Your room is clearer than mine AND your room is more clear than mine  Comparatives like these are many used in the same fashion such as neater/ more neat-- cleaner/ more clean etc. Having been into English grammar, I find myself bemused to figure their differences, thereby left wondering if anybody could help me comprehend their contextual connotation, Thanks in advance
My mom and I are having a dispute on much more easy versus much easier. For example, consider the sentence:     It's [much more easy]/[much easier] to do action X than action Y.   I say that much easier is correct and that much more easy is grammatically incorrect, while she says that both are okay. I understand that both are acceptable colloquially, but which is grammatically correct here? If you could explain why, that would be even better!
Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer. Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.   I'm not familiar to factorial and I don't have much idea, can someone show me how to prove this? Thank you. Which of the following is most correct?      The distance of the shortest path must not be higher than 10km.   The distance of the shortest path must not be greater than 10km.   The distance of the shortest path must not be bigger than 10km.   Or is there an even better word? Adding newmode with Xrandr - "800x480_60.00" I have 5-inch a 800x480 tft connected to the LVDS connector on a Portwell WADE-8020 mini-ITX embedded system board. I would like to build a XMBC/Kodi box for streming my music from my freenas PC with the tft showing what is been played, I got as fare as this...   sudo xrandr --newmode "800x480_60.00"  29.50  800 824 896 992  480 483 493 500 -hsync +vsync`enter code here   then,  sudo xrandr --addmode LVDS1 800x480_60.00   now that I get the correct resolution, I now have a black band on the top of the screen.  sudo xrandr --output LVDS1 --set "scaling mode"  "Full aspect"   However this did not solve the issue, also I know I need to amend the /bin/sh file with this from googling so I don't need to keep doing this at every boot. But I don't know how to as I'm very new to Linux.  #!/bin/sh xrandr --newmode "800x480_60.00"  29.50  800 824 896 992  480 483 493 500 -hsync +vsync xrandr --addmode LVDS1 800x480_60.00 How should I type author names in a bib file? Can someone please explain in a clear and concise way how am I supposed to enter the names of authors in a BibTeX file? I have entries with something like   @article{someid,    author = {Juan A. Navarro P\'erez, Ra\'ul de la Garza and Andr\'es Espinoza},    ...   but somehow the output seems kind of wrong! Footnotes layout in multicols environment I am using the package multicol to typeset a one-column (spanning the entire text width) heading and a two-column main text block. In order to do so, I begin the multicols environment along with the start of the text block. The one-column heading spans a small fraction of the text height in the front page and I need to set a footnote there, before starting the two-column environment. I'd like to have that footnote typeset under the first column in the two-column running text. How could I possibly do this?   Moreover, I'd like to have the footnotes typeset in a single column under one of the text columns -- I don't even mind having them as two-column footnotes, but what I do not want is a footnotes layout spanning the entire text width. I have tried with the command \twocolumnfootnotes from the class memoir, with the packages ledmac, dblfnote, and even with ftnright (the latter complains about its being used in a single-column document, due to that one-column heading). None has proved useful in this setting. As a less than MWE, just to convey a more concrete depiction of my scenario, let us consider:  \documentclass{memoir}  \usepackage{multicol}  \begin{document}  A single-column heading\footnote{Here I have my footnote.}  \begin{multicols}{2} Here I am in the two-column environment, and I want my footnotes being set in accordance with the document's ``columnwidth''.\footnote{A footnote in the two-column environment.} \end{multicols}   \end{document} Left inverse implies right inverse in a finite ring Let $R$ be a finite ring with identity $1$, and assume $\exists x,y\in R$ such that $ xy=1$. How can I show it implies $yx=1$? Effective way to find any file's Encoding I understand that they force you to implement methods and such but what I cant understand is why you would want to use them. Can anybody give me a good example or explanation on why I would want to implement this. Do we have any experimental evidence to confirm that light is an electromagnetic wave? Or is it confirmed simply by Maxwell's equations showing a similarity in speed? Regex exec only returning first match How to combine an SSD boot drive with a HDD data drive? I have an SSD with 64 GB and a 6 GB/s 1 Terabyte hard drive. I want to use the SSD only as a boot device and maybe for swap storage. On the 1 Terabyte hard drive, I want to have the main file system. As in Windows, I liked to have at least 2-3 Partitions example for music games programs and so on. Which partition layout do you recommend to me? When to use a linked list over an array/array list? I use a lot of lists and arrays but I have yet to come across a scenario in which the array list couldn't be used just as easily as, if not easier than, the linked list.  I was hoping someone could give me some examples of when the linked list is notably better. Importing coordinate data from Excel into QGIS I have an Excel file containing data collected over many years as latitude and longitude coordinates for archaeological sites. How can I import it into QGIS as a new layer? problems using apa6e with biblatex-apa As in  I'm trying to use apa6e and biblatex-apa together and having problems.  Before I arrived at these problems, over the course of many hours of much reading, I first managed to get BibTeX working as expected in a simple input file (by modifying sample2e.tex). Then I managed to get apa6e working as expected based on the author's example in apa6e.pdf (which uses apacite). But when I try to get apa6e working with biblatex-apa, I end up with problems.  Here's my input file:  \documentclass{apa6e}  \usepackage[american]{babel} \usepackage{csquotes}  % biblatex \usepackage[style=apa]{biblatex} \bibliography{biblatex-apa-test-references}  \title{An Example Document} \shorttitle{Psychology: the end} \author{Silly Name}  \authornote{\dots} \abstract{\dots}  \begin{document}  \maketitle  This is an example input\cite{7.01:2} file.  Comparing it with the output it generates can show you\cite{7.01:3a} how to produce a simple document of your own.  \printbibliography  \end{document}   Attempting to typeset this in TeXShop by running LaTeX, then BiBTeX (which based on console messages, does seem to correctly call biblatex rather than BiBTeX), then LaTeX again, I get the following error message which I am having great difficulty (no doubt due to my lack of experience with TeX and co.) decoding.  (./test6.aux) (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/ot1ptm.fd) *geometry* driver: auto-detecting *geometry* detected driver: pdftex (./test6.bbl) Underfull \hbox (badness 10000) in paragraph at lines 18--18  []\OT1/ptm/m/n/12 An Ex-am-ple Doc-u-ment   Underfull \hbox (badness 10000) in paragraph at lines 18--18  []\OT1/ptm/m/n/12 Silly Name   Underfull \hbox (badness 10000) in paragraph at lines 18--18  []\OT1/ptm/m/n/12 Author Note  [1{/usr/local/texlive/2011/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] Underfull \hbox (badness 10000) in paragraph at lines 18--18  []\OT1/ptm/m/n/12 Abstract  [2] Underfull \hbox (badness 10000) in paragraph at lines 18--18  []\OT1/ptm/m/n/12 An Ex-am-ple Doc-u-ment   Underfull \hbox (badness 10000) in paragraph at lines 25--25  []\OT1/ptm/b/n/12 References  ./test6.tex:25: Undefined control sequence. &lt;argument&gt; \mkbibdateapalongextra  (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/ot1pcr.fd) (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/ot1ztmcm.fd) (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/omlztmcm.fd) (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/omsztmcm.fd) (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/omxztmcm.fd) Overfull \hbox (8.03372pt too wide) in paragraph at lines 25--25 [][]  \OT1/ptm/m/n/12 Gilbert, D. G., Mc-Cler-non, J. F., Ra-bi-novich, N. E.,  Sugai, C., Plath, L. C., As-gaard, G., ... Botros,  ./test6.tex:25: Undefined control sequence. &lt;argument&gt; \mkbibdateapalongextra                                    {year}{month}{day}\iffieldundef {endyear}{... l.25   I tried many different sources in several different *.bib files before eventually trying the .bib database shown above and included with biblatex-apa. All trials gave a similar error.  Can someone help? I'm impressed that the poster above was able to do anything with apa6e and biblatex-apa, and if I only had her problem of having the reference page title show up in bold, I'd be really happy.  If you need to know, my tools are from a fresh installation of MacTeX that I immediately updated using the TeX Live Utility. I've checked my versions for apa6e (v0.3) and biblatex-apa (v4.2), and I think these are current. How do I make Endermen spawn more frequently? I'm playing vanilla Minecraft, and am getting ready to head to the end.  I need Eyes of Ender (and hence Ender Pearls), and in my main hunting grounds (a large desert area) as little as one Enderman may spawn per night.  Is there any way to "promote" Enderman spawning so I can get pearls more quickly? Root filling up although it should have some space This has been perplexing me for some time. I'm on Ubuntu 11.04. My root partition is filling up and I can't figure out what's causing it. Even stranger, when I run df -h, this is the output:  Filesystem            Size  Used Avail Use% Mounted on /dev/sda2             9.2G  8.8G     0 100% /   As you see, there should be about 400 MB free, but Avail shows 0. What could be causing this? I've even uninstalled some programs to free the space and it fills up again. Suggestions on how to find out which, if any, files are filling up the space are also welcome. How to split bibliography into "works cited" and "works not cited"? I need two bib-like sections: a "References" giving works explicitly cited in my text, and a "Bibliography" (or "Further reading" if you prefer) giving everything from my bibfile that didn't already appear in "References". The first is of course completely standard, but the second... I'm stumped.  Further loose constraints: I'm somewhat committed to biblatex and the biblatex-apa style. But I'll happily accept an answer not related to them if there's any chance I can adapt it. Relationship between SVD and PCA. How to use SVD to perform PCA? Fantasy novel about kid who controls magic through coin changer device I read this book in high school, and I can't remember what it's called. Some kid learns he has magical ability, but only finds out later that he controls it through some kind of coin changer he's been tinkering with the whole book. If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.