I'm trying to vertically center every row of the table, but I can't. How can I do it?  %\documentclass{article} \documentclass[margin=10pt]{standalone} \usepackage{array,booktabs,siunitx} \newcolumntype{Q}[1]{&gt;{\hfil$}p{#1}&lt;{$\hfill}} % centered, automatic math mode \usepackage[table]{xcolor} % for "\rowcolor" macro \usepackage{amsmath}  \renewcommand{\rmdefault}{phv} %\usepackage{mathpple} %\usepackage{palatino}  \usepackage{lxfonts} % %   \usepackage{multicol}  \begin{document} \centering \setlength{\extrarowheight}{20pt} % for a more "open" look \begin{tabular}{|*{5}{Q{2cm}|}} % or: {|*{b}{c|}} \hline \rowcolor{yellow} \textbf{$a$} &amp; \textbf{$b$}&amp; \textbf{$a+b$} &amp; \textbf{$a-b$} \\ \hline \dfrac{157}{3}   &amp; \dfrac{14}{9}       &amp;   \dfrac{485}{9} &amp; \dfrac{457{9}  \\ \hline \dfrac{704}{25}      &amp; 3      &amp;   \dfrac{779}{25} &amp; \dfrac{625}{25}     \\ \hline \end{tabular} \end{document}
I'm new with LaTeX and I'm trying to make a table with the elements centered vertically and horizontally. I've searched for this question, it seems like most people were trying to do things a little more complicated than this, resulting in complicated answers I couldn't understand. The table below is already centered horizontally, but the elements are aligned to the top of the cells instead of the center. How do I fix this?      \begin{tabular}{*{5}{|c}|}         \hline         $p$ &amp; $q$ &amp; $p \land q$ &amp; $p \lor q$ &amp; $p \to q$\\         \hline         T &amp; T &amp; T &amp; T &amp; T\\         \hline         T &amp; F &amp; F &amp; T &amp; F\\         \hline         F &amp; T &amp; F &amp; T &amp; T\\         \hline         F &amp; F &amp; F &amp; F &amp; T\\         \hline     \end{tabular}
I've been trying to change the language of my LaTeX document by replacing \usepackage[swedish]{babel} with \usepackage[english]{babel} but I only get this message:  ! Package babel Error: You haven't loaded the option swedish yet.   I've read in an other question at this forum that compiling enough would solve the problem, but that doesn't work for me. Does anyone know what I should do? Badge symbol in notification is of the site you're on, not where badge was earned Block quote with big quotation marks Caption above subtables with subcaption package breaks numbering of following table In the context of topological spaces, I see the following major countability properties:  A space is:   "separable" iff it has a countable dense subset "second countable" iff if has a countable basis "first countable" iff the neighbourhood system of every point has a countable local basis.   (Definitions taken from Counterexamples in Topology by Steen and Seebach, 2nd ed. 1978 -- there may be differences in wording from other sources.)  The question I have is: "separable" into what, exactly? By which I mean to say: what is the thinking behind calling such a condition "separable"?  It appears not to be related to the concept of "separation axioms", which do immediately and obviously invoke an intuitive notation of separation, neither does it seem to have anything to do with "separated sets".  (Anyone using the spelling "seperable" or "seperated" will be immediately downvoted. :-) ) What are some strategies that I can employ to handle a power gamer that constantly outshines the rest of the party? This is a friend of us all and we don't want to boot him, but combat simply isn't fun when the party has nothing to do while he mops up an encounter by himself. Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space? I have a non homework related question from a text and require a nice clear proof/disproof please  Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space?  my ideas:  if $H$ is the subset of the topological space $X$  if the subset is closed in the closed subspace, the complement is open in the subspace, which means the complement is of form $U\cap H$ for some $U$ open in $X$  if the subspace is closed the complement is open which means complement of $H=U$ for some open $U$ in $X$  kind thanks Favorites improvements - search, categorize, personal tags, add note, favorite answer I'm a big fan of the favorites feature. I usually mark questions with good answers of code snippets for later use.  Most of the time I can't find the favorite I'm looking for so quickly as desired. I know I marked the question in Stack Overflow, but it takes time to find it again, because of the following reasons:   lot of favorites lot of answers for a question (last time I was looking for an answer in the question ) the question title is not always what I'm looking for   To make favorites more useful I suggest the following features to be added:   Allow to mark an answer as favorite Allow to tag questions with own tags (those tags are personal and can not be seen by others) Search function over favorites Allow to add a personal note to a question The sum of an uncountable number of positive numbers Claim: If $(x_\alpha)_{\alpha\in A}$ is a collection of real numbers $x_\alpha\in [0,\infty]$ such that $\sum_{\alpha\in A}x_\alpha&lt;\infty$, then $x_\alpha=0$ for all but at most countably many $\alpha\in A$ ($A$ need not be countable).  Proof: Let $\sum_{\alpha\in A}x_\alpha=M&lt;\infty$. Consider $S_n=\{\alpha\in A \mid x_\alpha&gt;1/n\}$.  Then $M\geq\sum_{\alpha\in S_n}x_\alpha&gt;\sum_{\alpha\in S_n}1/n=\frac{N}{n}$, where $N\in\mathbb{N}\cup\{\infty\}$ is the number of elements in $S_n$.  Thus $S_n$ has at most $Mn$ elements.   Hence $\{\alpha\in A \mid x_\alpha&gt;0\}=\bigcup_{n\in\mathbb{N}}S_n$ is countable as the countable union of finite sets. $\square$  First, is my proof correct? Second, are there more concise/elegant proofs? What is the best way to dump entire objects to a log in C#? I just spent the last 10 minutes trying to put a new set of grips on to my mountain bike handlebars..  The old ones came off fairly agreeably and I've got the new ones 80-90% of the way on, however, at this point both my hands are stinging from the aggressive twisting and pushing - I have tried gloves, but I feel it's best left till my hands don't hurt anymore.  Is there a tried and tested way of doing this? Or is there a knack to this that I am missing? A 2x2 matrix $M$ exists. Suppose $M^3=0$ show that (I want proof) $M^2=0$ So, if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$ means $1=ax+by$, and want to show $a^2x+b^2y=1$. By squaring $1=ax+by$ both sides, I get, $1=(ax)^2+b(2axby+by^2)$. It doesn't help my proof. Please help me with this proof. I can show that for $x &gt; 0$ and $r_{i} &gt; 0$ we have $$ \left(\, x + r_{1}\,\right)\ldots\left(\, x + r_{n}\,\right)\ \geq\ \left[\, x + \left(\, r_{1}\ldots r_{n}\,\right)^{1/n}\,\right]^{n}.$$ However, I can't do this using straight up induction, strong or weak. Can someone do this?   You can show the inequality holds for $n$ if it holds for $n+1$ using $r_{n+1} = (r_1 \cdots r_n)^{1/n}$, so going down isn't a problem, but going up has eluded me. Additionally, you can show that if it holds for $n=a$ and $n=b$ then it holds for $n=ab$. Using powers of two and the above is sort of a way to prove the above by induction but it certainly isn't "normal".  You can also prove the above using Lagrange multipliers (which isn't surprising). The last proof I know is where you compare coefficients of $x^k$ and use the AM-GM inequality. I have been working with a string[] array in C# that gets returned from a function call. I could possibly cast to a Generic collection, but I was wondering if there was a better way to do it, possibly by using a temp array.  What is the best way to remove duplicates from a C# array? Calculate Euler equations of fluid dynamics without division? Removing non numeric characters from a string How can I install a Canon printer or scanner driver? I tried to install the MP190 drivers, but appeared a message show me that requires to have libcupsys2. I understand that libcup2 is an update of libcupsys2.   How do I solve this? Are there proprietary drivers for my Canon printer or scanner? I have a dataset for which I have multiple sets of binary labels. For each set of labels, I train a classifier, evaluating it by cross-validation. I want to reduce dimensionality using principal component analysis (PCA). My question is:  Is it possible to do the PCA once for the whole dataset and then use the new dataset of lower dimensionality for cross-validation as described above? Or do I need to do a separate PCA for every training set (which would mean doing a separate PCA for every classifier and for every cross-validation fold)?  On one hand, the PCA does not make any use of the labels. On the other hand, it does use the test data to do the transformation, so I am afraid it could bias the results.  I should mention that in addition to saving me some work, doing the PCA once on the whole dataset would allow me to visualize the dataset for all label sets at once. If I have a different PCA for each label set, I would need to visualize each label set separately. How to get the Runtime-Type of an Object dynamically (for Primitive Data Types and SObjects) Is it possible to get the Type of an Object (it's not an SObject)?  String s = 'test'; doSomething(s);  public static void doSomething(o Object) {     // need to find out if o is a string or an integer     type = IsThereAMethodToGetTheTypeOf(o) // ?     if(type='String') {         // do something for strings here ....     } else {         // do something else ....     } }   I think the Type class can't help me, because it has no way to get the type of an existing object instance, right? Any there any other way?  Since there is most likely no perfect solution possible within the current platform limitations, I posted an Idea on IdeaExchange here:   For SObject I have already this  public static string getType(SObject obj) {     if(obj==null) return '';     return obj.getSObjectType().getDescribe().getName()+''; }