Affordance discovery on clickable elements: icons vs buttons
When to use icons vs. icons with text vs. just text links?
Can regular expressions be used to match nested patterns? Is it possible to write a regular expression that matches a nested pattern that occurs an unknown number of times? For example, can a regular expression match an opening and closing brace when there are an unknown number of open/close braces nested within the outer braces?  For example:  public MyMethod() {   if (test)   {     // More { }   }    // More { } } // End   Should match:  {   if (test)   {     // More { }   }    // More { } } Matrices - Conditions for $AB+BA=0$ The Problem Let $A$ be the matrix $\bigl(\begin{smallmatrix}a&amp;b\\c&amp;d\end{smallmatrix} \bigr)$, where no one of $a,b,c,d$ is $0$. Let $B$ be a $2\times 2$ matrix such that $AB+BA=\bigl(\begin{smallmatrix} 0&amp;0\\ 0&amp;0 \end{smallmatrix} \bigr)$. Show that either   $a+d=0$, in which case the general solution for $B$ depends on 2 parameters, or $ad-bc=0$, in which case the general solution for $B$ depends on one parameter.   (this is question 22 of the last matrix exercise of Further Pure Mathematics by Bostock et al.)  Comments Writing $B=\bigl(\begin{smallmatrix} e&amp;f\\ g&amp;h \end{smallmatrix} \bigr)$ and multiplying out I get that    $(a+d)(f+g)+(b+c)(e+h)=0$ $ae+bg+cf+dh=0$   but I am unable to get the required restrictions on $a,b,c,d$. Is there a quick way of doing the problem that doesn't require manual computation? I thought of considering invertible and non-invertible cases but couldn't get anywhere. Help would be much appreciated. How do you use a variable in a regular expression? How can I iterate, loop, process, or otherwise do something, with each element from a comma separated list of things?  This question       , and the are already lots of very good answers everywhere. However I think it would also be valuable to have a single reference point where all such alternative techniques are explained in detail, with their advantages and disadvantages discussed.  All of plain-TeX, LaTeX, LaTeX3, LuaTeX, Context, etoolbox, pgffor, etc. answers are invited. Please consider explaining, for example:   How does the command/method deal with whitespace around items? How does the command/method deal with empty/missing items? (e.g. a,b,,c) How does the command/method deal with a trailing comma? Can the command/method work of a list stored on a macro? Is each iteration evaluated globally or on a local group? (i.e., if a command is defined during an iteration, does the command survive the loop?) Do items get expanded or somehow mangled before being processed? What about lists where items are key=value or some other kind of pairs? Does the method work for lists separated with something other than a comma? Any other thing I should know before deciding to use this method? Link to a note in Apple Notes, from another note In Apple Notes on the Mac, is it possible to reference a note from within another note (by way of hyperlink)? So, for example, if I had two notes:  Thoughts about pastries Pastries are great. Truly wonderful treats. But you know what my favorite types of pastries are? Donuts. I've even made a list of the types of [donuts I've eaten].  and  Donuts I've Eaten Chocolate, Glazed, Frosted, Encrusted…  How could I link the text [donuts I've eaten] from the first note to the second note? What was Mr. Anderson (Neo) selling on discs to Choi? Is there some trick to burning a cd with the CD/DVD creator?    I'm installing k3b because that's a known entity.  What is this, and where is the "burn" button?  Help just tells me this is Nautilus 3.4.1, but I don't see a .  There's no option to burn in the Files menu, nor does clicking on the whitespace indicate an option to burn anything. Listing multiple compound words How do I list multiple things that are compound words?  In my own language I'm used to writing these lists like this:  "I kicked foot-, basket-, and volleyball"  The sentence is supposed to mean that I kicked all types of balls (football, basketball and volleyball). However, it does not seem correct to me. Should I write them as whole words, with or without hyphen, or how? I have a question about calculating the degree of a finite field extension over $\mathbb{Q}$.  This is problem 18 in chapter 1 of Patrick Morandi's Field and Galois Theory. The problem asked to show that $$ \left[ \mathbb{Q}{ \left( \sqrt[4]{2},\sqrt{3} \right):\mathbb{Q} }\right] =8 $$ Here's my work : First, we have $$  \left[ \mathbb{Q} ( \sqrt[4]{2},\sqrt{3}):\mathbb{Q}\right] = \left[ \mathbb{Q}(\sqrt[4]{2},\sqrt{3}) : \mathbb{Q}({\sqrt[4]{2}}) \right] . \left[ \mathbb{Q}{(\sqrt[4]{2})}: \mathbb{Q} \right]$$ It's easy to show that $\left[ \mathbb{Q}{(\sqrt[4]{2})}: \mathbb{Q} \right] =4 $ because the minimal polynomial of $\sqrt[4]{2}$ over $\mathbb{Q}$ is $x^4 -2$. Next, I'm going to show that  $$ \left[ \mathbb{Q}(\sqrt[4]{2},\sqrt{3}) : \mathbb{Q}({\sqrt[4]{2}}) \right] =2$$ Consider the polynomial $f(x) = x^2 -3$. It's monic and $\sqrt{3}$ is a root of $f$, but I'm stuck in proving $\sqrt{3} \notin \mathbb{Q}(\sqrt[4]{2})$ (hence $f$ is irreducible over $\mathbb{Q}(\sqrt[4]{2}))$.  My question is: Is there any proof to show that $\sqrt{3} \notin \mathbb{Q}(\sqrt[4]{2})$ or another way to caculate the degree of this field extension?  Thank you for your help. Custom Adapter for List View Long, blurry reflections in wet road Does a photon having superimposed frequencies exist?  (wrt frequency detected by prism or other detectors, not wrt human eye as only rod-cells can detect one photon falling in the detectable (visible) frequency band and the single photon is perceived by eye+brain as grey irrespective of frequency).  Also, with white here, I do not wish to restrict the question implying all VIBGYOR frequencies or only RGB as each color is also a range of frequencies and white to trichromatic-sensor human eye is just output from three frequencies RGB.  Or can it be that materials which slow light down cause a photon of some single frequency and higher energy to split into VIBGYOR? || and the entire spectrum of human eye's detection range is VIBGYOR+W (as monochromatic light of high intensity can also be perceived white by human eye and it is not related to individual color sensors of human eye at all but that above a certain energy per unit volume (referring to detector area of eye cells), we perceive it white, (somewhat but not exactly) similar to combination of red and green which human eye+brain calls yellow.  I have added the additional description to make the question more precise. If my description causes confusion, please stay with the original question and use description just to get an idea of the intent of the question. I have to deal with a text classification problem. A web crawler crawls webpages of a certain domain and for each webpage I want to find out whether it belongs to only one specific class or not. That is, if I call this class Positive, each crawled webpage belongs either to class Positive or to class Non-Positive.  I already have a large training set of webpages for class Positive. But how to create a training set for class Non-Positive which is as representative as possible? I mean, I could basically use each and everything for that class. Can I just collect some arbitrary pages that definitely do not belong to class Positive? I'm sure the performance of a text classification algorithm (I prefer to make use of a Naive Bayes algorithm) highly depends on which webpages I choose for class Non-Positive.  So what shall I do? Can somebody please give me an advice? Thank you very much! Repeating (or not) "to" in a sentence involving infinitives set in parallel I googled it but I couldn't find the answer... maybe I didn't seek it in the proper way. My question is if &quot;to&quot; must be repeated in sentences such as the following ones:   In the past, women used to do the housework and to take care of children.  The aim of this meeting is to control their progress and to discuss the new working plan.    If I had to bet, I would omit the second to... But I am not sure about it. I know Wonder Woman has died in canon before, but in which issue did this happen? I need to read a properties files that's buried in my package structure in com.al.common.email.templates.  I've tried everything and I can't figure it out.  In the end, my code will be running in a servlet container, but I don't want to depend on the container for anything. I write JUnit test cases and it needs to work in both. Here is my candidate for  the most elementary proof that $\lim_{n \to \infty}(1+1/n)^n $ exists. I would be interested in seeing others.  $***$ Added after some comments: I prove here by very elementary means that the limit exists. Calling the limit "$e$" names it. $***$  It only needs Bernoulli's inequality (BI) in the form $(1+x)^n \ge 1+nx$ for $x &gt; -1$ and $n$ a positive integer, with equality only if $x = 0$ or $n = 1$. This is easily proved by induction: It is true for $n=1$, and $(1+x)^{n+1} = (1+x)(1+x)^n \ge (1+x)(1+nx) = 1+(n+1)x+nx^2 \ge 1+(n+1)x $. (If $-1 &lt; x &lt; 0$, if $1+nx \ge 0$, the above proof goes through, and if $1+nx &lt; 0$, $1+mx &lt; 0$ for all $m \ge n$ so certainly $(1+x)^m &gt; 1+mx$.)  This proof originally appeared in N.S Mendelsohn, An application of a famous inequality, Amer. Math. Monthly 58 (1951), 563 and uses the arithmetic-geometric mean inequality (AGMI) in the form $\big(\sum_{i=1}^n v_i/n\big)^n \ge \prod_{i=1}^n v_i$  (all $v_i$ positive) with equality if and only if all the $v_i$ are equal.  Let $a_n = (1+1/n)^n$ and $b_n = (1+1/n)^{n+1}$.  We will prove that $a_n$ is an increasing sequence  and $b_n$ is an decreasing sequence.  Since $a_n &lt; b_n$, this implies,  for any positive integers $n$ and $m$ with $m &lt; n$  that $a_m &lt; a_n &lt; b_n &lt; b_m$.  For $a_n$, consider n values of $1+1/n$ and $1$ value of $1$.  Since their sum is $n+2$ and their product is $(1+1/n)^n$, by the AGMI,  $((n+2)/(n+1))^{n+1} &gt; (1+1/n)^n$,  or $(1+1/(n+1))^{n+1} &gt; (1+1/n)^n$,  or $a_{n+1} &gt; a_n$.  For $b_n$, consider $n$ values of $1-1/n$ and $1$ value of $1$.  Since their sum is $n$ and their product is $(1-1/n)^n$, by the AGMI,  $(n/(n+1))^{n+1} &gt; (1-1/n)^n$  or $(1+1/n)^{n+1} &lt; (1+1/(n-1))^n$,  or $b_n &gt; b_{n+1}$.  Since $b_n-a_n  = (1+1/n)^{n+1} - (1+1/n)^n = (1+1/n)^n(1/n) =a_n/n $ and every $a_n$ is less than any $b_n$ and $b_3 = (1+1/3)^4 = 256/81 &lt; 4$, $b_n-a_n &lt; 4/n$, so $b_n$ and $a_n$ converge to a common limit.  These proofs do not seem to be really elementary,  since they use the AGMI.  However, they use a special form of the AGMI,  where all but one of the values are the same,  and this will now be shown to be implied by BI,  and thus be truly elementary.   Suppose we have $n-1$ values of $u$ and $1$ value of $v$ with $u$ and $v$ positive.  The AGMI for these values is  $(((n-1)u+v)/n)^n \ge u^{n-1}v$  with equality if and only if $u = v$.  We will now show that this is implied by BI: $(((n-1)u+v)/n)^n \ge u^{n-1}v$  is the same as  $(u+(v-u)/n)^n \ge u^n(v/u)$.  Dividing by $u^n$,  this is equivalent to  $(1+(v/u-1)/n)^n \ge v/u$.  By BI,  since $(v/u-1)/n &gt; -1/n &gt; -1$, $(1+(v/u-1)/n)^n \ge 1+n((v/u-1)/n) = v/u$  with equality only if $n=1$ or $v/u-1 = 0$. Thus BI implies this version of the AGMI. Use of comma separating two adjectives If I had the phrase       two blond haired, blue eyed people    would the comma be out of place?    should I hyphenate "blond haired" and "blue eyed"? In what order should I watch the various Stargate TV Series? I am unfamiliar with the (multiple) Stargate shows and films, other than the movie which I saw a while ago. I want to try watching the series to see if it is something that I like.   What are the non-subjective facts about the series (without spoilers) that I should be aware of when figuring out which series to start with, for example the original airing order of the series, chronological order of the series, frequency of references to a series other than the one that I'm watching, etc. Methods for autocompletion in TexStudio don't work I've made a mymacros.sty file which I would like my LaTeX files to be able to access with commands that I've defined. I've managed to get it to work by putting \usepackage{mymacros} in my preamble.   However when I try to autocomplete I can't. I looked at this question:     ), which recommends 3 ways of doing this, none of which work for me.    The first it recommends is to have mymacros.sty open in the editor. But this doesn't work.  The second is to activate the option Editor -> Automatically load included files in the configure TeXstudio options panel. However while I have an Editor tab , there is no such option there.  The third is to using .cwl files, however I'm not sure how to go about this. In the completion tab I've noticed that there is a mymacros.sty option that has come up, which I ticked but that has had no effect. Do I need to make my own mymacros.cwl file? I've tried to look this up but haven't had any luck.  Anyone have any ideas? Thanks in advance!