Let $\exists \lim\limits_{x \to \infty} f_n(x)$ and $\exists \lim\limits_{x \to \infty}f (x)$. $f_n, f : \mathbb{R} \to \mathbb{R}$ (Here $f_n$ is uniformly converge to $f$ on $\mathbb{R}$ ) Then, Does the statement &quot;$\lim\limits_{x \to \infty} \lim\limits_{n \to \infty} f_n(x)  = \lim\limits_{n \to \infty} \lim\limits_{x \to \infty}  f_n(x)$ (I.e $\lim\limits_{x \to \infty} f(x) = \lim\limits_{n  \to  \infty}\lim\limits_{x \to \infty}  f_n(x)$  )&quot; hold? Most of the problems I've ever seen the limit to finite real value not the infinity, So I can't figure out it hold.  But just my guess, though it looks like a true. If it is correct, how could I prove it? (Are there any counter example of that?)
$\lim_{x \rightarrow \infty} \lim_{n \rightarrow \infty} f_{n}(x) = \lim_{n \rightarrow \infty}\lim_{x \rightarrow \infty}f_{n}(x) $ in case of uniform convergence of $f_{n}(x)$ to $f(x)$  I used this while I was given that $f_{n}(x)$ converges to $f(x)$ uniformly. Is this correct and I was also thinking to prove this!
Is there a CSS parent selector? How to hide title bar in Firefox 57 Quantum? I used to use an extension to hide/show the title bar in Firefox, but since Firefox 57 was released most of the extensions were disabled.  In Chrome I just uncheck the option "Use system title bar and borders" and it's done.  Are there any ways to do that? Jquery validation not working with ckeditor Servlet returns "HTTP Status 404 The requested resource (/servlet) is not available" What is purpose of /etc/shadow and shadow cache files in Linux operating system? What is the purpose of the /etc/shadow file in Linux Operating system?  Also, is it same for SUSE clients? There is one shadow cache file is maintained what is purpose of that? I am currently working on a project to create a (not prepaid) postage label.  In java, I would go about doing this by creating a bufferedimage and adding various other images to it to create what I want.  What I want is to put text, converted to an image, onto a template letter, to make a proper postage label.    For example, imagine I was given a document with blank spaces such as:  "Name: _________"  This document is in the form of an image, and I want to use apex and visualforce (the page is already constructed, I am just stuck at the image manipulation part) to add whatever name the user types in onto the image and pack it and email the new image.  The question I have here is: where do I even start?  Java is a little nicer when it comes to image manipulation, as far as I can see.  I've looked into using a web service and sending a soapxml request to return a proper encoded image, but I haven't found a web service that can do this.  Any pointers would be nice. Thanks. How to adopt SD card as internal storage on Samsung devices? I'm making a Java application with an application-logic-thread and a database-access-thread. Both of them persist for the entire lifetime of the application and both need to be running at the same time (one talks to the server, one talks to the user; when the app is fully started, I need both of them to work).  However, on startup, I need to make sure that initially the app thread waits until the db thread is ready (currently determined by polling a custom method dbthread.isReady()). I wouldn't mind if app thread blocks until the db thread was ready.  Thread.join() doesn't look like a solution - the db thread only exits at app shutdown.  while (!dbthread.isReady()) {} kind of works, but the empty loop consumes a lot of processor cycles.  Any other ideas? Thanks. Compare Debian (left) and Ubuntu (right):  $ ifconfig                                 $ ifconfig bash: ifconfig: command not found          eth0     Link encap ... $ which ifconfig                           $ which ifconfig $                                          /sbin/ifconfig   Then as superuser:  # ifconfig                                 # ifconfig eth0      Link encap ...                   eth0     Link encap ... # which ifconfig                           # which ifconfig /sbin/ifconfig                             /sbin/ifconfig   Furthermore:  # ls -l /sbin/ifconfig                     # ls -l /sbin/ifconfig -rwxr-xr-x 1 root root 68360 ...           -rwxr-xr-x 1 root root 68040 ...   It seems to me the only reason I cannot run ifconfig without superpowers on Debian is that it's not in my path. When I use /sbin/ifconfig it does work.   Is there any reason I should not add /usr/local/sbin:/usr/sbin:/sbin to my path on Debian? This is a personal computer, I am the only human user.    Versions used (uname -a): Ubuntu:   Linux ubuntu 3.13.0-51-generic #84-Ubuntu SMP Wed Apr 15 12:08:34 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux   Debian:  Linux debian 3.16.0-4-amd64 #1 SMP Debian 3.16.7-ckt11-1+deb8u3 (2015-08-04) x86_64 GNU/Linux ref to subsection number only I know that it is defined such that there is no more than one y-value output for any given x-value input, but I"m wondering WHY it is defined that way? Why can't we apply everything we know about functions to equations that have more than one y-value output for any given x-value input?   In short, what is the benefit or reason to define a function this way?  At the same time, a little historical context would also be appreciated (i.e., when the concept originated and why).  Thanks,  Moshe This question is asked often in Ask Ubuntu, sometimes with few hints about the situation.   Please provide a list of possible reasons to help troubleshoot the problem. I asked this question  but I haven't gotten a useful answer. Could you tell me the difference in meaning between these sentences?        Do you think you will visit them next week?     Will you visit them next week?     Are you going to visit them next week?     Are you visiting them next week?     Are you going to be visiting them next week?     Are you planning to be visiting them next week?     Do you plan to visit them next week?      Will there be any difference in the answers?        I think I will visit them next week.     I will visit them next week.     I am going to visit them next week.     I am visiting them next week.     I am going to be visiting them next week.     I am planning to be visiting them next week.     I plan to visit them next week.      Can I use "planning to" instead of "going to"?  (E.g. "Are you planning to visit them next week? — Yes, I am planning to visit them next week.") Which of these sentences show that the subject of conversation has already been discussed? For example, I talked with a friend of mine about my plans to visit somebody. So my friend is aware of my plans.  And my last question. Which of these seven sentences express that the action will certainly take place? I have a string which is like this:  this is "a test"   I'm trying to write something in Python to split it up by space while ignoring spaces within quotes. The result I'm looking for is:  ['this','is','a test']   PS. I know you are going to ask "what happens if there are quotes within the quotes, well, in my application, that will never happen. If a series converges, then the sequence of terms converges to $0$. With the last update of Fallout Shelter, Bethesda has added these "limited time" quests.  Question is, how limited is that time exactly? What happens when the quests "end", will it still be possible to get the benefits? How can I make hibernate my desktop in UEFI with Secure boot on.  I used command "sudo pm-hibernate" to make hibernate my desktop but my machine did nothing (my desktop is booted up on UEFI with Secure boot on). But, if I boot my desktop on UEFI with Secure boot off, Hibernation is normal.  Sorry for my English, thanks, "I left smoking", "I quit smoking", "I gave up smoking", "I stopped smoking" are these same? For various such sentences in many cases I get confused, it seems different for different cases. I want to know if someone left doing something for permanantly then what should be used? Also give some examples for different cases. Suppose... "I left my bag" means "I forgot my bag". but If I want to say the same for permanentaly "I left bringing my bag". Where should we use "stop" and "quit" then? How can I use std::maps with user-defined types as key? Can we have a black hole without a singularity? Assuming we have a sufficiently small and massive object such that it's escape velocity is greater than the speed of light, isn't this a black hole? It has an event horizon that light cannot escape, time freezes at this event horizon, etc. However this object is not a singularity.  If a large star's mass were compressed to the size of, say, a proton, it would certainly have these properties but it would still not be a singularity as a proton does have volume.  The reason "physics breaks down" at singularities is because we cannot divide by zero, but as long as the proton-sized object has volume, physics won't "break down", yet we still have an event horizon and an object that is invisible (but not undetectable) from the outside.  I have read the answers to  related question. I'm not sure if they don't address my specific question or if I don't understand the answers.