Given a sequence of functions $(f_n)$, with $f_n : [a, b] → \mathbb{R}$ we say that it is uniformly Lipschitz if there exists $K &gt; 0$ such that for every $n$ and every $x, y ∈ [a, b]$ we have  $|f_n(x) − f_n(y)| ≤ K|x − y|$  Prove that if $f_n → f$ and (f_n) is uniformly Lipschitz then $f$ is Lipschitz (i.e. there exists $M &gt; 0$ such that for every $x, y ∈ [a, b]$ we have $|f(x) − f(y)| ≤ M|x − y|)$.  I have tried the triangle inequality, as in adding $|f_n(x) − f(x)|$, $|f(y) − f_n(y)|$, $|f(x) − f(y)|$ is greater than $|f_n(x) − f_n(y)|$, does this help?
Given $f_{n} : [a,b]\rightarrow \mathbb R$ is uniformly Lipschitz and $f_{n}\rightarrow f$, how can I show that $f$ is Lipschitz?  $f_{n}$ is uniformly Lipschitz $\leftrightarrow \exists K &gt; 0$ such that for all $n$ and for every $x,y\in [a,b]$ we have $|f_{n}(x)-f_{n}(y)| &lt; K|x-y|$.  $f_{n}\rightarrow f \leftrightarrow \forall~\epsilon&gt;0~~\exists~N$ such that $\forall~n&gt;N$ we have $\mid f_{n}(x) - f(x)\mid&lt;\epsilon~~~(=\mid x-y\mid?)$  Then we have  \begin{align} |f(x)-f(y)| &amp;\leq |f(x)- f_{n}(x)| + |f_{n}(y)-f(y)| + |f_{n}(x)-f_{n}(y)| \\ &amp;\leq |x-y| + |x-y| + K|x-y| \\ &amp;\leq (K + 2) |x - y| \end{align}  which shows that $f$ is Lipschitz. Can anybody tell me if this makes sense? Sorry if layout is poor.
Show badges in user profile in iOS app When viewing a user's profile from the iOS app, it would be nice to be able to see what badges they have, instead of just the counts. Mouse acceleration seems to be on by default, and I can't find anywhere in the launcher settings or the in game settings to turn it off.  It's very annoying as it makes it feel as if the mouse is lagging. Is there any way to turn it off? I want to filter a java.util.Collection based on a predicate. A couple of months ago, I suggested a set of badges for . The responses were... mixed. The  can be summarized:  In practice, all this would do is encourage people to ask yet more stupid, worthless questions and we have quite enough of that as it is.  We believe that one of the main things holding back many of our beta sites is that when people have questions they aren't in the habit of asking on the site. Even our flagship site, Stack Overflow, doesn't get many questions from its most knowledgeable users. Perhaps they don't have questions, but far more likely they find answers without needing to ask. Our subtle bias against asking (questions =&gt; clueless) means we lose out on what might be our best source of excellent questions. So we went back to the drawing board and designed a badge set that should not encourage worthless questions:  Asked a well-received question on X separate days, and maintained a positive question record.  In order to award badges, we need to define our terms:  positive question record   (total questions - negative questions - closed - deleted)/total questions &gt;= 0.5  It triple counts a question that is downvoted, closed, and deleted. If you ask one that hits that trifecta, you'll need to ask three better questions to dig yourself out. My own record of asking does not meet the criteria:   (44 - 0 - 12 - 12)/44 = 0.4545...  My  looks a lot better; I had a bunch of questions from the beta period that have been subsequently (and rightfully) deleted. With care, I could bring my record into positive territory with 4 questions. The takeaway is that people can't sweep past indiscretions under the rug by deleting them. And they can recover from a bad start as long as they don't ask more bad questions.  well-received question on X separate days A well-received question is one that's open, not deleted, and has a score &gt; 0. If you ask at least one well-received question in a  and none of your questions that day are deleted, downvoted, or closed, you get one more day of credit toward the badge. Whenever the badge criteria is checked, previous asking days are re-evaluated so that there's an incentive to fix downvoted and/or closed questions. The no-deleted-questions criteria is to prevent people from asking several questions at once and deleting any that aren't upvoted or answered to ask another day. (Though this is a losing strategy in the long run.)   My proposed badge names and levels:  Asked a well-received question on 5 separate days, and maintained a positive question record.  Asked a well-received question on 30 separate days, and maintained a positive question record.  Asked a well-received question on 100 separate days, and maintained a positive question record. In addition, since some outstanding individuals ask on more than 100 days, the gold badge may be awarded multiple times. Over on English, Oishi-sama (now a ) would have a remarkable . Bronze and silver badges are only awarded once. We've decided to hold off on multiple awards for now. See the . Neither the names nor the levels nor even the descriptions are set in stone. Please play around with  to get an idea of how the badge works using our public data. Since the query does not account for deleted questions, it's a bit more generous than the actual badges would be. This version of the badge set should encourage a habit of well-received questions over time and encourage people to fix poorly received questions.  I'd like to express my gratitude to the Parenting community for participating in our . In Terraria, is there an order in NPC appearance in addition to the minimum requirements for each one? I noticed a strange thing about Demolitionist that I do not see mentioned on .  Practically on my world I created immediately a good number of houses with  needed to accommodate an NPC.  The first NPC that arrived was the Nurse. Then I found many bombs but Demolitionist never came. He arrived just immediately  Merchant came, when I finally got the 50 silver coin needed for him.  Is this behavior correct? Is there and order in NPC appearance in addition to the minimum requirements for each one? C++ display stack trace on exception So why did the price tank all of a sudden and then came back to normal? What does it mean? Labelled in-line equation I am rebuilding an old server.  Only one of the five old sites need to go live and all five of the old sites point to the same IP address.  Unfortunately any time a request is made for one of the old sites via their own unique domain names they are passed the pages from the one site that I'm trying to make live.  I would just like the old sites to display a 404 instead of the one site that I'm actually trying to make live.  As an example:   Site 1 (192.168.0.1) [www.first.com] Site 2 (192.168.0.1) [www.second.com] Site 3 (192.168.0.1) [www.third.com]   I want to move site 1 live again.  So I turned on apache on the machine with the IP address of 192.168.0.1, with all of site 1's files in the /var/www directory.  When I browse to 192.168.0.1 or www.first.com I correctly see site 1. When I browse to www.second.com and www.third.com I also receive site 1 which is the problem.  Is there a way I can 404 any request which comes in without www.first.com?  Here is my sites-available:  NameVirtualHost *:80  LogFormat "%h %l %u %t \"%r\" %&gt;s %b" common  &lt;Files ~ "^\.ht"&gt;     Order allow,deny     Deny from all     Satisfy All &lt;/Files&gt;  &lt;Directory /&gt;   Order Deny,Allow   Deny from all   Options None   AllowOverride None   Options None &lt;/Directory&gt;  &lt;Directory /var/www&gt;   Order Allow,Deny   Allow from all &lt;/Directory&gt;  &lt;VirtualHost *:80&gt;         ServerName first.com         ServerAlias www.first.com         DocumentRoot /var/www         ErrorLog /var/log/first.com.err         CustomLog /var/log/first.com.log common &lt;/VirtualHost&gt;  &lt;VirtualHost _default_:*&gt;         ServerName unknown         DocumentRoot /var/www_404 &lt;/VirtualHost&gt; I'm looking for an algorithm that sorts strings similar to the way files (and folders) are sorted in Windows Explorer. It seems that numeric values in strings are taken into account when sorted which results in something like  name 1, name 2, name 10   instead of  name 1, name 10, name 2   which you get with a regular string comparison.  I was about to start writing this myself but wanted to check if anyone had done this before and was willing to share some code or insights. The way I would approach this would be to add leading zeros to the numeric values in the name before comparing them. This would result in something like  name 00001, name 00010, name 00002   which when sorted with a regular string sort would give me the correct result.  Any ideas? What are the practical implications of a name change for international travel and activities abroad? I am considering a name change, which seems to be a relatively straightforward action, when one remains in the same country: certain documents are replaced with new ones bearing the new name, and others are presented together with the name change document.  However, I travel internationally multiple times per year, and I often change temporary residence from one country to another. So I often deal with immigration and similar things. Furthermore, I have a lot of things going on like work and studies.  Quite obviously, if I change my name, I would often have to produce a proper translation of the name change document, which may include notarized translation thereof with apostille or, for example, traduction assermentée in France.  However, it would be great to hear about experiences of people, who have dealt with this issue first-hand, so I can weight the disadvantages against advantages of this correctly. In particular, I would like to know if anyone has encountered unforeseen difficulties with this, and how people rate the overall difficulty of such experiences. Control custom properties How can I add remove and create a callback/event for a custom property using bpy. I have a scene, called scene, and I want to add a custom property named x, defulat value 2 (as intereger), and a callback foo, to run when it is changed. I also need to be able to read the value from it, and delete it. How do I do this? How do I execute a string containing Python code in Python? In the previous version the logout button is under your username, which it can be found by clicking the down arrow. However, in the new version, after a couple minutes of searching, it is under the "site-switcher" button:        This is really illogical since the logout button is usually under your username, including Google and Yahoo! services.  I suggest bringing back the  which will definitely benefit new users and even old users. No notification (+15) for accepted answer Yesterday my answer was accepted, but I got no notification in top bar, moreover, top bar still shows that I earned 45 reps  while reputation tab shows right 60 rep.  Update: July, 11 Again having this problem: In the dropdown:  In the rep tab:  You see, first down votes in the drop down are missing. One of my favorite quotes is by Alvin Toffler which says:     The illiterate of the 21st century will not be those who cannot read   and write, but those who cannot learn, unlearn, and relearn.   The way I understand "relearn" in the quote is to learn something new that is different from what was originally learned.  I'm wondering in general if "relearn" convey learning the same thing again, or a different thing, or it depends on the context of the sentence. Is the same thing true for "learn again"? Options for object creation are greyed out I am trying to model a tree. I turned on the Add a sapling add-on in user preferences, however once I want to begin editing the settings, they come up but is grey and doesn't let me click on it.    I have also attached my blend file here: Why is the "Arnold Schwarzenegger" terminator referred to by two different product numbers (T-101, T-800)? . (See comments to the question: the OP tried to include a couple of long XML files, but that wasn't possible.)  What's the recommended approach to including code/data, when there's just too much of it to embed in the question?  I could think of a few approaches myself:   Paste the data to a pastebin and link (and wait for the links to die) Encode the (compressed) data in an image and include that (kludgy!) Implement an attachment feature in Stack&nbsp;Overflow (which will probably be abused) I would like to either prevent or handle a StackOverflowException that I am getting from a call to the XslCompiledTransform.Transform method within an Xsl Editor I am writing. The problem seems to be that the user can write an Xsl script that is infinitely recursive, and it just blows up on the call to the Transform method.  (That is, the problem is not just the typical programmatic error, which is usually the cause of such an exception.)  Is there a way to detect and/or limit how many recursions are allowed?  Or any other ideas to keep this code from just blowing up on me?