Prob. 4, Sec. 1.2 in Kreyszig's Functional Analysis: Example of a sequence converging to $0$ which is not in any $\ell^p$
find a sequence converging to zero but not the element of lp space for every 1<_p<infinity
$4 \sin 72^\circ \sin 36^\circ = \sqrt 5$ How do I establish this and similar values of trigonometric functions?  $$ 4 \sin 72^\circ \sin 36^\circ = \sqrt 5 $$ During the beta of Windows 10 it was hard know what version you were running unless it had it posted to the desktop. Once that wasn't there - how do you tell what version / build you are running?   This will become more of an issue as Microsoft starts releasing more builds with the new update mechanism. How to assign same Data to multiple object copies Extract, convert, store and reuse (x,y) coordinate components Why does Windows 7 ask for additional drivers when installing from a USB 3.0 drive? I am writing a document for which I need the margin to be exactly as follows: left, right, top and bottom text margin all equal to 1in, distance from bottom of the paper to page number equal to 0.75in (I don't have any footnote or header to set).  I tried to use the fullpage package in LaTeX but it does not give me the 0.75in to the page number. Is there a way to force that? I tried to set manually the margins for a 8.5x11 paper but I am not succeeding.    I tried but after writing:  \documentclass[PhD]{class_file} \usepackage[margin=1in,footskip=0.25in]{geometry}   I get the error message \paperwidth (0.0pt) too short.  I don't see the \paperwidth is set to 0.0pt anywhere though..  Also it seems to me that depending on which machine I use to compile my tex file, I get different margins, even when I set them up manually (without using geometry). Is it possible?    Using the geometry package things seem to work a bit better now (I changed machine and the problem with the paper width previously mentioned disappeared).   \usepackage[margin=1in,footskip=0.25in]{geometry}   gives me without problem upper, right and left margin of 1in. But the lower margin is 1.2in and I can't change it to be 1in even by using bottom=1in or bottom=0.8in. I really don't see how this can happen. Maybe a problem with the spacing between lines? The class files I am using can be fund at   I erased the margin settings of uclath12.clo as the margin I need are different from the ones that this file gives. Thank you. Can I cast spells in the middle of another spell resolving? Say I had  and I used  on something, could I respond to Cloudshift bringing the creature back into play with  or something similar? I just came onto a project with a pretty huge code base.   I'm mostly dealing with C++ and a lot of the code they write uses double negation for their boolean logic.    if (!!variable &amp;&amp; (!!api.lookup("some-string"))) {        do_some_stuff();  }                                      I know these guys are intelligent programmers, it's obvious they aren't doing this by accident.   I'm no seasoned C++ expert, my only guess at why they are doing this is that they want to make absolutely positive that the value being evaluated is the actual boolean representation. So they negate it, then negate that again to get it back to its actual boolean value.   Is this correct, or am I missing something? Can I access private members from outside the class without using friends? Disclaimer Yes, I am fully aware that what I am asking about is totally stupid and that anyone who would wish to try such a thing in production code should be fired and/or shot.  I'm mainly looking to see if can be done. Now that that's out of the way, is there any way to access private class members in C++ from outside the class?  For example, is there any way to do this with pointer offsets? (Naive and otherwise non-production-ready techniques welcome) Update As noted in the comments, I asked this question because I wanted to write a blog post on over-encapsulation (and how it affects TDD).  I wanted to see if there was a way to say &quot;using private variables isn't a 100% reliable way to enforce encapsulation, even in C++.&quot;  At the end, I decided to focus more on how to solve the problem rather than why it's a problem, so I didn't feature some of the stuff brought up here as prominently as I had planned, but I still left a link. At any rate, if anyone's interested in how it came out, here it is:   (I suggest reading it before you decide that I'm crazy). Python rounding error with float numbers Intellisense in IntelliJ no longer working Will I lose previous purchases when I change country in iTunes Protected Question does not show Add an Answer button This question is protected. To answer it, I must have at least 10 reputation.        Ignoring the association bonus of 100, I should .  Yet, the Android app does not show the blue "Add an Answer" button at the bottom. The app also does not show the protection status.  If I view the question in the desktop or mobile browser (and I'm signed in), I can add an answer there. Say that Player X is 2nd in the initiative. 1st is the Black Court vampire that is in a rage and taking a swing at Player X. Player X gets a built in defense [Athletics/Fists + 4dF] but can Player X instead use his action this turn to cast his Rote Evocation Shield?  It is not his turn in the initiative order. A Block is an Action that a Player can take on his turn.   Thematically though, it seems to make sense that the char could cast a Rote Evocation Shield in response to an attack ahead of him in the initiative order. At least thematically in the books. Also, the example in YS252, shows him reacting to an attack by Agatha Hagglethorn by bring up his shield.  I am hoping there is some as yet undiscovered dark corner where this concept is covered or squashed. To hyphenate or not? As a non-native speaker of English and an engineer by training, I always get confused about hyphenation and almost always end up referring to Google every time I need to make that decision.  Does anybody know of a concise, comprehensive style guide to hyphenation that explains this rather complex issue, once and for all? Could anyone explain when to use a noun or a gerund?  Are these sentences correct? What is the difference between usage of gerund and noun there?        I worked on the improvement of the article.   I worked on the article improving.   I worked on the improving of the article.                The investment idea was published.   Investing idea was published. Keyword for the outer class from an anonymous inner class In the following snippet:  public class a {     public void otherMethod(){}     public void doStuff(String str, InnerClass b){}     public void method(a){         doStuff("asd",             new InnerClass(){                 public void innerMethod(){                     otherMethod();                 }             }         );     } }   Is there a keyword to refer to the outer class from the inner class?  Basically what I want to do is outer.otherMethod(), or something of the like, but can't seem to find anything. When using sudo powers and calling gedit the top level menu with File Edit View Search Tools Documents Help is missing.  If I create user ID root and sign in once and call gedit will it create the necessary user configuration files that might fix this?  Will this also make the annoying error messages go away whenever I use sudo, gksu or pkexec as a regular user with elevated privileges togedit ?  Will there be other benefits with Nautilus and other Gnome derivative Ubuntu applications?  NOTE: by sudo powers you can google pkexec gedit 3.5k hits, gksu gedit 40k hits or sudo gedit 500k hits. I'm in the minority using the first method but I believe it will become the standard in Ubuntu 17.04.    June 12, 2017 Update Here are a list of errors you get when using pkexec gedit:  (gedit:13003): Gtk-WARNING **: Calling Inhibit failed: GDBus.Error:org.freedesktop.DBus.Error.ServiceUnknown: The name org.gnome.SessionManager was not provided by any .service files  ** (gedit:13003): WARNING **: Set document metadata failed: Setting attribute metadata::gedit-spell-enabled not supported  ** (gedit:13003): WARNING **: Set document metadata failed: Setting attribute metadata::gedit-encoding not supported  ** (gedit:13003): WARNING **: Set document metadata failed: Setting attribute metadata::gedit-position not supported   On this  there is a commitment to fix these distracting messages as of June 5, 2017. No indication is given for when the fix will be upstream nor if the functionality will be implemented or the error messages will simply disappear.  Note the bug report was filed over a year ago and over that time it only effects 18 people. Where are my installed applications? React on global hotkey in a Java program on Windows/Linux/Mac? A Java6 application sits in the system tray. It needs to be activated using a hotkey (e.g. Super-G or Ctrl-Shift-L etc) and do something (e.g. showing an input box).  How do I do that on:   Windows (XP or Vista) OS/X Linux (Gnome or KDE)