Proving $\| g^{-1}-f^{-1}\|\leq 2\|{f^{-1}}\|^2\|g-f\|$
Continuously invertible operators
How to change the forgotten root password? I forgot my root password...actually I think I know what it is because it is the same password I have for pretty much everything but in the Terminal in tell me "Sorry, try again." Is there a way to reset the password? If so how? Adding word 'Table' before each entry in list of tables I need to prefix each entry in list of tables and figures with appropriate text - table or figure for each. Also I need to remove chapter numbers from list, because tables are numbered consequently through the whole report.  I managed to do everyting I need with this simple commands:  \renewcommand{\thetable}{\arabic{table}} \renewcommand{\thefigure}{\arabic{figure}}  \makeatletter \providecommand\phantomsection{}% for hyperref  \newcommand\listoftablesandfigures{%     \chapter*{List of Tables and Figures}%     \phantomsection %\addcontentsline{toc}{chapter}{List of Illustrations}% %\section*{Figures}% %\phantomsection %\addcontentsline{toc}{section}{\protect\numberline{}Figures}% \@starttoc{lof}% \bigskip %\section*{Tables}% %\phantomsection %\addcontentsline{toc}{section}{\protect\numberline{}Tables}% \@starttoc{lot}} \makeatother   Now only one thing remains: to be consistent with text in list of tables and figures. What is it called when a non-verb is used as a verb? This is in very common use on the internet. I just read this:     "[The] hotel employee walks in, I say "uh, puppy" and she just NOPEd the [heck] out of the room."   This is often done by adding 'd to the word. Define a mathematical set Use of "Or", inclusive or exclusive? My wife and I are playing a game where you roll dice and move so many spaces in a grid "vertically or horizontally".   In the use of English it is very common to say, this or the other when it comes to making a choice  (exclusive or). Now I know that "or" can also be inclusive, for example "she couldn't read or write", or can be clearly used as an xor "you either come or not" making the statement true for only one of the options but not both.   My issue is where it is not clear whether it is an inclusive/exclusive or, the best example being our game.   I argue that you can move in either direction (inclusive) and the normal use of this conjunction in English should be inclusive unless specified otherwise.   Is this right? I asked about it on  and they told me to post it here.  Probably need to add the :active to the :hover meta class or something like that.  Example:      Hammer Time How to get multiple selected values of select box in php? Why does US Robotics destroy Lanning's house? Shortly after the death of Dr. Lanning, Detective Spooner travels to the doctor's house to look for clues.  While he is searching the house a demolition bot (which had been programmed to demolish the house the next day) goes on a rampage and destroys the house with Detective Spooner in it.   The house is fully furnished and appears to be in good condition. Why would US Robotics want to destroy the house with everything in it? Why not sell the house and everything inside? How can I change GNOME Shell theme? I've installed the GNOME Shell in Ubuntu 12.04 and I want to change the "Shell Theme", But it doesn't allow me to do that.  The alert says something like: "The GNOME-Shell extension is not activated", and I want to install it with the console, But it returns me an error.  How can I solve this problem? From Wikipedia: Fermi was known for his ability to make good approximate calculations with little or no actual data, hence the name. One example is his estimate of the strength of the atomic bomb detonated at the Trinity test, based on the distance travelled by pieces of paper dropped from his hand during the blast. Fermi's estimate of 10 kilotons of TNT was remarkably close to the now-accepted value of around 20 kilotons, a difference of less than one order of magnitude.  I have not been able to find any references explaining how he made this calculation. Please provide a reference or an example calculation.  See also: I know I use them, and my peers use them, but how much does the average user actually use tooltips to figure out functionality? You require a reputation of 50 to leave comments on others' questions/answers; the FAQ simply states this as a fact but does not explain it. I'm a new user and I have identified this as an issue very quickly through my own experiences so far. Looking at other questions seems to also provide justification against this 50 reputation requirement for comments on others' questions/answers.      In my own experience, I've seen a few questions like "how do I do x?" then the same poster has answered with "in the end I did it like this: ..." where their solution was perfectly sensible, but there may be some gotchas to watch for - in this case I want to vote up their answer and/or comment on it to point out the potential gotchas, but I can do neither!  To me all of the above seems justification against this rep requirement to comment, so what is the counter-argument and justification for it? Does a Rogue using Use Magic Device for a scroll or wand also need to emulate a class feature? I'm confused about Rogues and Use Magic Device. I've searched the core book and the Internet for the past 4 hours and can't find the answer to my simple question.   Since a Rogue doesn't have any spells, a spell list or caster level, do you have to emulate a class feature in addition to all other necessary checks to use items like scrolls and wands? 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. Consider the question :    The large number of down-votes displays as 199 rather than a score of -199.  This is clearly unintentional (and unfortunate for questions that possess such voting!), but can this be&nbsp;corrected? What the matter is vs. what is the matter used in the affirmative I want to know what the matter is with her.  I want to know what's the matter with her. I want to know what's her problem.   Is "I want to know what's the matter with her" and 'what's the matter'  incorrect as Cambridge dictionary suggests (). In their explanation it is suggested that the word 'matter' be replaced with 'problem' as is written in the 3rd example.    Thanks for whatever help you can provide on this.  I've read Rathony's link and agree that his link answered the question about inversion. Now my question is specifically about the correctness of using this wording and if it is correct is there a rule in its usage. I get      every few minutes on Kubuntu (KDE), and the panels disappear.  It restarts itself automatically, so it's not a real problem, just an annoyance, but it is a big annoyance.  I've tried sudo apt install --reinstall plasmashell plasma-desktop, but that made no difference.  When I try a backtrace from the error message, it says it's unable to produce a useful backtrace. How to mount a RAM disk on startup? I'm trying to mount a RAM disk on startup with this:  /Users/Aram/Development/Tools/ramdisk.sh  diskutil erasevolume HFS+ "RamDisk" `hdiutil attach -nomount ram://800000`   com.aram.ramdisk.plist  &lt;?xml version="1.0" encoding="UTF-8"?&gt; &lt;!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN"          "http://www.apple.com/DTDs/PropertyList-1.0.dtd"&gt; &lt;plist version="1.0"&gt;     &lt;dict&gt;         &lt;key&gt;Label&lt;/key&gt;         &lt;string&gt;com.aram.ramdisk&lt;/string&gt;         &lt;key&gt;ProgramArguments&lt;/key&gt;         &lt;array&gt;             &lt;string&gt;/bin/sh&lt;/string&gt;             &lt;string&gt;/Users/Aram/Development/Tools/ramdisk.sh&lt;/string&gt;         &lt;/array&gt;         &lt;key&gt;RunAtLoad&lt;/key&gt;         &lt;true/&gt;     &lt;/dict&gt; &lt;/plist&gt;   And then running:   sudo chown root:wheel /Library/LaunchDaemons/com.aram.ramdisk.plist sudo launchctl load -w /Library/LaunchDaemons/com.aram.ramdisk.plist   But I get these in the console:  1/08/12 1:29:25.982 PM fseventsd[64]: could not open &lt;&lt;/Volumes/RamDisk/.fseventsd/fseventsd-uuid&gt;&gt; (No such file or directory) 1/08/12 1:29:25.982 PM fseventsd[64]: log dir: /Volumes/RamDisk/.fseventsd getting new uuid: 102D7293-F1F1-4640-AA50-D547C365339F  1/08/12 1:29:24.561 PM sudo[1193]:     Aram : TTY=ttys000 ; PWD=/Library/LaunchDaemons ; USER=root ; COMMAND=/bin/launchctl load -w /Library/LaunchDaemons/com.aram.ramdisk.plist  1/08/12 1:40:17.052 PM com.apple.launchd[1]: (com.aram.ramdisk) Throttling respawn: Will start in 8 seconds   It works if I set KeepAlive to true, but then it creates a RAM disk every 10 seconds.  Is there a way to delay the script for 10 seconds before running? Use a concatenated (dynamic) string as JavaScript object key? I'm editing a book that includes about 25 papers written in LaTeX by different authors.  Since many of them use the same \label, to avoid collisions I redefined the \label command (and \ref and \pageref and \cite and \bibitem)  so that if the third paper has  \label{main_theorem} the aux file actually uses the tag "iii:main_theorem", and \ref{main_theorem} actually refers to the same tag.  I did a similar thing for \cite and \bibitem.  %*************** bib/cite hacks \let\TheReal@citex=\@citex \let\TheReal@bibitem=\@bibitem \let\TheReal@lbibitem=\@lbibitem \gdef\@lbibitem[#1]#2{\TheReal@lbibitem[{#1}]{#2\roman{chapter}}} \gdef\@bibitem#1{\TheReal@bibitem{#1\roman{chapter}}} \gdef\@citex[#1]#2{% \toks@={}\count@=0% \@for\@citec:=#2\do{% \advance\count@ 1 \ifnum\count@=1\edef\0{\the\toks@\expandafter\expandafter\noexpand\@citec\roman{chapter}}% \else\edef\0{\the\toks@,\expandafter\expandafter\noexpand\@citec\roman{chapter}} \fi% \toks@=\expandafter{\0}}% \TheReal@citex[#1]{\the\toks@}% } %************** label/ref/pageref hacks  %%%%%%%%%%%%% must be before ams pkgs \let\TheRealLabel=\label \let\TheRealRef=\ref \let\TheRealPageref=\pageref \gdef\label#1{\TheRealLabel{\roman{chapter}:#1}} \gdef\ref#1{\TheRealRef{\roman{chapter}:#1}} \gdef\pageref#1{\TheRealPageref{\roman{chapter}:#1}}   This all worked fine until I used hyperref, which seems to ignore the redefinition of \label, whether I load it before or after the above code.  Any suggestions?  It would be nice if the redefinition would work whether or not hyperref was loaded, so I don't want to just grab the defintion of \label out of the package and tweak it.  I'm also open to alternative methods.  Redefining \label and \ref just seemed the most straightforward (to me) solution.  Note that I also want to be able to refer to the inner labels from outside, as well.  For example, I might want to say "the main theorem of the third paper is  \ChapRef{iii}{main_theorem}  from within the introduction (a different chapter).