Login issue in 16.04
I forgot my username, how do I get it back?
If a ring element is right-invertible, but not left-invertible, then it has infinitely many right-inverses. var/cache/apt/archives occupying huge space I am in the process of cleaning up my system. And I see a lot of space occupied by this folder /var/cache/apt/archives (1.5GB). Is it absolutely necessary to keep all these archives? Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$ Show that  $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$  This is an exercise I was trying to do ( not homework ) and I got stuck as follows:  Working from $A \setminus ( B \setminus C )$:  $x \in A \wedge x \notin ( B \setminus C )$ $x \in A \wedge ((x \in B \wedge x \in C) \vee (x \notin B \wedge x \in C) \vee (x \notin B \wedge x \notin C) )$  At this point I'm not sure how to proceed.  Working from the other side $ ( A \setminus B) \cup ( A \cap C ) $:  $ x \in ( A \setminus B) \cup ( A \cap C ) $  $ x \in ( A \setminus B) \vee x \in ( A \cap C ) $  $ ( x \in A \wedge x \notin B ) \vee ( x \in A \wedge x \notin C ) $  $ x \in A \wedge (x \notin B \vee x \notin C ) $  $ x \in A \wedge x \notin ( B \cap C ) $  $ A \setminus ( B \cap C ) $  I could also use some formating tips like how display logical not and how to get the lines to display properly without blank lines inbetween. :-) Proof by induction that if $n \in \mathbb N$ then it can be written as sum of different Fibonacci numbers Proof that every natural number $n\in \mathbb N$, can be written as the sum of different Fibonacci numbers between $F_2,F_3,\ldots,F_k,\ldots$.  For example: $32 = 21 + 8+3 = F_8+F_6+F_4$  Research effort:  The base step it's simple:  Let $k=1$ it can be britten as $k=1=F_2$  For the inductive step I considered:  Let $k = k  F_2 =F_2+F_2+\cdots+F_2 = \sum_{i=2}^w a_iF_i, a_i =\{0,1\} $  Then if $k$ suffice I want to see if $k+1$ suffices too... But I'm not realy seeing how to use the inductive hypothesis, so I assume It's wrong.  Any thoughts on which can the inductive step be? Finding the confidence level and number of successes? Given that the sample size is $1500$ and the confidence interval of $p$ is $(0.050, 0.083)$. Find the confidence level and the number of successes.  I have so far that $E=Z_{1-\alpha/2}∗\sqrt{(p∗({p-1}))/n}$   Where $p$ is the center of the given interval, so $p = (0.050+0.083)/2 = 0.0665$  Also, the error $E$ as the difference of the midpoint and the endpoint of the interval so $E=0.0665-0.050=0.0165$   Plugging this into the equation I got that  $0.0165=Z_{1-\alpha/2}*\sqrt{((0.0665)(1-0.0665))/1500}$   Solving for $Z_{1-\alpha/2}$ gives $Z_{1-\alpha/2}=2.56$ and since $Z_{2.96} = 0.99$   $Z_{1-\alpha/2} = 0.01$  Is what I have so far right? If so, how do I find the number of successes? Is it just to multiply 0.99 by the number of trials?   So that way I would get $1500*0.99=1485$ ? Person, Persons, People, Peoples Can you please clarify the relation and differences between these nouns?   For example, is it proper to use "persons" instead of "people"? Are they the same? As I believe that "people" is plural, how come there exists the plural of the plural (=peoples)? Does it have any usage? I have an Ubuntu 12.04 machine on which I have installed VirtualBox with Ubuntu 12.04 as the guest OS.  How can I share files between the host and guest?   I have installed the guest additions also but still it’s not able to mount the sf_shared folders if even it’s mounted. This means I'm unable to retrieve the file from the host. For the Fibonacci numbers, show for all $n$: $F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$ What is the best way to find out a researcher's current affiliation? Let's say I know a name and a field, but not much more.   A google search seems like the most obvious approach, but unfortunately university personnel or research group pages often seem to be quite poorly maintained, and it is not uncommon that someone is listed even if they left more than a year ago.  Early-career researchers are particularly difficult to track down since they often have less of a "presence" on institution webpages and are likely to be moving relatively frequently. 'pyrcc4' is not recognized as an internal or external command? C:\Users\Department\.qgis2\python\plugins\np&gt;pyrcc4 -py2 resources.qrc -o resources.py      'pyrcc4' is not recognized as an internal or external command,      operable program or batch file.   How do I solve this problem? How can I discover any USB storage devices and/or CD/DVD writers available at a given time (using C# .Net2.0).  I would like to present users with a choice of devices onto which a file can be stored for physically removal - i.e. not the hard drive. Problem with \mkbibdateapalongextra of biblatex-apa biblatex-apa gives me this:  ! Undefined control sequence. &lt;argument&gt; \mkbibdateapalongextra                                {labelyear}{labelmonth}{labelday}\iffieldu...   I'm using the default (english) language, and have done the:  \DeclareLanguageMapping{norsk}{norsk-apa} \DeclareLanguageMapping{english}{american-apa}   thing.   Here's a short example:  \documentclass[english]{memoir} \usepackage{babel} \usepackage{roffe} \usepackage[backend=biber,date=short,maxcitenames=2,style=apa]{biblatex}  \DeclareLanguageMapping{norsk}{norsk-apa} \DeclareLanguageMapping{english}{american-apa} \addbibresource{Papers2.bib} \addbibresource{R.bib}  \begin{document} \cite{R-base}  \printbibliography \end{document}   This one replicates the problem. How do I re-position the displayed image on my laptop? I want to re-position the display on my ASUS K53SM laptop's screen because I somehow managed to damage some portion of it (and I don't want to spend on this laptop for the time being).  Please refer the following image:    I changed the resolution from 1366x768 to 1280*768 to avoid the bad portion of the screen, but the screen is now centered and the right portion of my screen is now rendered useless.  What I want to do is, set a custom resolution of my laptop and re-position it in a way that is utilizes all the working area of my screen.  How do I re-position the displayed image on my laptop? Imagine I have tons of RAM. Let's say 64GB. That's a lot for even gaming PCs. Now the default location of a pagefile in Windows is on the main OS drive, be it HDD or SSD, which are faster in general, but still not as fast as RAM.  Something tells me that disabling the pagefile on the hard drive or creating a virtual RAM drive and letting the pagefile be there could make Windows move all its virtual memory to RAM, and so increase the system's performance, but I'm not very knowledgeable in that area, so that might not be true at all.  I tried both, but I couldn't analyze the results to reach a definite conclusion with my knowledge level in memory things.  Would this work? If not, why? I want to have a page-filling and -breaking longtable, so I decided to try xltabular. Unfortunately xltabular seems to screw up the booktabs rules in the normal tabular environments, see:  \documentclass{article} \usepackage{booktabs, xltabular} \usepackage[active,tightpage]{preview} \PreviewEnvironment{tabular} \begin{document} \begin{tabular}{ccc}     \toprule     col1 &amp; col2 &amp; col3 \\     \midrule     row 2: &amp; more and moooooooooooore &amp; test \\     \bottomrule \end{tabular} \end{document}     Not loading xltabular resolves the issue.  Did I miss some package option or some incompatibilities? Is there a better package than xltabular which doesn't break booktabs?  (I am using TeXLive 2019 and compile with lualatex)    EDIT (by Skillmon)  I reduced the bug to the following MWE (which doesn't make much sense on its own), it looks like booktabs tries to be smart detecting something, but fails badly.  \documentclass{article} \usepackage{longtable} \let\xltabular\relax \usepackage{booktabs}  \begin{document} \begin{tabular}{ccc}     \toprule     col1 &amp; col2 &amp; col3 \\     \midrule     row 2: &amp; more and moooooooooooore &amp; test \\     \bottomrule \end{tabular} \end{document}   It seems to suffice that longtable is loaded and \xltabular is defined (even if it's just \relax). How to number and cross-reference \subsubsection-level headers How to run test methods in specific order in JUnit4? Is it possible to have several different views of one scene and set them as named "presets"? What is the proof that the universal constants ($G$, $\hbar$, $\ldots$) are really constant in time and space? Why doesn't "cd" work in a shell script? I just want to write a script which changes my directory.  I put the below commands in the file /home/alex/pathABC  #!/bin/sh cd /home/alex/Documents/A/B/C echo HelloWorld   I did   chmod +x pathABC   In the Terminal, while in /home/alex, I ran ./pathABC, but the output is just HelloWorld and the current directory is not changed.  So what is wrong?