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What does the big intersection or union sign of a set mean? In some cases, we will have to consider the union or the intersection of several, even infinitely many sets, defined in the obvious way. For example, if for every positive integer $n$, we are given a set $S_n$, then   $$\bbox[border:1px solid red]{\bigcup_{n=1}^\infty S_n}=S_1\cup S_2\cup\cdots=\{x\mid x\in S_n\text{ for some }n\},$$   and   $$\bigcap_{n=1}^\infty S_n=S_1\cap S_2\cap\cdots=\{x\mid x\in S_n\text{ for all }n\}.$$   Two sets are said to be disjoint if their intersection is empty. More generally, several sets are said to be disjoint if no two of them have a common element. A collection of sets is said to be a partition of a set $S$ if the sets in the collection are disjoint and their union is $S$.   Normally what I know is that you can make a union or an intersection between only two sets. In this expression, there is a big union of sets. I'm asking about the meaning of this expression – what does it mean? What does the infinity sign do at the top?  Things are even more complicated with De Morgan's laws, which use the same expression:     Two particularly useful properties are given by De Morgan's laws which state that   $$\left(\bigcup_nS_n\right)^c=\bigcap_nS_n^c,\quad\quad\quad\quad\left(\bigcap_nS_n\right)^c=\bigcup_nS_n^c.$$   Anyone who can explain to me the expression or De Morgan's laws would be much appreciated. Does a character with 10 Constitution only need to eat every 4 days? According to the food rules,     A character can go without food for a number of days   equal to 3 + his or her Constitution modifier (minimum   1). At the end of each day beyond that limit, a character   automatically suffers one level of exhaustion.   A normal day of eating resets the count of days   without food to zero.   According to this, a character with a Constitution modifier of 0 can eat normally every 4th day*, and get no penalties from hunger despite only eating twice a week. This seems a tad ridiculous, and I'm wondering if there are other rules that I'm missing that make it a bad idea to eat less often like this, or if eating every 4th day is a totally fine thing to do, by the rules.  * They can get away with four days, because they'll only get the exhaustion penalty if they don't eat by the end of the fourth. This is even assuming the 'minimum 1' doesn't apply to the con mod portion. I keep running into areas where I see a chest in a section of the room that seems completely walled-off. Is there any way to get to these, or is that just the randomly generated dungeon being a tease?  I had to splice two screenshots together to show an example of what I'm talking about:   Is there any way to get in there? How can I change an element's class with JavaScript? How can I change the class of an HTML element in response to an onclick or any other events using JavaScript? Why does the command shuf file > file leave an empty file, but similar commands do not? I know this is sort of a duplicate of another question () but I wanted to expand on the question in response to the answers given.  The command  shuf example.txt &gt; example.txt  Returns a blank file, because the shell truncates the file before shuffling it, leaving only a blank file to shuffle. However,  cat example.txt | shuf &gt; example.txt  will produce a shuffled file as expected.  Why does the pipeline method work when the simple redirection doesn't? If the file is truncated before the commands are run, shouldn't the second method also leave an empty file? Consider these two ways of coining a name: 1) Bolzano's theorem, Rolle's theorem 2) the Poincare conjecture, the Kantorovich theorem. What is the difference between these ways, why do people choose one over the other?  My guess is that the main difference is when you put 's at the end of a name, you strictly imply that the theorem/conjecture was written by this very person (Bolzano wrote Bolzano's theorem). But when it is "the [Name] theorem/conjecture," it doesn't mean that the person which name is used actually created this thing, maybe he just inspired it (Poincare might have only inspired the Poincare conjecture but did not propose it).  Sometimes there is only one way: ; you can not call it hairy ball's theorem. I've noticed that Visual Studio 2008 is placing square brackets around column names in sql. Do the brackets offer any advantage? When I hand code T-SQL I've never bothered with them.  Example:  Visual Studio:  SELECT [column1], [column2] etc...   My own way:  SELECT column1, column2 etc... How to collapse unused parameters in moderncv? I am writing my CV using the moderncv package. I already have adjusted the CV to meet my needs. Therefore I amplified the maximum number of parameters possible in the \cventry command. However, now I have some ugly spacing in case I do NOT use all parameters (see second \cventry in the MWE for illustration):  Any suggestions to make the spacing collapse in case not all parameters are occupied? As you can see from the MWE I already have adjusted for \ifthenelse command. I use texlive 2014.  \documentclass[11pt,a4paper,sans]{moderncv} \moderncvstyle{banking} \moderncvcolor{blue} \usepackage[scale=0.7]{geometry} \name{John}{Doe} \title{Resume title} \address{street and number}{postcode city}{country} \phone[mobile]{+1~(234)~567~890}  \renewcommand*{\cventry}[9][.4em]{%  \begin{tabular*}{\textwidth}{l@{\extracolsep{\fill}}r}%  \ifthenelse{\equal{\bfseries #4}{}}{}{{\bfseries #4}} &amp; \ifthenelse{\equal{\bfseries #5}{}}{}{{\bfseries #5}} \\%   \ifthenelse{\equal{\itshape #3}{}}{}{{\itshape #3\ifthenelse{\equal{#6}{}}{}{, #6}}} &amp; \ifthenelse{\equal{\itshape #2}{}}{}{{\itshape #2}}\\%  \ifthenelse{\equal{#7}{}}{}{{#7}} &amp; \ifthenelse{\equal{#8}{}}{}{\\ {#8} &amp; \\}% \end{tabular*}%  }  \begin{document} \makecvtitle \section{Education} \cventry{Grade}{Degree}{Institution}{year--year}{M.Sc.}{Majors}{Majors}{} \cventry{}{Degree}{Institution}{City}{}{}{}{} \cventry{year--year}{Degree}{Institution}{City}{Grade}{Majors}{Majors}{} \end{document} How many stickers do I need to complete my FIFA Panini album? I'm playing the , which is an Internet adaption of the classic Panini albums that are usually published for the soccer world cup, European championship, and possibly other tournaments.  The album has placeholders for 424 different stickers. The purpose of the game is to collect all 424. The stickers come in packs of 5, which can be obtained through codes found online (or, in case of the classic printed album, bought at your local newsstand).  I make the following assumptions:   All stickers are published in the same quantity.  One pack of stickers does not contain duplicates.     How can I find out how many packs of stickers I need to acquire in order to be reasonably sure (let's say 90%) that I have all 424 unique stickers? Simulate limited bandwidth from within Chrome? Add spanish spell check android studio "add/show comments" should dismiss notification number of quadratic residues in finite field Is there a way to determine how many quadratic residues are there in the finite field $F_q$ for $q = p^k$?  It seems if $q=p$ exactly $(p-1)/2$ are residues and the same amount are not. Does analogy holds for $q = p^k$?  Thanks for any input. Pure verbal nouns/deverbal nouns vs. gerunds This is a follow-up to a previous question which I am still trying to understand. I think I'm making progress in my understanding, but I would appreciate feedback to help me refine my thinking.  Here is the sentence:     Good writing requires hard work.   Originally, I thought that "writing" was acting as a gerund in this phrase.  After reading through the replies to that question along with back posts related to gerunds, I've since concluded that "writing" in this sentence is a , also termed a deverbal noun.  My reasoning?  —In the sentence above "writing" is modified by "good" and is thus acting more like a noun than a verb. —It has no direct object.  Is my thinking correct here?  If not, could someone politely help me to refine it?  However, what if I had written the following?     Writing well requires hard work.     or   To write well requires hard work.   In these examples, I'm thinking that "writing" would be a different kind of verbal noun—a non-finite verb acting as a gerund or infinitive, which is one piece of a larger complement noun clause.  The last bit is muddy for me, but I will leave it at that. Thank you in advance for your patience and insight. How to prove that the center of the dihedral group $D_{2n}$ is $\{1,r^{n}\}$ and the center of $D_{2n-1}$ is $\{1\}$?  I don't know how to prove it in this general case. Choosing research ideas to include in a statement of purpose Where do I put my systemd unit file? A real solution to ambiguous tags Introduction Even within a site's relatively focused range of topics (it's unlikely anybody on SO will think  refers to the solar system's star), some tags are inherently ambiguous. There are currently two unsatisfying options:  Declare that the tag is only to be used for one of the possible meanings, write a tag wiki explaining it, and link from there to the newly created tags for the other meanings, and keep cleaning up the tag whenever someone ignores the tag wiki popup explaining the tag. Use alternative tags for all meanings (e.g. cd-command and compact-disk, instead of cd), and keep removing the undesired tag whenever it pops up again. And it will. The  is not deterring users from creating unnecessary or redundant tags.  Blacklisting tags is a complicated ritual occurring once in a blue moon, at most, and involves a dragon, a team member, and sacrifices to be burnt. It also makes those other, unambiguous tags not easier to discover, if it were applied to ambiguous tags. I don't consider this to be a viable option in this case. Proposal Here's the proposed : Just like a tag can be declared a synonym of another tag, basically changing all references to the synonym to references to that other, canonical tag, it should be possible to make it a disambiguation tag (or ambiguous tag) for multiple other tags. It's a logical progression from &quot;You entered a term with the same meaning as this other term&quot; to &quot;You entered a term with the same meaning as one of these other terms, please choose the correct meaning&quot;. Use of the tag should force the user to choose one of the alternatives presented:  &quot;, did you mean  or ?&quot; &quot;, did you mean , , or ?&quot; &quot;You entered 'vm', did you mean  or ?&quot; &quot;You entered 'sas', did you mean  or ?&quot; &quot;You entered 'kvm', did you mean  or ?&quot; &quot;You entered 'mono', did you mean  or ?&quot; &quot;You entered 'dsl', did you mean  or ?&quot;  Not all of these examples might be good (I'm not sure e.g. about the first two SO examples), but that's not really the point here anyway — they should just convey how this could be used. Note how some of these tags would probably never be used if users had to type them, and yet everything shorter is ambiguous. This could probably be mostly solved by extending the synonym/tag wiki excerpt dropdowns shown when a user enters the tags, proposing the alternatives for an ambiguous tag entered by the user (like a synonym suggestion, but with multiple options). If ignored, the user could still be shown an error message like with blacklisted tags, but by designing the selection dialog well, it should be possible to prevent that in most cases.  Related topics   This topic is related, but the user seems to have accepted the inclusion of tag wiki excerpts in the tag suggestions drop-down as sufficient.   This requires extensive discussion and team involvement (i.e. the status quo)   This topic has no real solution, except manual retagging. I have a Non Root User abc and want to give the user sudo rights only to restart, start or stop - mysqld service. i.e sudo service mysqld restart. How can I do it so?     I would like to do the same to usergroup too!! Single word for floating dust visible in sunlight Is there a single word used in English for the visibility of dust particles floating in a stream of sunlight?     shutterstock.com