We are given the following definition:  If a sequence $(a_n)$ is bounded from below then there is a greatest lower bound for the sequence called the infimum.     $m=\inf(a_n)$ if  i) $(a_n) \geq m \ \forall n \in \mathbb{N}$.  ii) For each $\epsilon >0 \ \exists \ n_\epsilon \ \in \mathbb{N}$ such that $a_{n_\epsilon} < m + \epsilon $.       Show using the definition that, if $a_n=\frac{1}{n}$ then $\inf(a_n)=0$.   Here is what I have:  i) RTP: $\frac{1}{n} \geq 0 \ \forall n\in \mathbb{N}$.  Assume that $\frac{1}{n} < 0$ for some $n \in \mathbb{N}$.  $\implies n < 0$.   But we know that $n \in \mathbb{N}, n \geq 1$, and thus we can say that$\frac{1}{n} > 0\ \forall n \in \mathbb{N}$.  ii) Let $ \epsilon > 0$ be given.  RTP: $\exists n_\epsilon \in \mathbb{N}$ such that $\frac{1}{n_\epsilon}<0+\epsilon = \epsilon$.  Proof:  $\frac{1}{n_\epsilon} < \epsilon \implies n_\epsilon > \frac{1}{\epsilon}$, since both values are positive.  For the given $\epsilon > 0$, choose $n_\epsilon > \frac{1}{\epsilon} \in \mathbb{N}$.  Now from the Archimedes Postulate, we know $\exists n \in \mathbb{N}$ such that $n \geq n_\epsilon$.  $\implies n \geq n_\epsilon > \frac{1}{\epsilon}$  $\implies \frac{1}{n} \leq \frac{1}{n_\epsilon} < \epsilon$, since all values are positive.


I am working on SharePoint 2010, I have a custom list with columns Start date , End date, Created by, Approval Status. I have created a page where I am looking to filter the list and show the result depending on the approval status which is a column in custom list as shown in figure . Can some one help me out on how to approach for this.


Ensure that request comes from withing server

Suppose, I am building website. I want the user to be able to access the index.php file only. I also have other files like www.mydomain.com/aboutus.php files and user can access them if he types this in his address bar. I want the user to be able to access www.mydomain.com only.  How are such security features built?


I have forgotten my Apple Id but i know my password.And my phone need to be activated but the apple id was made mistakenly.Is there any possibility to know my Apple Id?


Java - String array null pointer exception

I get a null pointer exception. Why? I tried and debugged the code...Java says the String array is filled. But when i start the program without debugging mode, Java says nullpointerexception...  BufferedReader quelle = new BufferedReader(new FileReader(file));     String auftrag = quelle.readLine();     String[] daten = auftrag.split(";"); //... String test;      for(int i = 3;i<=daten.length-1;i+=3)     {          test = daten[i-3] + " " + daten[i-2] + " " + daten[i-1];         g.drawString(daten[i-3] + " " + daten[i-2] + " " + daten[i-1],x,y);         y += 16;     }


I am searching for a way by which I can find the displacement vector of a double pendulum as functions of time.( without using lagrangian mechanics)


I'm using Unity C#. How would I create the effect in my pool game, a line showing the direction of the second (not white) ball after collision.  Example:   I need to make the line coming from the ball (second/leftmost)  P.S. I made the other line by using Raycast to find the hit point and set that point last position of line renderer (white ball is a start position for line renderer and it casts the ray)


osx Terminal / Shell Script function modifier

I am currently shell scripting and I would like to know how to make a - option while making a function. When you would execute a command similar to the following:  test -f   Here is the function I am using:  function test() {       echo $1;       echo $2; }   How could I add a -t for echo twice option?  Input:   test -t Hello   Output:    Hello   Hello   I am using iTerm and oh-my-zsh.  Thanks, base2101


I have a web site that I developed on Vista using Vb.net9.  It makes a connection to Oracle.  for the connection I use System.Data.OracleClient.  It works fine on my machine, and our test server, but it does not work on the production server.  We installed the Oracle Client 11 on the server.  The error is System.Data.OracleClient requires Oracle client software version 8.1.7    We've tried, making a console app that opens the connection, connection runs fine, opens, displays a message and all is well there.  Then we make a simple web form, put it in the directory of the program, just a button, opens the connection, try..catch, grabs error, same error.  The console app was running under an Administrator, web site running under iwam.  Is it possible that iwam has a different path?


I have a .CSV file that have an arabic data and i need to import this file into the sql database using PHP. my code doing it just fine except that the arabic characters inserted into the database as 'ËËËË','ÚÚÚÚ'.  what should i do to insert that data right.  any ideas?   $filename = $_FILES['upload']['tmp_name'];   $file = fopen($filename, "r");   while (($emapData = fgetcsv($file, 1000, ";")) !== FALSE){   $emapData[0];   var_dump($emapData[0]);   //'ËËËË','ÚÚÚÚ'   }


Moving the Windows 7 hard disk from one machine to another

My laptop running Windows 7 Ultimate (non OEM) died on me today and it has tonnes of stuff on it - my projects, Visual Studio and office installations, etc. etc.  I am getting a new laptop from somewhere and was wondering if I could just unplug the hard disk from my original (dead) machine and plug it into the new one.  I remember trying this once with Windows Xp (on a desktop) and the OS crashed on boot and I had to reinstall everything again.  I have read about  but by the looks of it, it can be used only when the host computer is alive and kicking -- which mine isn't.  My old laptop was a Compaq Pressario v3000 (3 years old) on an AMD and the new one is going to be a new dual core Intel HP laptop.  Any ideas?  Thanks!


I have a set $$ \{ r \in \mathbb Q \mid r^2 >2, r>0 \}$$ I was wondering why it does not have the greatest lower bound. Isn't $0 \in \mathbb Q$ a greatest lower bound for this set in rational numbers?


Prevent Custom Message Dialog ( a modal dialog) focus loss in WPF

I'm developing an application and for the custom purposes of the app, I need a custom MessageBox.  I've created a new WPF Window and I'd like to force the user to interact with the custom message box before returning to the application, thus preventing them from using the application until a button inside the custom message box is pressed.  I've tried using .Focus() but it didn't work at all.  To give a perfect example of exactly what I want:  Try to press "Save As" in Outlook and then click on the "Mail" window again. You instantly get "redirected" to the "Save As" Dialog and can't do anything on the main window until the dialog is closed.  Any ideas how to make this possible?


SSH - remote fowarding - ensure connection is always active

I have 2 servers.    Server A is behind a router, to which I have no admin access.    It has a user: userA   Server B (example.com) is a cloud server with a public ip.   It has a user: userB     I am running the following command on Server A, to forward any connections made to Server B on Port 8022 back to Server A on port 22: ssh -R *:8022:localhost:22 userB@example.com  This creates a ssh connection and I have a session open for userB@example.com  If I then open another terminal (on another computer) and ssh into userB@example.com and once connected run ssh userA@localhost -p 8022 I have an active ssh connection to Server A  This is new to me but all seems to make sense.  I would like to ensure that the inital remote forwarding connection ssh -R is always active. This means if the connection drops I need it to reconnect. If Server A reboots I need it to connect on startup.   How would I go about doing this?   Is there a better approach?


What is the difference between SAN, NAS and DAS?


How do I calculate rotation caused by bounce friction?

Following on from : I have the ball quite realistically bouncing from surfaces it hits. Now I'd like to make it spin from the friction of the hit.  Showing this is simple enough: I rotate the ball by its angular velocity every tick and apply the same rotation when it's rendered.  When a ball hits a wall, I know that the speed of rotation is affected by...   the ball's initial speed when hitting the surface the friction coefficients of the ball and surface (physical constants) the angle of incidence (the angle between the ball's incoming velocity vector and the surface normal).   The angle of incidence is approximated by the dot product of the ball's impact and exit velocity vectors. (1 meaning high spin, -1 meaning no spin, and everything else relatively in between)  Multiplying all of the above together and making sure they were then transformed to the range 0 - 1, and multiplied by max rotation speed, the ball seemed to respond in rotation speed as expected. Except for one thing: It would always rotate clock-wise (because of positive values).    Is this a good method? Can you think of a simpler way?  If this method seems fine, what am I missing? How do I know when the ball should be rotating counter-clockwise?


Throughput and speed of data transmission cables

What are throughput and speed limiting factors in an ethernet or any other type of cable which is used for data transmission?


I need this scenario based query.  SalesID Line    Noofitems   Category    Desc SID12345    1   1           Metal-SI    Strong iron SID12345    2   1           Plastic     Disposal SID12345    3   1           Plastic     Disposal   Expected Output  SalesID     Totitems    Category            Desc SID12345    3           Metal-SI,Plastic    Strong iron,Disposal


I have this problem $\int \frac {-5x + 11}{{(x+1)(x^2+1)}} \text{d}x$  And i'm not sure how to deal with this. I've tried substitution and getting nowhere. I've peeked at the answer and there a trigonometric part with arctan. Do i use Partial fraction expansion here?   Thanks


Is there a statistical/information theoretic interpretation of this matrix in the context where A represents observations of data (and this matrix which shows up in e.g. solving linear systems and elsewhere)? Does it have a special name used in the context where A represents "rows of data"?


How reference assignement works in a loop? in Java

i'm practicing creating apps and i have a problem that i don't understand : why i'm getting this error with this code :       java.lang.NullPointerException: Attempt to invoke virtual method 'java.util.List com.baziremartin.pyramideapp.paquet.getCartes(int)' on a null object reference   the code :    mTestBTN.setOnClickListener(new View.OnClickListener() {             @Override             public void onClick(View v) {                 List<joueur> currentPlayers = new ArrayList<>();                 for(int i = 0; i < allPlayers.size(); i ++){                     currentPlayers.add(new joueur(allPlayers.get(i)));                     currentPlayers.get(i).setHand(paquet1.getCartes(4));                  }             }         });   I've already search and i think it is a reference syntaxe error but i don't understand whats is the good syntax.. (i have try a lot of differents things). Thanks for help i'm beginner in java.


How can I get Firefox to open torrent files with Transmission?

Every time I download a torrent file (.torrent), Firefox thinks I should open it with a text editor. How can I get it to open with Transmission? In Edit -> Preferences -> Applications, there's no setting for torrent files, and no apparent way to add a new filetype.


Short story or novel from the 1970s or before about two warring alien tribes

I know this is going to be a long shot but my father read a book around 1965-1967 about a space explorer who goes to a planet (he believes it is Mars) where he meets two warring alien tribes. One tribe is short and fat and one tribe is tall and skinny. He also remembers part of the story where the explorer believes one alien is urinating into the water supply and contaminating it but the alien is actually purifying it. Does this sound familiar to anyone? Thank you in advance.  ETA: He says this is not the novels with John Carter in them.


Is "Feel free to reach out to myself, Howard, or Jane." correct? Or, should it read "Feel free to reach out to me, Howard, or Jane.".


In Minecraft Xbox edition there is a setting that resets the nether. Does it just reset the nether? And does it affect the upper world?


How to properly write "Research and Development"

Which of the following would be considered proper when writing about research and development  "Research and Development" or "research and development"?  Also, is it proper to use the "&" when writing the full phrase out in a sentence, or does that only apply when using its initialization ("R&D")?


How to interpret coefficients in a Poisson regression?

How can I interpret the main effects (coefficients for dummy-coded factor) in a Poisson regression?  Assume the following example:  treatment     <- factor(rep(c(1, 2), c(43, 41)),                          levels = c(1, 2),                         labels = c("placebo", "treated")) improved      <- factor(rep(c(1, 2, 3, 1, 2, 3), c(29, 7, 7, 13, 7, 21)),                         levels = c(1, 2, 3),                         labels = c("none", "some", "marked"))     numberofdrugs <- rpois(84, 10) + 1     healthvalue   <- rpois(84, 5)    y             <- data.frame(healthvalue, numberofdrugs, treatment, improved) test          <- glm(healthvalue~numberofdrugs+treatment+improved, y, family=poisson) summary(test)   The output is:  Coefficients:                  Estimate Std. Error z value Pr(>|z|)     (Intercept)       1.88955    0.19243   9.819   <2e-16 *** numberofdrugs    -0.02303    0.01624  -1.418    0.156     treatmenttreated -0.01271    0.10861  -0.117    0.907   MAIN EFFECT   improvedsome     -0.13541    0.14674  -0.923    0.356   MAIN EFFECT  improvedmarke    -0.10839    0.12212  -0.888    0.375   MAIN EFFECT  --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1    I know that the incident rate for numberofdrugs is exp(-0.023)=0.977. But how do I interpret the main effects for the dummy variables?


Why do English writers avoid explicit numerals?

The junction has a stop sign on each of the four entrances.   The junction has a stop sign on each of the 4 entrances.   The first is preferred, for some reason, by many English texts. Why? I haven't seen this phenomenon in other languages.


Is the Vernam (One Time Pad) cipher useful?

By profession I’m a programmer. I don’t know a lot about how cryptographic algorithms are implemented, or even where I’d start, and I don’t know about cryptanalysis, but as I work in Blockchain technology, I know how to consume cryptographic algorithms. One might say I have a passing interest.  One thing that has piqued my curiosity, as it probably does many novices in cryptography is the Vernam, or One Time Pad cipher; supposedly 100% mathematically impossible to crack and incredibly simple to implement.  The problem seems to be around the keys used. Specifically:   Keys shouldn’t be reused Key sequences shouldn’t be repeated Keys need to be shared somehow    Other encryption algorithms solve (or don’t suffer from) these problems, but, if we can find a suitable, secure way to generate and share unique keys, does the Vernam cipher become useful?  Is there anything else that needs consideration in this respect?


Are there real world applications of finite group theory?

I would like to know whether there are examples where finite group theory can be directly applied to solve real world problems outside of mathematics.  (Sufficiently applied mathematics such as cryptography, coding theory, or statistics still count.)  Let me clarify: I am not interested in applications of elementary group theory which happen to involve finite groups (e.g. cyclic/dihedral/easy groups as molecular symmetries).  I am interested in applications of topics specifically coming from finite group theory as a discipline, like one might see in , , or .  "The Schur multiplier has order 2640, so we should point the laser that way."   "Is this computer system secure?"  "No - Frobenius kernels are nilpotent."  I'm aware of , but many of the applications listed there are inside mathematics or fall in the "applications of easy groups" category.  It is entirely possible that what I'm looking for doesn't exist, and that finite group theory is still an untouchable, pure subject, like number theory in the days of G. H. Hardy.  But perhaps not.  Does anyone know of any applications of the higher level stuff?


== and is not returning the same even though comparing an int

I'm using the pow function and found out I had a bug in my code because == and is were not having the same behavior.   Here goes an example: pow(3, 47159012670, 47159012671) == 1 returns True but pow(3, 47159012670, 47159012671) is 1 returns False.  I'd like to know what is it that I'm not getting.


How can I stop Nautilus from dereferencing symlinks?

I use symbolic links to tidy my home folder. This works well in the terminal, since the links create the illusion of normal folders:    In Nautilus, however, the links behave more like , immediately teleporting me to their target:    This is particularly troubling when¹ I later want to navigate "up" to the parent folder, as it strands me somewhere outside of the tree I've carefully tidied.  How can I make Nautilus show symbolic links as normal folders, like the terminal does?  Details   Nautilus did not dereference symlinks in Ubuntu 12.10:   Maybe this new behavior is just a bug? I'm not sure how to tell. Here's what I know:   It's not on the . I've skimmed the  and didn't see anything related. The Nautilus mailing list archive . I received no response from about 120 idlers when posing the question on the GNOME IRC channel. A change was made in Nautilus 3.6 to .  ¹ This is an example. A workaround for this particular scenario does not constitute an answer to my question. Since people seem to be interested in discussing it, though:   Using the Back button is not a suitable workaround; it does not always take me to the parent folder. You can navigate up by pressing Alt+Up. The desired behavior in this example is for "up" to navigate to the parent folder of the symbolic link. The current behavior is to navigate to the parent folder of the target of the symbolic link.


Missing permission - hide, disable, show error message/page?

In a web application I wonder what's best practice to design an element (text link, button) pointing to an action where users don't have access to (e.g. create new user). Esepcially when this element is not the primary element of the page, but just like one link of many links.  I see the following possibilities:   Hide the corresponding element (link to create) - in thise case users could wonder where the action to create a new element can be found Disable the corresponding element (link to create) - in this case the user could wonder why the element is disabled so an explanation would be needed Show an error message Show an error page - in this case the user would have to jump back


How to Use Enum in switch case for comparing string- C#

I have one enum like below  public enum Colors {     red,     blue,     green,     yellow }   I want to use it switch case  public void ColorInfo(string colorName) {     switch (colorName)     {         // i need a checking like (colorname=="red")         case Colors.red:             Console.log("red color");             break;     } }   I am getting following error   Cannot implicitly convert type 'Color' to string   Can anyone help on this ..


Can I develop Ios applications on a Windows 10 machine?

I own a windows 10 machine and recently I started studying programming for IOS, now a Mac doesn't seem to fit in my budget and this is just to start developing a service that is cross platform.


How does one prove the following using natural deduction: $a ∧ ¬a \vdash b ∧ ¬b$

I am trying to prove the following using natural deduction and this is what I have so far. I am not sure, however, if this is entirely correct.   If I could get some verification and be pointed to the right direction, that would be great.      a ∧ ¬a |- b ∧ ¬b 1     a ∧ ¬a     assump 0 2     b |- a ∧ ¬a  2.1   b          assump 2 2.2  ¬b         ¬I 2.1 3     b ∧ ¬b    ∧I 2.1, 2.2 4    ¬b |- a ∧ ¬a  4.1  ¬b          assump 4 4.2   b         ¬E 4.1 5     b ∧ ¬b    ∧I 4.1, 4.2   This is not a duplicate as the symbols and solutions provided with the question it being marked against are different.


Why is root the owner of my Desktop in Ubuntu 14.04?

When I am in my home folder there is a padlock on my Desktop icon. In properties there is written that root is the owner of Desktop and consequently I can't put anything on my Desktop.  I have recently installed this Ubuntu 14.04 and I would like to know why does the desktop icon belong to root while it wasn't so in Ubuntu 12.04 that I used earlier.  I know how to change the owner of a file using the command "chown" (or maybe this won't work for Desktop?) but I am afraid that it could somehow impair my security so first I would like to know the reason of this default setting.


Trying to install node v6, but apt installs v8

I am running ubuntu 18.04.1 LTS and I need to run node v6. I am following    curl -sL https://deb.nodesource.com/setup_6.x | bash -  # Install Node.js and npm apt-get install -y nodejs    I can see in the apt-get output  Hit:4 https://deb.nodesource.com/node_6.x bionic InRelease   before installing:  node -v -su: /usr/bin/node: No such file or directory   after apt-get install -y nodejs  $ node -v v8.10.0   but for some reason it installs node v8  How can I install v6?


How to proof the following identity: $ \sum_{k=0}^{n} \prod_{j=0\\j\neq k}^{n} \frac{t_k}{t_k-t_j} =1$

I've been trying to solve the determinant of the Vandermonde-matrix by using Laplace's formula on it (without transforming the matrix first).  It worked out quite well, I could almost instantly factor out the result that I was supposed to get, however not without the weird factor $$ \sum_{k=0}^{n} \prod_{j=0\\j\neq k}^{n} \frac{t_k}{t_k-t_j} $$  For the formula to hold, the factor has to be equal to $1$, and I've tried it for small $n$, however I'm not seeing why exactly this identity has to hold.  Therefore: Why does the identity $$ \sum_{k=0}^{n} \prod_{j=0\\j\neq k}^{n} \frac{t_k}{t_k-t_j} = 1 $$ hold for abitrary $t_i\in\mathbb C$?


Problem with trigger when Inserting new records on custom object

I am trying to insert new records into a custom object (production) via apex data loader. When I do so I get an error like       ReservationTrigger: execution of AfterInsert  caused by: System.QueryException: Non-selective query against large object type (more than 100000 rows). Consider an indexed filter or contact salesforce.com about custom indexing. Even if a field is indexed a filter might still not be selective when: 1. The filter value includes null (for instance binding with a list that contains null) 2. Data skew exists whereby the number of matching rows is very large (for instance, filtering for a particular foreign key value that occurs many times)  Trigger.ReservationTrigger: line 11, column 1   My trigger is   trigger ReservationTrigger on Reservations__c (after insert,after update) { // Get the IDs of related contacts Set<Id> contactIds = new Set<Id>(); for(Reservations__c oneReservation:trigger.new){     if(oneReservation.ReservationStatus__c == 'Confirmed'){         contactIds.add(oneReservation.Email__c);     } } // Count the distinct Reservation_Number__c from the Reservation objects of all related contacts Map<Id, Integer> countDistinctReservationMap = new Map<Id, Integer>(); for (AggregateResult aggRes : [SELECT COUNT_DISTINCT(ReservationCode__c) resNum, Email__c conId FROM Reservations__c WHERE Email__c IN: contactIds GROUP BY Email__c ]) {      Id conId = (Id) aggRes.get('conId');      Integer resNum  = (Integer) aggRes.get('resNum');      countDistinctReservationMap.put(conId, resNum); } // Now fetch the Contacts in a list List<Contact> listContacts = [Select Id, customRollupField__c from Contact Where Id IN:contactIds]; if(listContacts.size()>0) {      for(Contact con : listContacts) {           // fetch or get the distinct count or rollup from the map and copy it to the contact's field           con.customRollupField__c = countDistinctReservationMap.get(con.Id);      } } // Update the contacts update listContacts; }   Any Ideas why?


IDE cannot find CoreMinimal.h, Unreal Engine 4 course

I'm following  about learning the basics of Unreal Engine as I start up my CS degree, and I've reached a problem where CoreMinimal.h cannot be found.    was proposed in the Q&A community, however I still could not quite understand it! I'm still learning and would love some help ;)  Here is my code!  // Fill out your copyright notice in the Description page of Project Settings.  #pragma once  #include "CoreMinimal.h" #include "GameFramework/Pawn.h" #include "ShipController.generated.h"  UCLASS() class SPACESHOOTER_API AShipController : public APawn {     GENERATED_BODY()  public:     // Sets default values for this pawn's properties     AShipController();  protected:     // Called when the game starts or when spawned     virtual void BeginPlay() override;  public:      // Called every frame     virtual void Tick(float DeltaTime) override;      // Called to bind functionality to input     virtual void SetupPlayerInputComponent(class UInputComponent* PlayerInputComponent) override; };


What is the meaning of the idiom "If it were not for..."?

I have a question about mood  Note that the following sentences are same :  If I did not have money, I could not buy it  =I could not buy it without money   =If it were not for money, I could not buy it  =Since I have money, I can buy it.  I want to know forming of the expression : If it were not for (A)  I guess that this is shortened from some long clauses. Consider the following :   I have only one cat and it is from Korea =I have a cat, which is from Korea.  Usually we use second sentence. But it can be viewed as shortened form of first sentence. That is, about (A) I want to know the forming. Translation is nonsense. Especially we cannot translate "it" If we write the sentence into complete sentence in detail, what is it ?  Thank you in anticipation.


Find all the functions in $\mathbb{R}$, satisfying the given equation  $(x+y)(f(x)-f(y)) = (x-y)f(x+y)$ for all $x,y$ in  $\mathbb{R}$.  I tried to find something like a pattern that would become a constant. If I simplify, I get      $xf(x)-xf(x+y)-xf(y)=yf(y)-yf(x+y)-yf(x)$ What should I do now? Is this going to help? Thank you.


List within list variable assignment trouble: values get overwritten during assignment

I am working with a list of lists in python and I came across a curious issue with it. For example, if I first create a list populated by placeholder [1,2,3] lists:  a = [[1,2,3]]*5   I would get the following result: a = [[1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3]].  If I was to change a specific value of the inside list such as this:  a[1][2] = 5   I would get the following result: a = [[1, 2, 5], [1, 2, 5], [1, 2, 5], [1, 2, 5], [1, 2, 5]]. It looks like each of the index = 2 values of the inside list are not changed to my new variable. In this example all the variables are linked between the 5 inside lists. Now, if I was to create this list manually with the following command:  b = [[1,2,3],[1,2,3],[1,2,3],[1,2,3],[1,2,3]]   And then repeat the assignment:  b[1][2] = 5   I would get the following result: b = [[1, 2, 3], [1, 2, 5], [1, 2, 3], [1, 2, 3], [1, 2, 3]]  It looks like in the case of list a, I have linked variables but in the case of list b, I do not. Could someone explain what is the reason for this? Is there any way to make list a behave like list b without creating a brand new list?  Any info would be greatly appreciated!  Thanks!


$\{(n, \frac{1}{n}) : n \in \mathbb{N}\}$ in the subspace topology of $\mathbb{N} \times \mathbb{Q}$ of $\mathbb{R}^2$

Consider $\mathbb{N} \times \mathbb{Q}$ as a subspace topology of $\mathbb{R}^2$ with usual topology. Consider the set $A = \{(n,\frac{1}{n}) : n \in \mathbb{N}\}$. Is $A$ closed, open ? What is the boundary of $A$ in $\mathbb{N} \times \mathbb{Q}$?  My Attempt:  The basic open sets on $\mathbb{N} \times \mathbb{Q}$ will be of the form $n \times (a,b)\cap \mathbb{Q}$ where $(a,b)$ is open on $\mathbb{R}$.  So for a fixed $n$, $\{(n, \frac{1}{n})\}$ is a closed subset of $\mathbb{N} \times \mathbb{Q}$. $A$ is a countable union if closed set.  To be open for any point $a \in A$ we shall get a basic open set $B$ s.t. $a \in B \subset A$. It does not hold. So $A$ is not open set.  $\mathbb{N} \times \mathbb{Q} - A = \cup_n [n \times ((-\infty, \infty) - \frac{1}{n}) \cap \mathbb{Q}]$ is a countable union of open sets  $n \times ((-\infty, \infty) - \frac{1}{n}) \cap \mathbb{Q}$. So $\mathbb{N} \times \mathbb{Q} -A$ is an open set and so $A$ is a closed set.  The boundary of $A$ is empty.  Is my attempt correct? Thank you for your help.


I am trying to interpret the three boxplots below in light of another plot before finalizing my glmer models (GLMM) in R.  The boxplots below show the relationship between a listener's group (T, TA and TQ) and whether the listeners would match a selection or mismatch it to a predicted response (the DV match is binary: match/mismatch).   Both Listgp and match are factors; thus, I first used the xtabs function, then plotted the boxplots.    My basic model is as follows.   glmer<-(match~Listgp + (1|stimulus) + (1|listener), data= msba, family= "binomial")   Now, first, I notice that there are no whiskers in the upper and lower quantiles. I read somewhere that this means that the bottom and the top of the box would be at the exact position of the lower and upper quantiles. Is this the case here too?   Second, I am trying to interpret these boxplots in light of the plot that follows them which is straightforward for me.   In the boxplots, the range of variance for the T group is bigger than the TQ or the TA. In addition, the TQ  group seems (according to the boxplots) to be matching the patterns more, followed by the T and finally the TA.   On the other hand, according to the plot, the TA group matches the patterns more than the TA and the TQ. Basically, the TA mismatches the patterns more than the two other groups.   So my question is, do the two plots give the same or different information and is my above interpretation correct?      The first 6 lines of the data are as follows.  head(msba)   list.Listgp   cond.by gender age level.of.ed. Avg.skills.T read.A comp.A speak.A 1    T1      T Qualtrics   Male  29      college           10     NA     NA      NA 2    T1      T Qualtrics   Male  29      college           10     NA     NA      NA 3    T1      T Qualtrics   Male  29      college           10     NA     NA      NA 4    T1      T Qualtrics   Male  29      college           10     NA     NA      NA 5    T1      T Qualtrics   Male  29      college           10     NA     NA      NA 6    T1      T Qualtrics   Male  29      college           10     NA     NA      NA   writ.A   st.    match st.length st.context st.nature freq. 1     NA  man     match     short      plain      Real  7.80 2     NA Dhabb mismatch     short   emphatic      Real 50.02 3     NA   qad mismatch     short          q      Real 96.57 4     NA   ?an    match     short pharyngeal      Real 15.78 5     NA   min mismatch     short      plain      Real 59.07 6     NA dhidd mismatch     short   emphatic      Real 54.50   I plotted other boxplots but this time with the variable stimulus (which is also is a factor). These ones have whiskers! (Because I don't have enough reputation points, I will have to remove the 2nd plot so that I can paste the boxplots with stimulus)      I used these codes for the xtabs.   monosbaT.xtabs <- xtabs(~ match + st. , data = monosbaT) monosbaTA.xtabs <- xtabs(~ match + st., data = monosbaTA) monosbaTQ.xtabs <- xtabs(~ match + st., data = monosbaTQ)    Then, in the lattice package I plotted them using these codes.   par(mfrow = c(1,3)) boxplot (monosbaT.xtabs, main = "T", legend.text= c("match", "mismatch"), xlab= "stimulus", ylab= "match", col= "lightblue3", ylim=c(0, 25), breaks=seq(0, 25, 8)) boxplot (monosbaTA.xtabs, main = "TA", legend.text= c("match", "mismatch"), xlab= "stimulus", ylab= "match", col= "lightblue3", ylim=c(0, 25), breaks=seq(0, 25, 8)) boxplot (monosbaTQ.xtabs, main = "TQ", legend.text= c("match", "mismatch"), xlab= "stimulus", ylab= "match", col= "lightblue3", ylim=c(0, 25), breaks=seq(0, 25, 8))  par(mfrow =c(1,1))   My dataset has 1224 obs. of  17 variables.


searching for specific String, renders completely different result, but why?

I do have some piece of code, I find unfathomable to comprehend. I save a longer string in a variable and then try to find a specific piece of string inside of it. The clue is that I can output the various substrings, but it will not find the specific string and stop the process...  The code goes like this:  import java.io.*; import java.util.*;  public class Readin {      public static void main(String[] args) {          String specChar = "DISD";         String gen = "MLRVFILYAENVHTPDTDISDAYCSAVFAGVKKRTKVIKNSVNP";          for (int i = 0; i < gen.length() - 3; i++) {             char char1 = gen.charAt(i);             char char2 = gen.charAt(i + 1);             char char3 = gen.charAt(i + 2);             char char4 = gen.charAt(i + 3);              String concatChar = new StringBuilder().append(char1).append(char2).append(char3).append(char4).toString();             System.out.println(concatChar);              if (specChar == concatChar) {                 System.out.println(specChar);                 break;             } else {                 System.out.println("Error");             }         }     } }


Does macOS have a command to retrieve detailed CPU information like /proc/cpuinfo on Linux?

Linux has a command to retrieve detailed CPU information using cat /proc/cpuinfo. Using this command, users can get CPU and CPU's core information like below.  processor   : 0 vendor_id   : GenuineIntel cpu family  : 6 model       : 142 model name  : Intel(R) Core(TM) i5-7267U CPU @ 3.10GHz stepping    : 9 cpu MHz     : 3096.000 cache size  : 4096 KB physical id : 0 siblings    : 2 core id     : 0 cpu cores   : 2 apicid      : 0 initial apicid  : 0 fpu     : yes fpu_exception   : yes cpuid level : 22 wp      : yes flags       : fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx rdtscp lm constant_tsc rep_good xtopology nonstop_tsc unfair_spinlock eagerfpu pni pclmulqdq ssse3 cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx rdrand hypervisor lahf_lm abm 3dnowprefetch invpcid_single pti retpoline fsgsbase avx2 invpcid rdseed flush_l1d bogomips    : 6192.00 clflush size    : 64 cache_alignment : 64 address sizes   : 39 bits physical, 48 bits virtual power management:  processor   : 1 vendor_id   : GenuineIntel cpu family  : 6 model       : 142 model name  : Intel(R) Core(TM) i5-7267U CPU @ 3.10GHz stepping    : 9 cpu MHz     : 3096.000 cache size  : 4096 KB physical id : 0 siblings    : 2 core id     : 1 cpu cores   : 2 apicid      : 1 initial apicid  : 1 fpu     : yes fpu_exception   : yes cpuid level : 22 wp      : yes flags       : fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx rdtscp lm constant_tsc rep_good xtopology nonstop_tsc unfair_spinlock eagerfpu pni pclmulqdq ssse3 cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx rdrand hypervisor lahf_lm abm 3dnowprefetch invpcid_single pti retpoline fsgsbase avx2 invpcid rdseed flush_l1d bogomips    : 6192.00 clflush size    : 64 cache_alignment : 64 address sizes   : 39 bits physical, 48 bits virtual power management:   Does macOS/OS X have a command to retrieve detailed CPU and CPU cores information equal to Linux /proc/cpuinfo? I really want to know a CLI command to retrieve the Mac's CPU core ID.  I tried sysctl machdep.cpu, but it didn't retrieve CPU core ID.


Erratic behavior from 16-bit counter IC SN74LV8154

My test circuit is shown below.  I've tried various configurations but keep getting jumps in the output counts.  Seems to be repeatable and consistent.  For instance, the first jump always occurs around 7k-8k counts.  I saw another post where the problem seemed to be with power supply filtering.  I've tried many different filtering caps on my regulator output, the register clock signal and the counting clock signal.  Advice would be greatly appreciated at this point.    Arduino code can be reviewed    Arduino Output:    UPDATE   Scope trace for RCLK input:   Scope trace for CLKA input:   5V supply with 555 running:   5V supply without 555 running:   UPDATE  Tried replacing the counter chip with a new one and got the same result as before.  Also, when I slowed down the input signal to 10 Hz I was able to see that the first jump occurred between decimal 8114 and 8150.  The first decimal value after the jump was 16390, almost exactly double!  00011111 10110010   Decimal: 8114 <-- Count before fault  00011111 11100100   Decimal: 8164  <-- Expected Count after fault  01000000 00000110   Decimal: 16390  <-- Actual Count


Window account is getting the below error when trying to connect into the SQL instance via management studio 2014.  The SELECT permission was denied on the object 'configurations', database 'mssqlsystemresource', schema 'sys' (Error 229)  The SQL instance is 2014, the user doesn't get the error if I make the login sysadmin.   The login has connect permission to the instance and even if i give it dbowner to the master database it cannot connect.   Default database is master also.  It is not an orphaned user I have tried the GRANT VIEW DEFINITION - no luck I have checked and the login doesnt have any DENY permissions   When i go into the properties of the login > Securables > effective tab > it gives the error:  The SELECT permission was denied on the object 'fn_my_permissions', database 'mssqlsystemresource', schema 'sys'.  So that is obviously related also   Any ideas?


If $(a_n)$ is a complex sequence such that $\sum_{n=1}^{\infty}\frac{a_n}{k^n} = 0,\forall k\in \mathbb{N}$ then $a_n = 0$ for all $ n$

Let $(a_n)$ be a complex sequence such that $$\sum_{n=1}^{\infty}\frac{a_n}{k^n} = 0,\forall k\in \mathbb{N}$$   Prove that $a_n = 0$ for all $ n$.   I'm sure there are many ways to accomplish this, but I'm feeling low on inspiration right now. Could anyone give me a hint?


How can I write an alias for cd such that it will fire ls after going into the directory to which I just cd'ed into?

Lets say I want to do cd home and then ls -lrth. I want these two things combined into a single command. I tried writing an alias, but it didnt work. Can you help me ?


I want to label a scale based on a variable value and I wrote a metapost code like this.  $ := 1; for i = -.3cm step .6cm until 3.6cm:     label.bot(str$,(i,-3.7cm));     $ := incr($); endfor;   It just labels "$" instead of its value. How to output the variables value?


How do you determine if a point sits inside a polygon?

Given the coordinates of a point $(x, y)$, what is a procedure for determining if it lies within a polygon whose vertices are $(x_1, y_1), (x_2, y_2), \ldots , (x_n,y_n)$?


I was going through a reading and this construction confused the student:     “Will we be able to talk?” I asked, my eyes red and swollen from   crying, a balled up tissue squeezed tightly between my sweaty palms.   She understood the words; it was the construction that confused her. I could explain what it meant in that context, but I didn't have a good explanation for that construction, generally. So in the above example, how would you classify "my eyes red and swollen from crying, a balled up tissue squeezed tightly between my sweaty palms"? Is it an appositive? Some kind of relative clause? Something else? A noun phrase?


How to use normal output with systemctl instead of less/more?

For example: systemctl list-units --type service by default uses redirection to less/more, how to disable it?


How do I set Ubuntu as my default OS on a Chromebook?

I recently downloaded Ubuntu for my Samsung 5 Chromebook from:    Whenever I restart the computer, it goes back to Chrome OS. How can I make it so that it boots into Ubuntu?


What kind of capacitor could build up, and maintain a charge acquired from lightning?

The microwave tower next door has a lightning arrester attachment. The charge probably goes harmlessly to ground. If it were possible to siphon part of the charge as it went to ground, how would one choose the capacitor (capacitance rating, punch through voltage, etc)?


How to prove polynomials with degree $n$ does not form a vector space?

This is one of my linear algebra problems:     Prove that polynomials of degree $n$ does not (The professor made these words bold intentionally) form a vector space.   From what I read, the set of polynomials of degree $n$ should be a vector space, because:   There is an "One" and a "Zero" in this set; We can find inverse for addition and multiplication from this set; It follows all the axioms of addition. It follows all the axioms of scalar multiplication.   Then can someone give me some hints to prove it does not form a vector space?


Should a game clean up after itself when exiting?

Should a game/engine clean up after itself(close windows, shut down renderers, close files, free memory) when its closed?  The OS should do that anyway, and usually in a faster way.  I guess most developers don't really care as they need proper cleanup for everything anyways(With dynamic asset-loading, and changing maps, etc.), but won't ensure that everything gets cleaned perfectly.  But is there any positive to cleaning up vs not cleaning up or the reverse?  I am using C++.  What about game consoles? Do they all clean up after themselves?


Approximation to $\sqrt{5}$ correct to an exactitude of $10^{-10}$

I am attempting to resolve the following problem:     Find an approximation to $\sqrt{5}$ correct to an exactitude of $10^{-10}$ using the bisection algorithm.   From what I understand, $\sqrt{5}$ has to be placed in function of $x$ but I am not sure where to go from there.  Also, a function in Mathematica are given to do the calculations in which the function $f(x)$, $a$ and $b$ (from the interval $[a, b]$ where $f(a)$ and $f(b)$ have opposite signs), the tolerance and the number of iterations.


I'm developing a website and I want to integrate a Live Web TV.  I have this dedicated server :  Quad Core Q6600 4x 2.40+ GHz 4GO RAM 1TO Disk Space Unmetered Bandwidth 100Mbps (goes down to 10Mbps if I reach 3TO of bandwidth. Possibility to swtich to 1 Gbps if I pay more)    I think I will use Red5 (installation will be made by Re5 Team) because it's open source and free of charge. Bitrate will be about 500kbps   I predict to have about :   100 users watching my live event I will proadcast a Live for Only 2 hours daily.  Videos on-demand should be always available for recroded events.   Can my server support this kind of activity ? Or do I need more ressources? Note that I have my customers websites hosted on this server. Do I have to make a VPS plan to the WebTV and seperate ressources ? Of course if this server supports that traffic.  I really don't want to go with company who provides this kind of services because they are too expensive.


"A/An" preceding a parenthetical statement

When a/an precedes a parenthetical aside (sometimes seen in informal/conversational writing), should the vowel rule depend on the first word in parentheses, or the next word in the "regular" flow of the sentence?     I need a (memorable) idiom (preceding an m word; use a)   or     I need an (memorable) idiom (preceding an i word; use an)


How do Variational Auto Encoders backprop past the sampling step

From my understanding of VAE's, there's a step during training in the middle where, after the encoder produces a mean and standard deviation, random samples are drawn from the given learned distribution to create the encoded vector that the decoder works to decode. I understand how one uses the KL divergence to force the learned distribution to be approximately the standard Gaussian, but I don't understand how the reconstruction loss can be back propagated past this sampling step. Random sampling is not a differentiable operation, so how can the gradients propagate past it? Is my understanding of VAE's wrong?


How to smoothly mix material on edges of said materials?

I'm somewhat new to blender and i have a problem with mixing materials:  Material A and B are similar (roughness, and colors) but material B has "holes" in it. These holes need to be in specific location on that mesh, and only there.   I need to somehow mix thesee materials so that is transformes smoothly to one another, and i dont know how.  I thought about "merging" them and mixing them with gradient texture as a factor but given that the materials are messy, and they blend in multiple places i don't think it can work, or at least i don't know can it work.  Any help would be appreciated


Is there a command which does the same like \clearpage (typesetting all floats which have not been typeset yet) but then does not insert a pagebreak but continues with the following text/graphics on the same page?


How to fix "/etc/apt/sources.list" could not be read error?

I tried to reinstall sopcast with the following command:   sudo tee -a /etc/apt/sources.list   but nothing happened, then I try the next command:  sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys CD30EE56   and I get the following error:   E: Type 'sudo' is not known on line 60 in source list /etc/apt/sources.list E: The list of sources could not be read.   Could anyone please help me?


I want to split a string with Tabstops. What is the correct char[] equivalent for usage with   Split.(char[] x, int i)


How come not all Stack Exchange sites have the cite option?

I noticed recently on  that there is a cite option that will spit out a citation if you wish to reference a question or answer in a paper or whatever that may need citation.    This seems pretty useful and I can see why more academic related Stack Exchange sites may need this feature, but I was wondering why doesn't every Stack Exchange site have it? Wouldn't it be valuable to be able to cite from any Stack Exchange site? It seems appropriate for any of our sites.  I found a related question I linked below, but there were no answers on it. But I'm trying to distinguish this question apart from that asking it more as a question of why it isn't available and then a follow up as potentially a feature request.  Related:


How to document LaTeX custom packages and document classes?

While I can use something like Doxygen to document a C library (functions, constants and structures defined/written by me), I couldn't find something equivalent in LaTeX to document \newcommand(s) \let(s) and other stuff in my .cls and .sty files.  Since LaTeX is common used as output (even by Doxygen), I'm struggling to find "Google keywords" for this specific matter.  Am I supposed to document a class/package by creating a separate LaTeX file specific for this? Or maybe, is literal programming the recommended way for LaTeX?  Thanks in advance.


When we describe the working principle of the transformer, we say that we want to minimize the loss of electrical energy, therefore we reduce the current Q=I^2Rt, so heat reduces as well, but to keep the same power we increase the voltage, but Q=U^2/R *t. so why voltage doesn't give us the heat effect.


Hi i want to develop an android application. In which I want to put effects like hue and saturation kind of effects on the video using ffmpeg. So is there any sample command for these kind of things?


Why does this matrix give the derivative of a function?

I happened to stumble upon the following matrix: $$ A = \begin{bmatrix}     a       & 1  \\     0       & a  \end{bmatrix} $$  And after trying a bunch of different examples, I noticed the following remarkable pattern. If $P$ is a polynomial, then: $$ P(A)=\begin{bmatrix}     P(a)       & P'(a)  \\     0       & P(a) \end{bmatrix}$$  Where $P'(a)$ is the derivative evaluated at $a$.  Futhermore, I tried extending this to other matrix functions, for example the matrix exponential, and wolfram alpha tells me: $$ \exp(A)=\begin{bmatrix}     e^a       & e^a  \\     0       & e^a \end{bmatrix}$$ and this does in fact follow the pattern since the derivative of $e^x$ is itself!  Furthermore, I decided to look at the function $P(x)=\frac{1}{x}$. If we interpret the reciprocal of a matrix to be its inverse, then we get: $$ P(A)=\begin{bmatrix}     \frac{1}{a}       & -\frac{1}{a^2}  \\     0       & \frac{1}{a} \end{bmatrix}$$ And since $f'(a)=-\frac{1}{a^2}$, the pattern still holds!  After trying a couple more examples, it seems that this pattern holds whenever $P$ is any rational function.  I have two questions:   Why is this happening? Are there any other known matrix functions (which can also be applied to real numbers) for which this property holds?


Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$   I was a bit lost with this proof until I found a  from a previous homework assignment in this class which said "If $a$ is an integer, prove that one of the numbers $a$, $a + 2$, $a + 4$ is divisible by 3. These problems seem very similar to me and would lead me to assume that they would be proven similarly, although I am unsure as to how I would approach this for prime triplets as I am brand new to them. Any help is appreciated


Duplicating rows based on a count column SQL Server

I have the following table:  MyTable PlaceID NameID  Code    CodeCount 1       1       1234A   2 1       2       1234A   3 1       3       1234A   1 2... 2... 3... 3...   I want to select 1234A where PlaceID = 1, the number of times equal to the sum of the CodeCount. So, the result would be six rows like this:  MyResult Code     1234A 1234A 1234A 1234A 1234A 1234A   Eventually, this selection will have a bunch of different codes for a single PlaceID. YES I know I'm duplicating data, in the end it's not going to be a lot and I'll explain why I'm doing this below.  First, I needed to get the sum of the counts:  DECLARE @cdcnt INT = (SELECT SUM(CodeCount) FROM MyTable WHERE PlaceID = 1 AND Code = '1234A')   Then I can use this value as a control in a while loop to select the value that many times:  DECLARE @i INT = 0; WHILE @i < @cdcnt BEGIN     SELECT DISTINCT Code     FROM MyTable     WHERE PlaceID = 1 AND Code = '1234A'     SET @i = @i + 1 END   The problem is I get 6 separate selections, instead of one selection with 6 rows. How do I create MyResult shown above, instead of 6 separate selections?   Why I am doing this: I want to use a random number generator to pick a Code with the frequency at which it appears in aggregate for each PlaceID (there will be other Codes added, I'm still figuring out how to do just one). I am open to suggestions for different ways of doing this, but it's the only way I could figure out how. If there's a function already built to pick from a list according to a set frequencies, I'm all ears.


The identity $(u\times v)\cdot(x\times y)=\begin{vmatrix}u\cdot x&v\cdot x\\ u\cdot y&v\cdot y\\\end{vmatrix}$

I know by brutal calculation this identity holds always:  $$(u × v) \cdot (x × y) = \begin{vmatrix}  u \cdot x & v \cdot x \\  u \cdot y & v \cdot y \\  \end{vmatrix}$$  for arbitrary vectors $u$, $v$, $x$, $y$.  I'd like to know where it come from naturally.  Thank you.


CD $Variable not working when used in a (Bash) Shell Script

File name: Test.sh  #!/bin/bash  ZDir="$(echo /usr/src)" cd "$ZDir"   When I execute the script ./Test.sh, the command cd doesn't do anything.  If I try to do it directly in the bash terminal, it works like a charm. Also, echo, used inside and outside the script, returns me the correct value (/usr/src).  Does anyone know why this happens? Again: cd $ZDir works if used outside the script, directly in the terminal...  Edit: Could'nt find the answer on the "duplicate" one but that G-Man user right there answered exactly what i needed to do. Just included a && followed by the next command i needed to do and worked. Functions can also be used for this... cdZDir() {     cd /usr/src;     make;     make install; }  Then just call in the function.


sudo apt-get install python-pil on Ubuntu 12.04?

I'm restricted to sudo apt-get install and I need to install python-pil so the command should be sudo apt-get install python-pil,but here is the problem:  sudo apt-get install python-pil Reading package lists... Done Building dependency tree        Reading state information... Done Package python-pil is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'python-pil' has no installation candidate   How to resolve this?


I have got a new HP OMEN 15-dc1049nl with Nvidia GTX 1660ti with  windows 10. I installed Ubuntu 20.04 successfully on other two my laptops. Now I want to install it on the OMEN, but when I try to boot from the USB I get the following error:    What did I do wrong?  I don't think it's a problem with the USB, because it worked with other laptops


Unrecognized special character with comment package

Why are the character with accent not recognized ?  \documentclass[a4paper]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage[french]{babel} \usepackage{comment}  \includecomment{withsolution}  \begin{document} \begin{withsolution} à \end{withsolution} \end{document}   returned error:  ! Paragraph ended before \UTFviii@three@octets was complete.   If I put it outside the comment environment, it works. Thanks for the help.


Figure spanning two columns in IEEE Trans template?

I am using  for a paper. The problem I am facing is that I have a figure that I want to span two columns instead of a single one. Is there a way to do it?


As you may have noticed, Jarrod's been hacking away at some design changes to the "close as duplicate" UI. These are  of some discussions we've been having internally regarding the "close" UI as a whole, with the goal being a smoother, easier-to-understand experience for all involved. Streamlined UI  The new pop-up provides four different functions:  Allow input of a specific possible duplicate ()  Display suggested duplicates (as originally implemented by )  Display search results for keyword-based searches (in the same fashion as the new suggested duplicates list)  Allow previewing the selected question with answers.   The search field reacts as you type, and there's visible, bread-crumb style navigation near the top of the dialog that allows you to quickly preview different potential duplicates (or back out of the dialog entirely). Answered questions only The search results include only answered questions (per the usual SO definition of "answered", where the question must have an accepted or up-voted answer). Additionally, close targets are restricted to answered questions even when specifying the ID or URL directly (with the exception of questions from the same author, and meta posts). Moderators can override this last restriction if necessary. The rationale here is that it can be fairly hard to discern whether or not an unanswered question is actually a duplicate, and even when it is closing doesn't really accomplish very much. When searching for a "canonical" answer in particular, duplicates without answers (or with bad answers) are just noise in the results. I think this makes sense in theory - so how is it working in practice?


I need help rationalizing the following expression using a conjugate:  $$\dfrac{1}{\sqrt{3} + \sqrt{2}-\sqrt{5}}$$  I have had no luck rationalizing this expression with a conjugate of the denominator.


Can derivatives be defined without a limit (as are integrals defined in Apostol's Calculus)

In the Apostol's Calculus (at first) integrals are treated without limits but derivatives are postponed to come after limits, their conceptual foundation.  I want to know that could the author have defined derivatives similar to the he defined integrals? If yes can you write how? If not, what is the conceptual difference between derivatives and integral that makes this happen?  edit: (My question is different from the general question of defining derivatives in terms of other things as it demands a similar way the author defines integrals.)  EDIT2:The author uses the darboux integral,Which is equivalent to the riemann integral;Now it now remains to be seen if there is a way to define a darboux-esque  derivative too?


How can i get size of an array in the called function?

It's just a self-assessment question as a result of curiosity; so please cope with it.             I know that in C we pass things by value. In case of arrays the scenario is different. We cannot pass them by their values and if we don't; a demotion from array type to pointer type will occur. We need to pass the value of the pointer to the first element of the array or pointer to the array itself. Yeah, this is what people call as array decay. As, the original type information of array is lost while passing we cannot obtain the size information of the passed array in the called routine unless we pass by reference.            Have a look at the following code:  #include <stdio.h> #include <stdlib.h>  void cal(int (*b)[3])  {     printf("%d",sizeof(*b)); }  int main() {     int a[3] = { 2,3,4 };     cal( &a );  }   Output:  12                                                               Okay, we got what we want. But what I concluded is that the number of elements in the array are always required when you declare a pointer to a non-variable array like this :  int a[] = { 3, 4, 5 }; // declaring an array of size 3 int (*p)[3]; // declaring a pointer to an array with length 3 p = &a ; // assignment   So, you are implicitly passing the length of the array to called function and there always exist a different way of doing it by passing an extra length argument to the called function in the case when you don't pass the reference of the array.  P.S. You always need to pass the length whether you do in an explicit manner or in implicit one and it is just like hardcoding things.  Is there exist an other techniques for having the size information of the passed array in the called function or I'm hitting right on the money? And, how will you deal with the dynamic ones'?


Why ceil() function return unexpected value?

n = ceil(1234 / (double)1); cout << n << endl;   Here output is 1234 but if I write n = ceil(99999999999999999 / (double)1); cout << n << endl;  This time I get 100000000000000000 as output. Why this happen?


This problem comes from exercise from my lecturer  Let $A$ be a square matrix such that $\mbox{rank}(A)=1$. Prove that $\det(A+I)=\mbox{trace}(A)+1$.  ($I$ is the identy matrix)  I usually haven't any idea in solving linear algebra problem.


same function name with different number of params override my base function

lets say I have a base class B and 2 classes that derived from it:  class B { public:      A_type* Check_Memory(const LeafInterface* leaf = 0); }  class D1 : public B {}  class D2 : public B {     A_type* Check_Memory(const LeafInterface* leaf, U32* faults); }   now, when I call:  D1 d1; d1.Check_Memory(leaf);   it call the function from the base class as expected,  but when I do the same with:  D2 d2; d2.Check_Memory(leaf);   instead of calling the function from the base class, I get the following error: function does not take 1 arguments.  does my only solution is declaring another function in D2 that call the base function? is there more elegant way in C++ for doing it?


Will I have to re-install ubuntu when 18.04 is officially released?

I recently purchased a new laptop, and I decided to take the plunge and get Ubuntu 18.04, despite it still being in beta. While there have been a few minor quirks here and there, for the most part it's worked fine for me, and I'm pretty happy for it.  When ubuntu 18.04 is officially released on April 26th, will I have to download it onto a bootable thumb drive and update that way, or will my version be equivalent to the full version as long as I continue to regularly install updates?  In summary, What is the correct way to update from a beta version once the full version has been released?


I stumbled upon some syntactically weird looking code recently when porting a c++ project from Windows to Linux.  if ( isObjectNear( objectPos, objectLength ) + .025, 0.125 ) { ...  }"   In this if-statement a parenthesis was misplaced causing the statement to consist of two expressions separated by the comma. The boolean "isObjectNear(..)" method had default parameters which allowed the call to be made using Microsoft's compiler despite the obvious mistake.  It was when building on Linux with GCC the problem was discovered giving the error message:      error: value computed is not used [-Werror=unused-value]                                                            The code in my case is more interesting than relevant to the question and the following code serve the purpose of the question more clearly with the return-value in comments:  if ( true, 0.5 ) ... // returns true since 0.5 > 0 ( 0 == false)  if ( true, 0.0 ) ... // returns false   if ( 1.0, false ) ... // returns false  if ( true, false, false, ..., true ) ... // returns true   So back to the question "Why is a if-statement with comma-separated expressions allowed by Microsoft's C/C++ compiler?"


In Google Drive, how can you link directly to "Download" a zip file and not view the contents?

When you share a Zip file in Google Drive, you land on a page to view all the files inside the zip file and to download the entire file the user has to click File → Download. I've noticed a lot of users don't get this so I actually have to tell them to click File → Download when all I really want to do is give them a link to directly download the file.


How to find the sum of the following series:  $\frac {1}{5}-\frac{1.4}{5.10}+\frac{1.4.7}{5.10.15}-\cdot\cdot\cdot\cdot\cdot\cdot\cdot$  Any hints.


Reopened questions get a "modified" time stamp in the questions list

just showed up on 's front page like this:    ... which makes no sense, because the question hasn't been modified since May 25th, and the person who edited it wasn't CatLord anyway:    Turns out what actually happened was that CatLord cast a fifth reopen vote to reopen the question.    So that stamp in the questions list should probably say this instead:     reopened 4m ago CatLord 10.7k   Or just:     reopened 4m ago


HTTPS redirection of Stack Exchange sites

Today suddenly I noticed that, I can access Stack Overflow by browsing both the URL:  and . I also have checked some of the other Stack Exchange sites like the current one, and they all have similar behavior. In my experience I have seen normally sites with HTTPS have a feature by which if any request comes with HTTP, it get redirected to the HTTPS. That is why, I am curious to know that if it is intentional to not to redirect to HTTPS in Stack Exchange sites.


How to calculate critical values for R for a large dataset

I have gone through various formulas but all were used for a small data set like 100, 200 rows, but I want to know how to calculate critical values of r for a large data set containing >5000 rows.   I have calculated using T.INV(1-alpha/2,df)/((sqrt(T.INV(1-alpha/2)^2+df)), but this formula is for small data sets, when I used it for a large data set, mentioned above, I got results which were not expected.


How to read such figures with % as "up (by) 120%" and "increased (by) 120%". Do they mean the same?

Such phrases describing growth rate as in the above examples are very common, but sometimes I'm confused about how to read them correctly. My understanding is:  If our 2019 sales are up 120% (or has increased 120%) from year 2018, it means, for instance, US$ 100 million in 2018, and US$ 120 million in 2019  If our 2019 sales are up by 120% (or has increased by 120%) from year 2018, it means, for instance, US$ 100 million in 2018, and US$ 220 million in 2019   If the above understanding is correct, then how should I interpret "..... is up 20% from last year"? Is it different from "up 120% from last year"? Or maybe those expressions include some ambiguities?


Baiduspider is crawling my site even when forbidden by robots.txt, how do I prevent it?

My site has heavy traffic because some bot. I checked access_log, some bot Baiduspider go to my site 10-20 times per minute. I do not need Chinese traffic. I have searched and read    I added rule into the robots.txt then restarted Aache, but it doesn't work. Baiduspider still crawls my site.  User-agent: Baiduspider Disallow: /  User-agent: * Disallow: /feed/ Disallow: /trackback/ Disallow: /wp-admin/ Disallow: /wp-includes/ Disallow: /xmlrpc.php   I found their feedback page  I can translate the page to my language, but I cannot translate and insert captcha.   Then I have searched and find some article:  But when I add it into .htaccess, I cannot access my site,(you do not have permission to access this site) Am i inserted in a wrong position? need a help.  # BEGIN WordPress <IfModule mod_rewrite.c> RewriteEngine On RewriteBase /  RewriteCond %{HTTP_USER_AGENT} ^Baiduspider.* [NC,OR] RewriteRule ^.* - [F,L]  #some custom rewrite rule RewriteRule ^article/([^/\.]+)/?$ /article/$1.php [L,QSA]  RewriteRule ^(.*)$ http://www.example.com/$1 [L,R=301] RewriteCond %{REQUEST_FILENAME} !-f RewriteCond %{REQUEST_FILENAME} !-d RewriteRule . /index.php [L] </IfModule>   BTW, my server is CentOS7 apache 2.4.6. I also tried "httpd.conf", but I never find any article about apache 2.4.6 <IfModule setenvif_module>, all the articles are <IfModule mod_setenvif_c>... apache 2.4.6 do cancel order allow,deny rule, I have no idea how  to modify and add into my httpd.conf.  Anyway, I just want to refuse Baiduspider Thanks.


Deferring admission to a computer science graduate program

Background: I have the opportunity to pursue a Computer Science graduate degree at a well respected program (around top 20). I spoke with the professors at the university and I feel like I am a good fit with their research program. My ultimate pursuits are to complete a PhD in CS. I've done research as an undergraduate and it has only confirmed my notion that I want to pursue a research track career.  More background: I applied to jobs (in case I was rejected to all the programs I applied for) prior to hearing back from my respective graduate programs. I accepted a position for an industry job (this was to secure I wouldn't be both unemployed & not in school).  Dilemma: Turns out my top graduate school is very interested in me, and I'm very interested in them. I would rather go to graduate school than work in industry forever. The industry job pays very well. I am split between A) working for a maximum of 1 year(It would only be 1 year, seriously I do not care about the money enough to work past a year) and B) going straight to graduate school.   My concerns are as follows, if I choose A):    Could I potentially defer my admissions? If I am not allowed to defer my admissions, would I have a good chance of re-applying and being accepted a year later? Would my potential advisers look down on me for deciding to work a year?   I already made my mind up it would be a 1 year gig if I decide A). I know some people say once you make money, you may not be able to readjust to the graduate salary pay. But I don't think that will apply to because I'm going to live very frugally with or without industry pay.


How to deserialize the following JSON to get the list of values?

I have used the code below to deserialize the json but throwing an error.   Map<String,Object> root =(Map<String,Object>)JSON.deserializeUntyped(res.getBody()));      "Callout error Invalid conversion from runtime type List<ANY> to Map<String,ANY>"    I want to deserialize the JSON using an apex class to get the list of values?  {    "controllerValues": {},    "defaultValue": null,    "eTag" : "",    "url" : "",    "values" : [     {             "attributes": null,             "label": "PicklistValue1",             "validFor": [],             "value": "PicklistValue1"     },     {             "attributes": null,             "label": "PicklistValue2",             "validFor": [],             "value": "PicklistValue2"     }    ] }


I'm going through  and came across this:  $ type rm rm is hashed (/bin/rm) $ type cd cd is a shell builtin   Just a little earlier, the guide listed the various types of commands understood by Bash: aliases, functions, builtins, keywords and executables. But there wasn't mention of "hashed". So, in this context, what does "hashed" mean?


Determinant of matrix of one's plus or minus the identity matrix

What is the best way to calculate the determinant of a matrix of one's (each entry in the matrix is a 1) plus or minus the identity matrix of size $n \times n$?


Can a route be included in more than one destination ticket?

The rules that come with the game do not specifically state the a route (between two cities) can be included in more than one destination string, but this is assumed when we play.   Is that a correct assumption?


Find all primes $p$ such that $x^3+x+1\equiv0\pmod p$ has $3$ incongruent solutions.

Find all primes $p$ such that $$x^3+x+1\equiv0\pmod p$$ has   $3$ incongruent solutions.   By a standard result in number theory, it has $3$ incongruent solutions iff there exists $q(x),r(x)\in\mathbb{Z}[x]$ with $\deg r(x)<3$ such that $$x^p-x=(x^3+x+1)\,q(x)+p\cdot r(x).$$ I am unable to proceed from here. I tried to write out the coefficients of $q(x)$ and multiply out, but it was in vain. How do I solve this problem? Thanks in advance!  I am unclear about what tags to add, so please fix this.


Is there a tool that combines zcat and cat transparently?

When handling log files, some end up as gzipped files thanks to logrotate and others not. So when you try something like this:  $ zcat *   you end up with a command line like zcat xyz.log xyz.log.1 xyz.log.2.gz xyz.log.3.gz and then with:  gzip: xyz.log: not in gzip format   Is there a tool that will take the magic bytes, similar to how file works, and use zcat or cat depending on the outcome so that I can pipe the output to grep for example?  NB: I know I can script it, but I am asking whether there is a tool out there already.


Remove launcher icon for uninstalled snap app?

I installed Cantor from the software center. (I didn't realize it would install the snap version, which I did not want). I then removed it using snap remove cantor from the command line.  However the Cantor launcher icon still appears in the Gnome-shell "app grid".  I checked ~/.local/share/applications/ and /usr/share/applications/ and there is no *.desktop file for Cantor present in either location.  How can I remove this launcher icon?


Is my Nikon 18-200mm 1:3.5-5.6G lens with broken front glass beyond repair?

My lens broke somehow. I didn't drop it as far as I remember, but the cause of the drop isn't really the point... a part of my lens broke, and my lens cap is stuck to it. Is my lens a goner? Can I buy a replacement for the specific part or will I have to fork out the near $400 to replace it? Where is the best place to cry?  This is a Nikon D90 with an AF-S Nikkor 18-200mm 1:3.5-5.6 G II ED


AC adapter won't power fan at full speed

I have a spare 92mm case fan rated 12V and ~600mA I've used to build a solder fume extractor. When I was prototyping it, I tested the fan with a 12V 2.5A AC adapter and it worked fine, ran at full speed, and was drawing 450-460 mA. I didn't want to tie up that AC adapter with this device, so I purchased a 12V 1A AC adapter to dedicate to the project.  I finished the project today and plugged in the new 12V 1A adapter. The fan would not run at full speed, and the speed surged up and down about once per second. I checked the adapter and it is putting out 12V, and I do have the polarity correct, and the fan is rotating the correct direction.  I tested it again with the larger adapter, and it is still drawing around 450mA, and the fan runs at full speed with that adapter.  I can't imagine what might be going wrong here. Do I have a bad adapter, or am I missing something?  Edit: I've figured it out. Turns out I had another 12V 1A adapter in an old Radio Shack kit, and it gave me the same poor result. I tried again with the 2.5A adapter, and this time checked the startup current: approximately 1.5A. The 1A adapters just can't supply enough current to get the motor to start up to full speed. I just need a higher capacity adapter.


i am not getting the desired regd_num and name i want regd_num as 567 but it shows 67 and similary in case of name i want raj but it shows C can you please help me how to read the strings properly in an union  #include<stdio.h>  union student{     int reg;     char name[20];     int marks[10];  };  int main() {     union student s;     int i;     float avg,sum;      printf("Enter the register number:");     scanf("%d",&s.reg);     printf("\nEnter the name:");     scanf("%s",s.name);     printf("\nEnter the marks:\n");     for(i=0;i<3;i++)     {         scanf("\n%d",&s.marks[i]);     }     sum=s.marks[0]+s.marks[1]+s.marks[2];     if(s.marks[0]>=0&&s.marks[1]>=0&&s.marks[2]>=0)     {         if(s.marks[0]>=40&&s.marks[1]>=40&&s.marks[2]>=40)         {             avg=sum/3;             printf("\nRegd.No:%d",s.reg);             printf("\nName:%s",s.name);             printf("\nPercentage: %0.2f",avg);         }         else             printf("Grade is Failed");     }     else         printf("Invalid mark. Mark should between 0-100"); }


I'm developing some plugin where I would like to enable custom pages. In my case some custom page would contain a form like contact form (not literally). When user will fill out this form and send it, there should be the next step which will require more information. Lets say that the first page with form would be located at www.domain.tld/custom-page/ and after successful form submission, the user should be redirected to www.domain.tld/custom-page/second. Template with HTML elements and PHP code should be also custom.  I think that a part of the problem is possible to achieve with custom URL rewrites, but the other parts are currently unknown to me. I really don't know where should I start looking and what's the correct naming for that problem. Any help would be really appreciated.


As a Mongolian citizen planning to travel on a cruise, do I need a visa to each country or island where the cruiseship stops? If I already have a visa to the UK, will that be accepted in any country/island that does not require a visa of a UK citizen?


today morning I woke up and saw our MongoDB databases are removed and just this DB HOW_TO_RECOVERY_BASE is there. that have a collection which is README and here is content:   {     "_id": {         "$oid": "5e94ba92ab2c988a0e61117e"     },     "content": "All your data is a backed up. You must pay 0.015 BTC to 1DGkm33MMPRzjn2ruDEJeZdBuytBmCwqfZ 48 hours for recover it. After 48 hours expiration we will leaked and exposed all your data. Also do not forget about GDPR. You can buy bitcoin here, does not take much time to buy https://localbitcoins.com with this guide https://localbitcoins.com/guides/how-to-buy-bitcoins After paying write to me in the mail with your DB IP : recovery_bas3@protonmail.com" }      fortunately, I made a backup last month using rsync command. now I can't find how I can restore my whole server using this backup. and how can I safe my centos VPS and prevent this type of attack?


Transfer Minecraft data between Xbox One and PS4

I have not been able to find any answers to this question:  My friend and I both have PS4's, and we both like Minecraft. We have a saved world, but he has it on his Xbox One, I don't have an Xbox One. Is it possible to transfer the Minecraft data from the Xbox one to his PS4?


Prove norm doesn't come from inner product.

Please help me prove this. I'm not sure how to apply the parallelogram law to the norm.


What would be the eigenvalues for a Householder matrix defined as: $H = I - 2 u u^T$? Can someone explain it  to me intuitively or with a simple proof?


What is the remainder of $\,3^{3^{3^{\:\!\phantom{}^{.^{.^.}}}}}\!\!\!$ divided by $46$?  The level of powers is $2020$.  First there is no parenthesis so it means 3 power of 3 which is also power 3 and so on 2020 times  Second I think that we can use Fermat's Little Theorem but I don't know how, and maybe there is a better way.


Can we hit a local/private server using IP address with HTTP request in Salesforce ?? or the server should always be public.... can we access a private IP address of local host/server using the HTTP methods that salesforce.com provides. how to hit the local server...  I have make the callout which was written in .Net (hosted on localserver) which will get the data from stored procedure in SQL.  When i was trying to get the data from SQL to Salesforce , i was able to get the data when i was using the advanced rest tool. But when i tried in salesforce callouts http methods  with end point url after  setting remotesitesetting , i could not get the  data.User-added image  it gives me an error of '503 service unavailable'.  ,when i tried to execute a block of code in Salesforce, i  made callout to  the .Net webservice  file  to test the data, i got an error 'Server unavailable,status code = 503'.  My another important question is ''If the Webservice is hosted on the local or intranet, will the salesforce API (which is on the cloud) able to access that webservice  Thanx in advance


I'm trying to forcibly drop a PostgreSQL 9.4.4 database from a Bash script using psql:  #!/bin/bash db="mydb" psql -d $db -c "SELECT pg_terminate_backend(pid) FROM pg_stat_activity WHERE datname = '$db';"   I'm using the solution shown in this  but it doesn't work. What I see is this:   FATAL: terminating connectoin due to administrator command server closed the connection unexpectedly          This probably means the server terminated abnormally          before or while processing the request.    What am I doing wrong? I own the database and my user role has the "Superuser" attribute as shown when I do \du from the Postgres console.


What was sci-fi book where the main character could read computer networks

In 1990 I was buying some science journal, and it used to publish excerpts from sci-fi and fantasy books. In such a way I got acquainted to Ursula Le Guin and etc.  I remember there was a (maybe short) story where the main hero could hack networks, devices and get info or manage them.  In this new Intelligence TV series, the main hero also can hack computer systems.  I would be glad if you could point me to the story.  Thank you very much!


What do you call feeling what someone else feels?

I am looking for a word that describes:  A) When you are spinning, someone else feels dizzy  B) feeling full watching someone else  eat  C) feeling happy watching someone else be happy.  My first thought was sympathy, but that only applies to feelings of "pity and sorrow for someone else's misfortune" (Google).


char temp1[4] = "abc"; char *temp2 = "123"; strcpy(temp1,temp2);   if I want to copy a string literal to an array, it works well, but if I do it in the opposite way, I get an error:  char temp1[4] = "abc"; char *temp2 = "123"; strcpy(temp2,temp1);   The feedback from compiler is "Segmentation fault".  So what's the differences? Is there anyway to copy a string to a string literal?  Thx.


Last night i factory reset my mums mums MacBook pro.  I had got to the point where I had to re install mac os x. I selected the hard drive I wanted it on and it prompted me with a apple id sign in. I knew from then that my or my mothers apple Id wasn't going to work because my mum told me she had got it off trade me ( like ebay but in NZ )  I've tried making a bootable usb drive to re install lion os x but it didn't work, or I just didn't do it right. Its a MacBook Pro 2010 mid I think and I am stumped on what to do, now that it has no operating system on it or anything on it now, only thing that works is the utilities mode.  All help is very appreciated.   Thanks


unable to open database file in python 2,7 or 3.8

I'm coding python 2.7/python 3.8 in linux, and i've been trying to code following function,, def main(database):     try:         connection = None         connection = sqlite3.connect(database) ##this is the error i think         if connection is not None:             print('success')             break         else:             print('oops')             break     except mysqlite3.Error as e:         print(e) if __name__ == "__main__":   main('$HOME/.databases/database.db')  returns following. unable to open database file  i'm wondering, if my python can't somehow access any other directory than directory, where python file is located (/home/user/apps/sqlite3.py), because if i use following code, it works. if __name__ == "__main__":   main('myDB.db') #now the file is located same directory that the python file is located.


In special cases, can you use "one such family are" vs. "one such family is"?

Is it correct to say "one such family are..." as opposed to "one such family is..." in some circumstances?  Say, for instance, as used in  on gene families:     [...] One such family are the genes for human haemoglobin subunits; [...]   The problem occurs when the family is a collection of things. It sounds weird if you say "One such family is the genes for human haemoglobin subunits" and saying "One such family is the family of genes for human haemoglobin subunits" is too wordy.  Does the problem make sense?


I know for a fact that for some verbs like 'say', 'indicate', 'know', 'claim', the deletion of 'that' is usually optional, though it's safer to include it. However,  does the same apply when 'that' is used to linked a subject to a independent clause?   To clarify with an example:   The worst thing is you don't even know who did it.  Or  The worst thing is THAT you don't even know who did it.   Which one is grammatically correct, if not both?  Note: I am having trouble finding something to refer to that specifically discusses the omitting of 'that' after verb-to-be. Providing me with a link would be greatly appreciated.  Many thanks in advance.


Compute $\lim\limits_{n\to\infty}(x_{n+1}-x_n)$ if $x_n =\sum\limits_{k=1}^{n-1}f(\frac kn)$ and $f$ continuous (but not continuously differentiable)

The following question from  (Exercise 1.32. page 6) is an "open problem" :  Let $f: [0,1] \to \mathbb{R}$ be a continuous (and not a continuously differentiable) function and let $$x_n = f\left(\dfrac{1}{n}\right) + f\left(\dfrac{2}{n}\right) + \dots + f\left(\dfrac{n-1}{n}\right).$$ Calculate $\lim_{n \to \infty} (x_{n+1}-x_n).$  I am very interested in doing research on this problem but I am not sure whether the problem still is unsolved. [The book has written in 2010(?)] I searched the internet but I couldn't find anything about it esp. searching a long formula without a name attached to it is more difficult (to me). I am new in research and there are lots of difficulties to me  () to find out proper clear answers to the following questions: 1- Is the mentioned problem unsolved, yet? 2- How to find out all the signs of progress have been done on the specific problem? (It is much easier to gather most of the related things about, say, Catalan's constant but I have no idea about ways of searching an-exercise-of-a-book looking problem in  or printed journals).


We use "the news is good" instead of "the news are good."  What is the rationale behind this? Are there similar situations in English?


Prove that the only sets in $R$ which are both open and closed are the empty set and $R$ itself.

I am trying to prove the above proposition. I tried to prove it by way of contradiction letting $S$ be such nonempty proper subset of $R$. Then $T=R-S$ would also be a nonempty proper subset of $R$ which is both open and closed. The method I thought of to lead contradiction is to create a sequence like this.   Take $s_0$ from $S$ and $t_0$ from $T$. Then consider the point $\frac {s_0+t_0}{2}$ and if this point belongs to $S$ call it $s_1$ otherwise $t_1$. Repeat this process then eventually there is a sequence $s_m$ and $t_m$ which both converge to the same limit. But then since both sets are closed the limit point belongs to both sets, which is a contradiction.   It's clear that such a sequence exists intuitively but I'm having trouble rigorously constructing such a sequence. Since I have no idea which set each of the newly constructed point belongs to, I don't know how to prove by $\epsilon-N$ definition of a sequence that both sequences converge to the same number. Can anybody help me?   Moreover, how may I be able to generalize this proposition to the $R^n$ setting?  Thanks.


Further customizations -- top bar and desktop icons

Bit of a general question here. Is it possible in Ubuntu 18.04 to move things around on the top bar? For example, the date and time in the center -- can it be moved to the right to sit next to the network and power icons? Is this only possible on what I've read is called a "Unity" desktop? (sorry if it's a silly question, quite new to Ubuntu still).   Also, is it possible to use any icon one likes for things like the Trash bin on the desktop? For instance, I have an icon theme installed, but I don't like the Trash icon, could I use the icon from Gnome or Humanity for it instead if I wanted to?


How might I schedule a C# Windows Service to perform a task daily?

I have a service written in C# (.NET 1.1) and want it to perform some cleanup actions at midnight every night. I have to keep all code contained within the service, so what's the easiest way to accomplish this? Use of Thread.Sleep() and checking for the time rolling over?


Construction an a command line bash script with spaces in path names

I need a simple script to call gcc but I've got a long list of libraries that I need to pass to it in a directory who's path has a space on it.  In place of gcc for testing my script I've used:  #!/bin/bash for var in "$@" do     echo "$var" done   This is one of the umpteen attempts I've tried:  #!/bin/bash LIBDIR="lib dir" LIBS= LIBS+="lib1 " LIBS+="lib2 " CMD="./debug.sh " for LIB in $LIBS do     CMD+="-I ${LIBDIR}/${LIB} "  done ${CMD} exit   Obviously the problem is that bash cannot tell which spaces are meant to separate the arguments and which are not, but no matter how I place quotes or backslashes I cannot figure out how to 'quote' some of the spaces and not the others.


NODEJS mongodb how to put variable inside like query

I need to put variable inside mongodb like query. This is my code    query={username: /req.params.data/}   Users.find(query,function(err,users){     if(err){       console.log(err);      }     else{       console.log(users);     }   });   req.params.data is a variable.I need to look for user that contains it.


I purchased a used Note 4 off ebay and want to make completely sure there are no spy apps or malware on it. I know some spy apps can be installed into the system partition and survive a factory reset. I discovered an app called cerberus that could do this and could be used to spy on me and blackmail me. How do I completely clean my phone of all spy apps or malware and completely wipe everything including the system partition erasing everything.


Is acceleration due to gravity constant?

I was taught in school that acceleration due to gravity is constant. But recently, when I checked Physics textbook, I noted that  $$F = \dfrac{G  m_1   m_2}{r^2}. $$  So, as the body falls down, $r$ must be changing, so should acceleration due to gravity.


What is the best way of testing that a string is empty?

I usually do this:  void Incoming(String str) {     if (str == "")     {      } }   But I've seen others' code do this:  void Incoming(String str) {     if (str == String.Empty)     {      } }   In my case I know str shouldn't be null. So would the following be a good idea instead, given it will cause an exception if the string is null rather than hiding the problem:  void Incoming(String str) {     if (str.Length == 0)     {      } }   And I've noticed this being used too, but this seems to accept the string might be null, rather than going and fixing the reason it is null. Is it a good idea to silently handle strings being null?  void Incoming(String str) {     if (String.IsNullOrEmpty(str))     {      } }


Indeterminate Progress bar for webview in fragment

I am trying to show a circular indeterminate loading indicator for a webView however despite reading a load of answers on here, my builds are failing. I get the error java.lang.NullPointerException: Attempt to invoke virtual method 'void android.widget.ProgressBar.setVisibility(int)' on a null object reference. I have set up the progress bar in the fragment.xml file like so:  <ProgressBar     android:id="@+id/prgrsbar"     style="?android:attr/progressBarStyleLarge"     android:layout_width="wrap_content"     android:layout_height="wrap_content"     android:layout_centerHorizontal="true"     android:layout_centerVertical="true"     android:visibility="gone"     android:indeterminateDrawable="@drawable/progress" > </ProgressBar>   and created an empty progress.xml file in drawable with this in it:  <?xml version="1.0" encoding="utf-8"?> <selector xmlns:android="http://schemas.android.com/apk/res/android"> </selector>   Finally, here is my fragment's onCreateView activity code that I am using:  @Override public View onCreateView(LayoutInflater inflater, ViewGroup container,                          Bundle savedInstanceState) {      //code here        View rootView = inflater.inflate(R.layout.fragment_first, container, false);      String url = "http://winn-brown.co.uk/shmee/";     WebView view = (WebView) rootView.findViewById(R.id.webview);     view.getSettings().setJavaScriptEnabled(true);     view.loadUrl(url);      view.setWebViewClient(new WebViewClient() {          private ProgressBar prgrsBar;         public void onPageStarted(WebView view, String url, Bitmap favicon) {             super.onPageStarted(view, url, favicon);             prgrsBar.setVisibility(View.VISIBLE);         }          public void onPageFinished(WebView view, String url) {             // do your stuff here             Log.i("message", "website loaded");          }     });       return rootView; }   On this line private ProgressBar prgrsBar; it says "Private field 'prgrsBar' is never assigned, despite having the id in the fragment's xml file. Apologies if I am missing something obvious here.


Can I change the checkbox size using CSS?

Is it possible to set the size of a checkbox using CSS or HTML across browsers?   width and size work in IE6+, but not with Firefox, where the checkbox stays 16x16 even if I set a smaller size.


How can a photon exist on its own without a mass?

For example, thermal energy exists and has no mass, but is carried by particles which have mass. A photon is described as a particle - how can a photon exist on its own, travel in space and even push other particles with mass if it has no mass itself?


line break in SAS bulk generated email body

I am trying to generate bulk emails through SAS, based on instructions of  by Eric Tilanus.  I cannot put a line break and all the put statement products appear in the same line in the email body.  I am using SAS 9.4. Sample code is below.  Do you know how I can get a line break?  data _null_;     length body $1024;     set DSIN end=last;  file outbox;      put '!EM_TO!' email;      firstLine= catx(' ',"first line",put(dttm,datetime19.), "blah");     put firstLine;      /* how can I get a line break here? */      put "second line";      put '!EM_SEND!';     put '!EM_NEWMSG!'; if last then put '!EM_ABORT!'; run;   Here is the email body generated:  first line 06JUL2015:21:25:40 blah second line   UPDATE:  has useful info. Outlook truncates line breaks. Putting two spaces before the string bypasses Outlook's automatic line break truncation.


Can I somehow revive unrecognizable (micro) SD cards?

I am unsure as to whether to ask here, or on .  I have a box full of micro SD cards, which I have used over the years for Raspberry Pis. I was searching through them for one to use, and most seemed to be unrecognized.  I am not even sure how an SD card can go wrong, let alone 6 or 8 from a box of 10. Of course, it is possible that I recognized them as defective, but kept them "just in case".  Should I just through them away, or is there any way to rescue them?  Please note that I am not concerned with their current contents.


Why division by infinity is not done immediately in limits

I was going through the proof that derivative of $\ln x$ is $\frac{1}{x}$. Here is what it shows. $$ \lim_{\Delta x\rightarrow 0}{\frac{\ln\ ( x+\Delta x) -\ln\ x}{\Delta x}}$$ $$ \lim_{\Delta x\rightarrow 0}{\frac{1}{\Delta x} \ln\left(\frac{x+\Delta x}{x}\right)}$$ Let $\displaystyle \Delta x=\frac{x}{n}$ then we have  $$\frac{1}{x} \ln \lim_{n \rightarrow \infty}\left( 1+\displaystyle \frac{1}{n}\right)\displaystyle ^{n}$$ \begin{equation*} \frac{1}{x} \ \ln\ e=\frac{1}{x}. \end{equation*}  Why does $n$ does not divide 1 to get 0 giving natural log of 1 raised to power n which will give 0 and the final derivative will be 0.


How to set the filename when downloading a file?

I'm working on MVC 4. I have generated Excel file dynamically using following simple code. My hosting is on Azure.  I have created a Root path and then try to save that Excel file.  Problem is when my ActionResult method response comes back it is giving default popup to open a file but file name is having a GUID instead my provided file name.  Excel file generation code:  Microsoft.Office.Interop.Excel.Application xlApp =          new Microsoft.Office.Interop.Excel.Application();  // ... //Save         LocalResource resource = RoleEnvironment.GetLocalResource("MyValue");         string tempPath = resource.RootPath + "DemoFile.xls"; return tempPath;   tempPath returns path like C:\AppData\Local\dftmp\Resources\11a2435c-998c-4fe8-aa55-8bb42455b4ca\directory\DemoFile.xls.  The Download File popup does not give file name as DemoFile it gives some GUID why so?       ActionResult method code:  public ActionResult DownloadExcel() {     string path = ExcelGenerationCode(fileName);         Stream s = new FileStream(path, FileMode.Open, FileAccess.Read);         return new FileStreamResult(s, "application/vnd.ms-excel");     }   Also tried to give name property  public ActionResult DownloadExcel() {     string path = ExcelGenerationCode(fileName);         Stream s = new FileStream(path, FileMode.Open, FileAccess.Read);         return new FileStreamResult(s, "application/vnd.ms-excel")         {             FileDownloadName = "myexcelFILE1.xls"         };     }   getting below error when give filename parameter.   i have plenty of space and memory.


Let us consider the following example :    \documentclass[12pt,twoside,a4paper]{book} \usepackage[usenames,dvipsnames]{pstricks} \usepackage{epsfig} \usepackage{pst-grad} % For gradients \usepackage{pst-plot} % For axes \begin{document} \scalebox{1} % Change this value to rescale the drawing. { \begin{pspicture}(0,-0.02)(2.68,0.02) \psline[linewidth=0.04cm](0.0,0.0)(2.66,0.0) \end{pspicture}  } \end{document}   Whenever I compile this code with kile in Ubuntu14.04 shows four errors :    Undefine control sequence }    Undefine control sequence }    Undefine control sequence }    Undefine control sequence }  But I don't know why such errors are occurring. Please help.


This question concerns the yes command found in UNIX and Linux machines: Basically, what is the point (if any) and history of this tool? Are there practical applications for it? Can an example be shown where it is useful in a script or chained (via pipe or redirect) with another tool?  The manpage is below:  YES(1)                    BSD General Commands Manual                   YES(1)  NAME      yes -- be repetitively affirmative  SYNOPSIS      yes [expletive]  DESCRIPTION      yes outputs expletive, or, by default, ``y'', forever.  HISTORY      The yes command appeared in 4.0BSD.  4th Berkeley Distribution        June 6, 1993        4th Berkeley Distribution   Sample output:  $ yes why why why why why ^Cwhy


Continuing Page Numbering (Roman to Arabic)

I'm here with weird stuff again.  How can i continue numbering while changing numbering style to Arabic from Roman? For example let's assume I have total of 7 pages and I want to number the first 3 of them as : i,ii,iii; then I change back to Arabic again and continue counting as 4,5,6,7.


Best fitting in a curve of the form $Ax^B+C$

I am trying to fit data of the form $(x_i,y_i)$, $i=1,\ldots,n$, in a curve of the form $y=Ax^B+C$, where $B\in (0,1)$. All three constants $A,B,C$ are to be determined optimally (no particular norm for the moment). Also, the $x_i$'s are positive integers, if that helps.  Is there any standard method to attack such a problem?


Due to natural rotation of Milky Way all Earth life gets increased intelligence

I read this story in the late 1970s, perhaps very early 1980s.  All life (with a brain I guess) on Earth suddenly develops increased intelligence. Scientists determine this is due to the normal 250-million-year rotation of the Milky Way. There is some large part of space ("dust cloud"?) that the solar system rotated through (and recently out of) that inhibited brain function in some kind of way. Now that this is no longer the case all higher lifeforms become smarter.  One example given that I have always remembered clearly is about a dog now being smart enough to open a freezer, take out some frozen meat, and then wait for it to thaw before eating it.  Seeing that I read it way back when, I will have read a translated version. So I cannot be certain that the original is in English.


Story in a domed city: Jester or Joker whose job is to create chaos to prevent the city stagnating

The story is set in a domed city, where all dangers and strife have been removed... almost. The most important character is called the Jester or maybe the Joker. His job is to create chaos and he is immune from all prosecution. His role prevents the city stagnating, presumably based on the notion that deviance and threat are what binds society together, without which, the need for societal bonds collapses.  What is the name of this story/book?


I've read that you have to watch the video to be able to share, and like. There should be a share button, but on mine there is no video to watch. They're just photos, and if I click on them, it just takes me to the original place they were at.  I also had refreshed the page multiple times, yet the button does not show.