Why won't vendors restock?
How does vendor restocking work in Fallout 4?
Show that given seven real numbers, it is always possible take two of them, such that $\left\vert\frac{a-b}{1+ab}\right\vert<\frac{1}{\sqrt{3}}$ Show that given seven real numbers, it is always possible take two of them, such that $$\left\vert\frac{a-b}{1+ab}\right\vert&lt;\frac{1}{\sqrt{3}}$$   The "Pigeonhole principle" states that if $n$ items are put into $m$ containers, with $n &gt; m$, then at least one container must contain more than one item, but how I an define my "container" such that meets the condition of the problem? My understanding is that a random variable is actually a function $X: \Omega \to T$, where $\Omega$ is the sample space of some random experiment and $T$ is the set from which the possible values of the random variable are taken.  Regarding the set of values that the random variable can actually take, it is the image of the function $X$. If the image is finite, then $X$ must be a discrete random variable. However, if it is an infinite set, then $X$ may or may not be a continuous random variable. Whether it is depends on whether the image is countable or not. If it is countable, then $X$ is a discrete random variable; whereas if it is not, then $X$ is  continuous.  Assuming that my understanding is correct, why does the fact that the image is uncountable imply that $Pr(X = x) = 0$.  I would have thought that the fact that the image is infinite, regardless of whether it is countable or not, would already imply that $Pr(X = x) = 0$ since if it is infinite, then the domain $\Omega$ must also be infinite, and therefore  $$Pr(X = x) = \frac{\text{# favorable outcomes}}{\text{# possible outcomes}} = \frac{\text{# outcomes of the experiment where X = x}}{|\Omega|} = \frac{\text{# outcomes of the experiment where X = x}}{\infty} = 0$$  What is wrong with my argument?  Why does the probability that a continuous random variable takes on a specific value actually equal zero? What evidence is there supporting an alternative parentage for Jon Snow? I've heard speculation that Jon Snow's actual parents may be Rhaegar and Lyanna Stark, but in reading the books I'm not sure what evidence could be used to support this conclusion.  I thought there might have been something in the conversation Davos had before being smuggled into White Harbor, but I couldn't stretch anything that far.  What evidence do proponents of this theory cite?  Does any of it involve stuff in the texts or just sweeping generalizations of the characters' personalities (e.g. "Ned Stark is too honorable to father a bastard"). How do I shuffle cards for a card game? I am trying to develop an card game for Android Can anyone suggest me how to write code for effectively shuffling the playing cards? Remove only the commas present within the double quotes In a text file, I want to remove , (commas) and also the " (quotes) (only if the double quotes  contains  numbers separated by commas).  56,72,"12,34,54",x,y,"foo,a,b,bar"   Expected ouput  56,72,123454,x,y,"foo,a,b,bar"   Note: I show the above line just as an example. My text file contains many lines like above and the numbers separated by commas present within the double quotes should vary. That is,  56,72,"12,34,54",x,y,"foo,a,b,bar" 56,92,"12,34",x,y,"foo,a,b,bar" 56,72,"12,34,54,78,76,54,67",x,y,"foo,a,b,bar" 56,72,x,y,"foo,a,b,bar","12,34,54" 56,72,x,y,"foo,a,b,bar","12,34,54","45,57,84,92","bar,foo"   Expected output:  56,72,123454,x,y,"foo,a,b,bar" 56,92,1234,x,y,"foo,a,b,bar" 56,72,12345478765467,x,y,"foo,a,b,bar" 56,72,x,y,"foo,a,b,bar",123454 56,72,x,y,"foo,a,b,bar",123454,45578492,"bar,foo"   There a n number of numbers present within the double quotes separated by commas. And also leave the double quotes which contains characters as it is.  I love sed text processing tool. I'm happy if you post any sed solution for this. Prove that an infinite ring with finite quotient rings is an integral domain How can we show that if $R$ is an infinite commutative ring and $R/I$ is finite for every nonzero $I \unlhd R$, then $R$ is an integral domain?   I tried proceeding by contradiction: assume $a$,$b$ $\in R \backslash \{0\}$ and $ab=0$; then $R/(a)$ and $R/(b)$ must be finite, say $R/(a)=\{k_i + (a) : 1 \leq i \leq m\}$ and $R/(b)=\{l_j + (b) : 1 \leq j \leq n\}$. Does this mean $R$ must be finite? Or what about using the fact that $R/(a,b)$ finite?  Thanks for any help with this! Why can't I log into my minecraft account I was given a laptop with a totally dead display. I do not want to pay to replace the broken display, but I would like to use the laptop as a server and connect to it via SSH to control it.  I have pulled out the internal hard drive from the broken laptop, and I want to install Debian GNU/Linux and the SSH server onto this HDD using a working Debian laptop.  However, the hardware in the two laptops is very different, and I am wondering what kind of problems I would run into when I plugged the drive back in to the laptop with the broken display because of this?  How would I make this work? What is the proper way for me to install a bootable copy of Linux onto a HDD that will be used by a computer with different hardware? How do I fix a "Problem with MergeList" or "status file could not be parsed" error when trying to do an update? How to let `dpkg -i` install dependencies for me? Hello,   I create an app using the Promoted Links in Sharepoint 2013. I chose to do this because the feature has the awesome hover effect and is easy to customize the image.  The issue is that I have been trying to figure out how to change the tile sizes. They are awesome the way they are, however I just need them smaller. I still want the hover effect as well and for the text to match the same ratio as the tile. I have tried web zones, I have done each ID but with no luck. I have attached a sample image of the tiles I'm referring to. Please help. If $\mathop{\mathrm{Spec}}A$ is not connected then there is a nontrivial idempotent Recover data from SD card I have a 2&nbsp;GB Kingston  card which is about three years old. I put it in a reader today in my Windows Vista computer, wrote a 32&nbsp;MB file onto it, safely removed it, and then tried to read it elsewhere. Nothing. Putting it back in the Windows Vista computer it now says:     You need to format the disk in drive F: before you can use it.   What should I do? I have access to many computers and OSes if your recommendations need that. I would be very sad if I lost all the contents of the card. Most of the data is backed up, but there are a few things that aren't. :(  Doing a   # dd if=/dev/sdg of=~/tmp/sd.bin   gives me a 2&nbsp;GB file, and  the file it seems like lots of my data is still there. How can I put it back together? What is a NullReferenceException, and how do I fix it? Strictly diagonally dominant matrices are non singular What are recommended, general strategies to start block-cipher design and/or analysis? I (and many others for that matter) have always been fascinated by the inner workings of the modern building block of cryptography: block ciphers.  Now, the ressources on the "black art" of design and analysis of these ciphers are sparse; especially for the entry level. Available information like  seems to be somewhat outdated (due to its age).  What's the general consensus of the “best” (read: recommended) strategy to start designing and/or analyzing modern cryptographical block ciphers?    Nota bene: Think of this as a general, wiki-alike question – for learning purposes only. (Besides that, this Q&amp;A would represent a place we can point people to when alike algorithm design questions arise.) How can I break on an unhandled exception in ASP.NET? When debugging an application in Visual Studio, there are 2 options for breaking on exceptions. Break as soon as an exception is thrown, and breaking only when an exception isn't caught. This works fine when developing desktop applications. However, when developing ASP.NET applications, all exceptions are eventually caught by the code in IIS.  Is it possible to disable this behavior, so that the debugger breaks when my ASP.Net application code fails to catch an exception?  Edit: Just to be clear, I don't want to break whenever an exception is thrown, as many times they are handled just fine by my code, and I don't want to stop on every exception. I only want to stop on the exceptions that aren't handled by my code.  Edit: This seems to not be an issue in Visual Studio 2008. In Visual Studio 2003, all exceptions were treated as user handled, because the ASP.NET runtime caught all the exceptions so as not to bring down the web server process. It seems that in Visual Studio 2008, this type of exception catching is not counted when checking for user-unhandled exceptions. If $x+{1\over x} = r $ then what is $x^3+{1\over x^3}$? If $$x+{1\over x} = r $$ then what is $$x^3+{1\over x^3}$$  Options: $(a) 3,$ $(b) 3r,$ $(c)r,$ $(d) 0$ I'm arriving from New Delhi, India (Indian passport) with JAL at Narita on 11th July at 07:30 and departing for San Francisco with JAL at 00:05 on 12th July from Haneda. Do I need a transit visa as I'll be switching airports and spending a few hours at JAL City Haneda Airport Hotel?  Previously I had connecting flights from Narita to San Francisco and obtained shore passes to relax at Narita Nikko Hotel. Now I'm travelling with my elderly Mom and do not want complications at Narita immigration or later in the day while going from Narita Airport to Haneda airport. Please advise. Before upgrading to 14.04 when I clicked on a file in the dash, it opened the file.   This still happens on my 12.04 machine.  In 14.04 when I click on a file in dash search results, it offers me 3 options: 'Email', 'Open' and 'Show in Folder'.  How can I get back the previous behaviour - i.e. to immediately open the files on the first click?