node.   This works well for many problems, but sometimes I find that multiple goal nodes are valid.  For example, in a game, an NPC might have to go to a switch to shut a door. If there are multiple switches that shut the door in question, it doesn't matter which switch it goes to - it just needs to go to one of them.  How can I augment my pathfinding algorithm to find the path to the best goal (the shortest path)? As in, the algorithm searches for multiple goals and when it finds just one, it returns the path to that one.  One solution would be to run the algorithm as many times as there are valid goals, but you can guess why that might be inefficient. Whole disk unallocated? Gparted error or partition overlapping?