$f \in \mathcal l^{\infty}{'} $ ; $f(x)\ge 0$ whenever $x \in \mathcal l^{\infty} $ is a sequence of non-negative terms ; is $f$ bounded?
Any positive linear functional $\phi$ on $\ell^\infty$ is a bounded linear operator and has $\|\phi \| = \phi((1,1,...)) $
Python: pop from empty list Do you recommend using semicolons after every statement in JavaScript? In many situations, JavaScript parsers will insert semicolons for you if you leave them out. My question is, do you leave them out?  If you're unfamiliar with the rules, there's a description of semicolon insertion on the . Here's the key point:     If the first through the nth tokens of a JavaScript program form are grammatically valid but the first through the n+1st tokens are not and there is a line break between the nth tokens and the n+1st tokens, then the parser tries to parse the program again after inserting a virtual semicolon token between the nth and the n+1st tokens.   That description may be incomplete, because it doesn't explain @Dreas's example. Anybody have a link to the complete rules, or see why the example gets a semicolon? (I tried it in JScript.NET.)   is related, but only talks about a specific scenario. Output for Print Is there a way to output for Print. I want to save in a higher DPI than the default 72dpi say 300dpi that's a good quality for printed pieces. I tried downloading an add-on but don't know if I am installing it correctly it isn't showing up but the bar in python is green. I'm using the 2.69 version of Blender. If no such feature exists what size have any of you found best for print quality. Thank you A friend of mine asked me the following question:      Suppose you have a basket in which there is a coin. The coin is marked   with the number one. At noon less one minute, someone takes the coin   number one and put into the basket two coins: the number two and the   number three. At noon less $\frac{1}{2}$ minute, he takes the coin   number two and put into the basket the coins number $4$ and the number   $5$ and so on. At noon less $\frac{1}{k}$ he takes the coin number $k$   and put two other coins.       The question is: How many coins I can find in the basket at noon?   Intuitively the answer is $\infty$ because I added one coin for infinite times. But the correct answer seems to be $0$ because every coin numbered $k$ has been removed at noon less $\frac{1}{k}$ of minute. What is the correct answer? Thanks. I'm setting up an Nginx web server and and want to perform load balancing using the round robin method.  This is what I have found thus far:  upstream backend  {    server backend1.example.com;    server backend2.example.com;    server backend3.example.com; }   According to the page they says i need to add the above lines to my nginx.conf file and upload it to server to load balance.  I do not understand what it means by server backend3.example.com;.  How do I setup a backend instance? How often should I remove the charger from my rMBP? I want my battery to remain healthy. I used to charge it full then remove the charger after it's done, then put it back on when it goes down to 10% .. However this is becoming hectic and I was wondering if I can keep it plugged in the whole day and probably remove just an hour or so before going to sleep.  What is the best way to charge and discharge my Retina Macbook Pro while keeping the battery healthy ? Getting error using JMeter behind a proxy I am new to JMeter and trying to run a test from behind a corporate proxy. I read on the same from apache site and followed the same process so as to run the test. However, i am still  unable to record a test from behind the proxy.      This message always appears after pressing on 'Start' recording:     After that, I have changed apache port to 8000 as in below and made it different      This time after pressing on start was this message NRPE unable to read output, but why? Hubble's law says that the universe is expanding. How come the Milky Way and the Andromeda galaxies are on a collision course? How will they end up colliding with each other? Exclude bounties from affecting privileges "All our X" vs. "all of our X" Is the word "of" optional in this instance? Is either of these considered preferable to the other?        Taste all our delicious treats.   Taste all of our delicious treats. How to bypass "Verify your account" (Factory Reset Protection) I won a Samsung Galaxy S6 Edge, signed into it with my Google account, played around with it, wiped it, and sold it.  Now the person can't get past setup because it's saying he must login with an account previously synced to the phone.   Is there anything I can do from my side to remove this lock? Can't format / delete locked partition from GParted? How can I render an object with an hdr background? I have an object with an hdr for the background. What do I do in Cycles to render the background with my object?  How is this different from an ordinary render in Cycles?  The hdr is a big one, 350MB. After reading , the most popular answer use the identity $$\sum_{t=0}^n \binom{t}{k} = \binom{n+1}{k+1}.$$  What's the name of this identity? Is it the identity of the  modified.  How can we prove it? I tried by induction, but without success. Can we also prove it algebraically?  Thanks for your help.    EDIT 01 : This identity is known as the  because, on Pascal's triangle, when the addends represented in the summation and the sum itself are highlighted, a hockey-stick shape is revealed. Please add TeX rendering on the Android app MathJax isn't currently working on the Android app, which makes it totally useless for the 'technical' sites like  or .  For example, in the Android app:    Same post in a (mobile) browser:     Please add this functionality! What it's the best way to generate a string of \t's in C#  I am learning C# and experimenting with different ways of saying the same thing.    Tabs(uint t) is a function that returns a string with t amount of \t's  For example Tabs(3) returns "\t\t\t"  Which of these three ways of implementing Tabs(uint numTabs) is best?  Of course that depends on what "best" means.     The LINQ version is only two lines, which is nice.  But are the calls to Repeat and Aggregate unnecessarily time/resource consuming? The StringBuilder version is very clear but is the StringBuilder class somehow slower? The string version is basic, which means it is easy to understand.   Does it not matter at all?  Are they all equal?   These are all questions to help me get a better feel for C#.     private string Tabs(uint numTabs) {     IEnumerable&lt;string&gt; tabs = Enumerable.Repeat("\t", (int) numTabs);     return (numTabs &gt; 0) ? tabs.Aggregate((sum, next) =&gt; sum + next) : "";  }    private string Tabs(uint numTabs) {     StringBuilder sb = new StringBuilder();     for (uint i = 0; i &lt; numTabs; i++)         sb.Append("\t");      return sb.ToString(); }    private string Tabs(uint numTabs) {     string output = "";     for (uint i = 0; i &lt; numTabs; i++)     {         output += '\t';     }     return output;  } ModelBuilder not adding output feature class to Table of Contents? I'm trying to create a tool in ModelBuilder that will take a new point from a user, create a feature class for this point and display it on a map.  What I've done is:   I've created a feature class for a point-like feature in ArcCatalog. I've prepared a really simple model in ModelBuilder, that starts with a feature set variable (which takes the feature class as a schema and symbology file). The variable is marked as a parameter. Next I'm using the Copy Features tool that takes the variable as input and saves it as a feature class in my scratch workspace. The output feature class is marked as a parameter with the 'add to display' option.   After the module is run I get a shapefile in my scratch workspace. I can add it manually to TOC and it contains the selected point. However no matter what I do, I can't display it in TOC automatically after the model completes.  There is a known issue described in several places that doesn't allow to display newly created layers in TOC when model finishes with the 'add to display' option. However there's a quick workaround, which is to mark the output layer as parameter. In my case it doesn't work.  I'm using ArcGIS for Desktop 10.1 on Windows 7 x86_64. "I had my house [be] burned down" I have found out that using the verb be in passive constructions such as:      I had my house be burned down    is incorrect, therefore it should be      I had my house burned down.    But is it possible instead of be to use get? E.g.      The wire is passed through the pliers in a specific way to avoid having it get bent.   The rope had its surface wear.   The rope had its surface get worn.   The rope had its surface worn.   The first two sound very odd to me, but just for clarification could you please point out the errors and which ones are correct? Or is using get, be it in -ing or the to infinitive, in any situation along with have incorrect? Why is the gap between the translation and the last line of the gloss so wide in my interlinear gloss? I notice if I take away some letters, the translation line goes to where it should be, but this big block of white space is pretty untenable. Ideas?    \documentclass[11pt,a4paper]{book}  \setcounter{secnumdepth}{4} \usepackage{gb4e} \usepackage{tipa} \usepackage{setspace} \usepackage[T1]{fontenc} \begin{document} \begin{exe} \ex \glll Jichax    Qamaqix lij parki,  aynacha,    amsta,  parki, q'awanaks,   khuyt'asis  sarawjchix. \\ \{jicha-x(a)    Qamaqi-x(a) lij(u)  parki   aynacha amsta   parki q'awa-nak(a)-_{c}$\oslash$-s(a)   khuy(u)-t'a-s(i)-s(a)   sara-wj(a)-ch(i)-i-x(a)\}    \\ now-\textsc{top}    Fox-\textsc{top}    all acclivity   declivity   ascent  acclivity ravine-\textsc{pl-acc-ad} whistle-\textsc{m}-\textsc{refl}-\textsc{subr} go-\textsc{bfr-cnj-3sim-top}\\ \glt `And so, Fox must've gone whistling on all the ascents, slopes, ascents, mountainsides, and even in the ravines.' \end{exe} \end{document}