I detect a lot of mistakes only when I read the paper printed. For some mysterious reason, I do not see these errors on my screen.  So I used to print a lot, and only to type-check. I use double-sided printing of course but there are still plenty of space wasted ; with LaTeX big margins (among other things), I have to print more pages than necessary.  I am wondering if there is a document class designed to save paper by optimizing the space. Perhaps a class which will set the text in several columns, put some minimal margins, reduces space between titles, ... Of course, the result will be ugly but it is just to type-check, not to publish.  I know I could set myself settings in order to achieve exactly what I want. But the idea is to have to change only the document class from article or book to this saving paper class when you are at the type-check stage.   Do someone know such class?
I found there are so much excellent answer to questions about how to product high quality typesetting output. But I wonder how to save ink with LaTeX. What we need to think about to manage cost. page layout or something else?
Is infinity a real number?  If not, why not?  I want some very good arguments.   Thanks.  $$\rightarrow\leftarrow\Huge\Huge\Huge\boldsymbol\infty$$ Why is the Yang-Mills gauge group assumed compact and semi-simple? What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories?  I'd think that these hypotheses lead to physically "nice" theories in some way, but I've never, even from a computational perspective. really given these assumptions much thought. To tell about a guess about a case in the past, why use "would+have+past participle" instead of "must+have+past participle? I have seen this sentence in an article on bbc, which is about how people lived thousands of years ago. &quot;When this Neolithic home was built, it would have had a cosy roof of turf..&quot; When I read it, I got confused. Because the fact seems as a simple past situation or guessing/assumption about something in the past. it simply gives information about a past event, eg &quot;when I was a child, I had a blue toy car. I have been making a lot of research on whether or not this structure &quot;would+have+past participle&quot; could be used instead of the simple past or &quot;must+have+past participle&quot;, but I could not find any satisfying explanation. Almost all grammer contents cover this structure is used when we imagine the opposite of what actually happened in the past eg. &quot;referring to a missed opportunity&quot; (eg. &quot;if you had come to the party, you would have seen Tom.&quot;), But, in this case of this sentence, &quot;type 3 conditional&quot; is irrelevant. It is not an if sentence,  It simply gives information about how this house was like or was probably like when it was built long ago. Just like it would be If and old lady would want to tell about &quot;how she was like when she was a child years ago. she would simply say &quot;when I was a child, I had long curly hair.**. So &quot;when I was a child, I would have had long curly hair.&quot; would be wrong. So, my question is: 1-Does this structure &quot;would+have+past participle&quot; completely replace simple past sentences? or can be it be used instead of simple past? 2- If this structure was simply used because the author was not %100 sure about the fact as it was a long long time ago -so he wanted to make a guess or assumption, why did he not simply use &quot;must+have+past participle&quot; or &quot;it was likely that blah blah&quot; which must be used for guessing or assumptions about past happenings. Would it not have made more sense if it was like: &quot;When this Neolithic home was built, it must have had a cosy roof of turf. Add 'Page' above page numbers in Table of Contents I am using my school's latex . Unfortunately, since this package was last updated, we are now required to add the word 'Page' above the topmost page number on each page of the Table of Contents. This cls file includes the following bit of code, which puts 'Page' at the top of the first page, but not any subsequent pages (see attached)  \newcommand\chapteruaf{ \if@arabic\relax\else\if@chapterone\setcounter{page}{1}\else\relax\fi\fi \@chapteronefalse                     \if@openright\cleardoublepage\else\clearpage\fi                     \thispagestyle{myheadings}%                                                                                                    \global\@topnum\z@                     \@afterindentfalse                     \secdef\@chapter\@schapteruaf} \def\@schapteruaf#1{\if@twocolumn                    \@topnewpage[\@makeschapterheaduaf{#1}]%                                                                                     \else                    \@makeschapterheaduaf{#1}%                                                                                                     \@afterheading                  \fi} \def\@makeschapterheaduaf#1{%                                                                                                    {\parindent \z@ \centering     \reset@font     \normalsize \bfseries  #1\par                                                                                                  \vspace{-18.3pt}\hspace{143mm} Page                                                                                            \nobreak   }}   First page of the TOC:   second page of the TOC:   Any thoughts here? I have played with this a bit, and can't get it to work. Thanks. If $x,y$ are positive reals such that $x+y = 2$ show that $x^3y^3(x^3+y^3) \leq 2$.   I thought about working backwards on this one. We can try to prove that $x^3y^3(x^3+y^3) \leq 2$ is true by first realizing that $x^3+y^3 = (x+y)(x^2-xy+y^2)$ and substituting in for $x+y = 2$. We then get $x^3y^3(x^2-xy+y^2) \leq 1$. How do I prove this is true? "Closed" (square) root symbol I found a cool trick in the  which allows the square root sign to be altered such that it &quot;closes&quot; over its contents. Here's an example:  (&quot;closed&quot; root on the left, normal one on the right) The way they do this is as follows: % New definition of square root: % it renames \sqrt as \oldsqrt \let\oldsqrt\sqrt % it defines the new \sqrt in terms of the old one \def\sqrt{\mathpalette\DHLhksqrt} \def\DHLhksqrt#1#2{% \setbox0=\hbox{$#1\oldsqrt{#2\,}$}\dimen0=\ht0 \advance\dimen0-0.2\ht0 \setbox2=\hbox{\vrule height\ht0 depth -\dimen0}% {\box0\lower0.4pt\box2}} The cool thing is that (as far as I've tested it) this works regardless of the math font and with pdftex as well as xetex. However what is not possible is mulitple roots, such as \sqrt[3]{a}. Those produce incorrect output when this &quot;trick&quot; is being used. So my question is, is somebody able to tweak this code so that it works for multiple roots as well? "No such file or directory" when trying to remove a file, but the file exists? Free ornaments font I'm looking for a free ornaments font. I know about  and pifont. Where can I find more glyphs? What is the size of this microcontroller? Having trouble reading a data sheet What if I run a virus/trojan Windows EXE on Ubuntu with Wine? Does Quicksilver's walkman speed up with him? How can I identify an anonymous inner class in a NotSerializableException Do I need a visa to transit (or layover) in the Schengen area? I found many related questions on this site but I am still not sure about the rules. How can I decide if I need a visa to transit? Schengen members as of May 2021 are as follows:  Austria Belgium Czech Republic Denmark (excluding Greenland and the Faroe Islands - but an open border with the Schengen Area is maintained) Estonia Finland France (excluding overseas departments and collectivities) Germany Greece Hungary Iceland Italy Latvia Liechtenstein Lithuania Luxembourg Malta Netherlands (excluding Aruba, Curaçao, Sint Maarten and the Caribbean Netherlands) Norway (excluding Svalbard) Poland Portugal Slovakia Slovenia Spain (except Ceuta and Melilla) Sweden Switzerland How can I make iconv replace the input file with the converted output? I have a bash script which enumerates through every *.php file in a directory and applies iconv to it. This gets output in STDOUT.   Since adding the -o parameter ( in my experience ) actually writes a blank file probably before the conversion takes place, how can I adjust my script so it does the conversion, then overwrites the input file?  for file in *.php do     iconv -f cp1251 -t utf8 "$file" done How do I programmatically create a new content type? An alternative to translation for non-English speakers? Determine the convergence of $ \sum_{n=1}^{\infty}\left[1-\cos\left(1 \over n\right)\right] $ What is a concise function that formats a (String) decimal into a currency format in Apex? goal: write the most concise function that formats a (String) decimal into a currency format in Apex. Feel free to trainwreck the code for points, I've kept mine exploded for readability purposes. Every Window in Windows 8 got this icon if it gots the focus. When clicking on it, nothing seems to happen.   How does this icon work? Why does Microsoft Word 2010 show an error for the following sentence?     1.&nbsp;Where should this car be parked?   Word 2010 also suggests changing the sentence to     2.&nbsp;Where this car should be parked?   Is the sentence (1) wrong? If yes, why? What about sentence (2)?