When writing a sentence, can I change from past-tense to present-tense in the middle of it? For example,     Joey realized that the ball is green.   or     Joey realized that the ball was green.   I am talking about a ball which is always green. The second example implies that the ball was green and that it may or may not still be green. However, Joey realizes it in the past. Is the first sentence grammatically correct?
I know the past tense carries the past tense in every dependent clause, but referring specifically to places or to things that are eternal, like the Earth, seems a bit weird and therefore we sometimes (I believe incorrectly) say     He didn't know that New Jersey was actually on the East Coast.   Because it still is. Or     He thought the Earth was round.   So is it square now?  Logically speaking, would you consider the use of past tense here a bit confusing in a day-to-day speech in these examples? Would you instinctively opt for using the present tense?
Is there a simple way to reduce the amount of white space around the TikZ in the MWE pasted below (in particular in the x direction)?  \documentclass{article} \usepackage{xcolor} \usepackage{tikz}  \begin{document} VRCRCRCRCC \tikz[baseline] \node[fill=yellow!30, anchor=base,inner sep=0.7pt, outer xsep=-2pt] {ABCDE}; VBZBZBBBBG \end{document}     PS: This question may be a duplicate of . I posted it nevertheless since 1) my example is much simpler (and hence may have a much simpler solution) and 2) I don't see how the answers given there could help in my case. If you disagree feel free to mark my question as "exact (!) duplicate of ...". I recently saw a question about a problem (or possible bug) with some product on Stack Overflow. At first, I wanted to suggest that the asker post his question to that product's support forum.  When searching for the URL of that forum, I noticed that the product developer closed its support forums and now advises users to post all their questions on Stack Overflow instead.  Is this within the intended use cases of Stack Overflow, or is this abuse? Which style is preferred? Is there a good reason for one vs. the other?  Thanks in advance!  1) cmds.each do |cmd|    end  2) cmds.each { |cmd|    }   Example code:  cmds = [ "create", "update", "list", "help" ]  # Block style one # cmds.each do |cmd|   puts "loop1, cmd: #{cmd}" end  # Block style two # cmds.each { |cmd|   puts "loop2, cmd: #{cmd}" } In the following code I loop through a map and test if an element needs to be erased.  Is it safe to erase the element and keep iterating or do I need to collect the keys in another container and do a second loop to call the erase()?  map&lt;string, SerialdMsg::SerialFunction_t&gt;::iterator pm_it; for (pm_it = port_map.begin(); pm_it != port_map.end(); pm_it++) {     if (pm_it-&gt;second == delete_this_id) {         port_map.erase(pm_it-&gt;first);     } }   UPDATE: Of course, I then  which I didn't think would be related but answers my question. If $f$ is entire and $|f|\geq 1$, then show $f$ is constant. I know I'm going to use Liouville's Theorem, but my main question is why is $1/|f(z)|$ entire as well if $f$ is entire? Is this just a basic property: if $f$ is entire, then $1/f$ is entire? Thanks for the help. how to output text to both screen and file inside a shell script? Currently I have a shell script which logs messages to a log file like this:  log_file="/some/dir/log_file.log" echo "some text" &gt;&gt; $log_file do_some_command echo "more text" &gt;&gt; $log_file do_other_command   When executing this script, there is no output to screen, and, since I'm connecting to the server via putty, I have to open another connection and do "tail -f log_file_path.log", because I can't terminate the running script and I want to see the output in real time.  Obviously, what I want is that the text messages are printed on screen and into file, but I'd like to do it in one line, not two lines, one of which has no redirection to file.  How to achieve this? Looking at the questions and answer to these two questions.  &amp;  and neither mentions the longevity of magic. I recall several instances of magic failing to last; the money that was spread at the  and the broken  on.  If I recall correctly when Voldemort died, the curses on several people were lifted.  I don't recall if any other spells fell apart with his death.  Is there any canon evidence on the the length of time a spell will live? If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group. Assume that $\pi$ is an automorphism of a finite group $G$. Let $S$ denote the set $\lbrace g \in G: \pi (g)=g^{-1} \rbrace$. Show that if $|S|&gt;\frac{3|G|}{4}$, then $G$ is an abelian group.    Anyone has any idea on how to solve this ? I have no idea how to start. LaTeX template for typesetting a novel I'd like to use LaTeX to typeset a novel. Could you recommend me any template?  What I mean is a template (some .tex file) where I can include my chapterN.tex files (mainly plain text) and get a pretty good design with zero work :) I am considering buying a Dell XPS 15 laptop. The laptop has a Nvidia 420m card which should work with Linux but I keep reading that the Nvidia Optimus technology isn't supported on Linux. I am not really interested in switching from Nvidia to Intel to save power but need to know that the Nvidia card will in fact work if I installed Ubuntu.  If anyone has experience using a Nvidia card with Optimus technology or even better the exact laptop in question (Dell XPS 15 with 1GB NVIDIA® GeForce®  GT 420M) it would be great.  A major problem holding people back from adopting Linux is this sort of hardware issue. I am a long term Ubuntu user and supporter who can't afford to make a mistake with a purchase like this. I don't want to spend £500+ to find I have no graphics acceleration because Windows 7 is not an option. Unit testing is, roughly speaking, testing bits of your code in isolation with test code. The immediate advantages that come to mind are:  Running the tests becomes automate-able and repeatable You can test at a much more granular level than point-and-click testing via a GUI    My question is, what are the current &quot;best practices&quot; in terms of tools as well as when and where to use unit testing as part of your daily coding? Lets try to be somewhat language agnostic and cover all the bases. Is it possible to detect 32 bit vs 64 bit in a bash script? I am writing a bash script to deal with some installations in an automated way... I have the possibility of getting one such program in 32 or 64 bit binary... is it possible to detect the machine architecture from bash so I can select the correct binary?  This will be for Ubuntu machines. I resized the root partition with GParted, from 20 GB to 40 GB, but the filesystem still reports a size of 20 GB.  How can I use all 40 GB?    Update  The resized partition was an LVM Physical Volume (/dev/sda2), and the boot partition is ext4 (/dev/sda1). Solidify conundrum? I stumbled across a solidify issue, I cannot wrap my head around. I have a simple mesh, consisting of three faces.  When adding a solidify modifier, I expect to get an object with three walls, where every angle is square. However, whatever I try, tweaking the various solidify parameters, what I get is something like the following, with a skewed rim.  Did I hit a bug, or is it a limitation of the solidify modifier? Is there a workaround? How do I contact other users? How can I contact another user, if that user has not specified any contact details in their profile? Comparing two integers without any comparison Is it possible to find the greatest of two integers without any comparison? I found some  solutions:   if(!(a/b)) // if a is less than b then division result will be zero. {     cout &lt;&lt; " b is greater than a"; } else if (!(a-b)) // we know a is greater than or equal to b now.  check whether they are equal. {     cout &lt;&lt; "a and b are equal"; } else     cout &lt;&lt; "a is greater than b";   But if(c) or if(!c) is a comparison to zero. In addition it doesn't work for negative numbers. In fact I need a solution that avoids any if statement. Instead I should use switch statements and arithmetic operators. ThanX. Is system cleanup/optimization needed Does Ubuntu need regular cleanups like Windows. For example:   Cleaning the logs Temporary files Package cache Dependencies left over   I am not referring to web browsers only.  In case I never do a cleanup, will I have a system like new without my hard drive being full of temporary files, packages, etc.?  Will the performance degrade overtime if a cleanup is not done. I want to know the general formula for $\sum_{n=0}^{m}nr^n$ for some constant r and how it is derived.  For example, when r = 2, the formula is given by: $\sum_{n=0}^{m}n2^n = 2(m2^m - 2^m +1)$ according to   Thanks! Real analysis - proof approach help Help needed in understanding proof: Every odd prime $p$ has exactly $(p-1)/2$ quadratic residues and $(p-1)/2$ quadratic nonresidues. Help needed in understanding proof: Every odd prime $p$ has exactly $(p-1)/2$ quadratic residues and $(p-1)/2$ quadratic nonresidues.   We assume there exist $k$ incongruent quadratic residues and each yield two solutions of the equation $x^2 \equiv a (\mod p)$. Also each of these solutions are incongruent, right ? So we have $2k$ solutions to quadratic congruences.  Then there are $p-1$ squares of the least residues, $1$ through $p-1$. But these need not be incongruent (consider $p = 7$ and $1^2, 6^2$). Then $2k = p-1$, why ?  Could someone explain to me in details what the reasoning is ?