I've searched many places and I can't find something close enough to my situation. Basically, I searched on other posts suggesting to use tabu instead of tabular because I would have to use \(content\) everywhere I have mathematical expressions.  How do I add equal spacing so that I can read the text.   Second, I want to split the cell above sin diagonally so that I can insert text that describes the first row and column. Thanks!  \documentclass{article}  \usepackage{mathtools} \usepackage{tabu}  \newcommand{\degree}{^\circ}  \begin{document}  \(   \begin{tabu}{|c|c|c|c|}      &amp; 30\degree &amp; 45\degree &amp; 60\degree \\ \hline     \sin \theta &amp; \dfrac{1}{2} &amp; \dfrac{\sqrt{2}}{2} &amp; \dfrac{\sqrt{3}}{2} \\ \hline     \cos \theta &amp; \dfrac{\sqrt{3}}{2} &amp; \dfrac{\sqrt{2}}{2} &amp; \dfrac{1}{2} \\ \hline     \tan \theta &amp; \dfrac{\sqrt{3}}{3} &amp; 1\vphantom{\dfrac{\sqrt{2}}{2}} &amp; \dfrac{1}{2} \\    \end{tabu} \)  \end{document}
How do you guys go about controlling column padding in tables?   Update  To clarify, I'm looking for a way to control both vertical and horizontal padding. So, if I had a simple table like in the following code snippet, I could pad the columns and make them look a bit less... ugly. :P   \begin{tabular}{|l|l|}     \hline     column 1 &amp; column 2 \\      \hline     I really would like this less &amp; crammed\\     \hline \end{tabular}   I tried this by using the command \vspace but it leaves gaps in the vertical lines.
I'm a begginer in blender, so please forgive me if the question looks silly to you!  Almost all the objects in my scene disappeared (except 2) as if I deleted them by mistake. The thing is all the objects are still listed in the right side graph. The all have the eye button activated, but yet nothing is visible anymore! As I don't have a backup file, I simply can't find any tricks to fix this...  Thank you for you help! What is the purpose of the /etc/shadow file in Linux Operating system?  Also, is it same for SUSE clients? There is one shadow cache file is maintained what is purpose of that? Allow converting comments to answers Allow converting comments to answers, so they can become accepted answers.  I asked a question. Someone commented on it, and it was an awesome comment that fully answered the question. As the original questioner, I would like to convert that comment to an answer in order to accept it.  Or, if you prefer, I would be okay with being able to simply mark the comment as accepted. I am working in Illustrator (15.0.2 (CS5) or 16.0.0 (CS6)) and when I try to move objects small distances, they snap to the nearest two pixels on some invisible grid. I can't find anything in the preferences. Here are some screen shots: new array.sty and colortbl.sty incompatibility? Server login attempts NOT blocked after configuring fail2ban Hyphenation in compound adjectives Possible Duplicates:                In the sentence "Portland is known to be one of the most bike friendly cities in the US", is a hyphen necessary in "bike friendly"? As far as I know, the hyphen is only required when leaving it out would cause ambiguity. Wikipedia uses the example of "a small appliance factory" vs "a small-appliance factory".   As far as I can tell, the sentence above is pretty clear. A quick google search for "bike friendly city" brings up instances of both hyphenated and non-hyphenated usage. Thoughts?  Please excuse the poor formatting, sent from my iPhone. Calculating well densities in selected counties using ArcPy? Let $\Gamma$ be a set of formulas and $\phi$ be a formula. Show that $\Gamma \cup \{\neg \phi\}$ is satisfiable if and only if $\Gamma\not \models \phi$.   This seemed pretty obvious but I wanted to see if my proof made sense:  Proof: $(\Rightarrow)$  To derive for a contradiction, suppose that: $\Gamma \models \phi$. That means for all truth assignments $v$, for $\gamma \in \Gamma$, if $v(\gamma) = T$, then $v(\phi) = T$.  But this contradicts our assumption that $\Gamma \cup \{\neg \phi \}$ is satisfiable by the fact that $v(\phi) = T$ cannot happen so: $\Gamma \not \models \phi$ .  $(\Leftarrow)$   So by the definition of $\Gamma \not \models \phi$, we have that there is some truth assignment $v$ which satisfies $\Gamma$ but does not satisfy $\phi$. So  that means $v(\phi) = F$ since $v(\phi) \not = T$ which implies that $v(\neg \phi) = T$ which means $v$ satisfies $\Gamma \cup \{\neg \phi\}$.    I feel like I'm missing something in the forward direction, but at the same time... It looks pretty trivial as well. Am I missing anything crucial?  Thank you! Why is mathematical induction a valid proof technique? Context: I'm studying for my discrete mathematics exam and I keep running into this question that I've failed to solve. The question is as follows.    Problem: The main form for normal induction over natural numbers $n$ takes the following form:   $P(1)$ is true, and for every $n, P(n-1)\to P(n).\qquad\qquad\qquad\text{[Sometimes written as $P(n)\to P(n+1)$]}$   If both 1 and 2 are true, then $P(n)$ is true for every $n$.  The question is to prove the correctness of the form above.    My work: My idea was to make a boolean statement and if it's a tautology in a true false table. That means the statement is always correct.  I've tried many times but I've failed.  Here is the original question in Hebrew:  n טענה כלשהי לגבי מםפר טבעי  $P(n)$ תהי   אם מתקימיים שני התנאים הבאים:  1- הטענה $P(0)$ נכונה  2- לכל n>0, $P(n)$ נכונות הטענה $P(n-1)$ גוררת את נכונות הטענה   אז $P(n)$ נכונה לכל מספר טבעי n  הוכיחו את נכונות משפט זה Let $K$ be a field and $f \in K[x]$ a polynomial of degree $n&gt;0$. Assume that $E$ is an extension of $K$ such that $f$ can be expressed as a product of linear factors over $E$:  $$f(x)=\gamma (x-\alpha_1)(x-\alpha_2)\dots(x-\alpha_n).$$  I want to show that $\lvert K(\alpha_1,\dots,\alpha_2) : K \rvert$ is a divisor of $n!$. I also want to show that if $\lvert K(\alpha_1,\dots,\alpha_n): K \geq (n-1)!$ then $f$ is irreducible over $K$ or $f$ already has a root in $K$.  The problem has a hint. It says: "Use induction on $n=\deg f$. If $f=gh$ in $K[x]$ with $\deg g =r$ and $\deg h=n-r$, then $r!(n-r)!$ is a divisor of $n!$.  Any idea for solving this problem would be appreciated. Is it possible to build a .dmg file (for distributing apps) from a non-Mac platform? And if yes, how? Why do we use $x - y$ rather than $x + y$ in the definition of the convolution? Is it just convention? (If we are thinking of convolutions as weighted averages, for instance against "good kernels," it should make no difference.)  Why $(f * g) (x) = \int f(y) g(x - y) dy$ rather than $(f * g) (x) = \int f(y) g(x + y) dy$?  Edit: I'm finding it really hard to choose a best answer. There are at least three very good ones here. Forward/Inverse Search Does Not work on certain tex files If you are hurrying to reply, System → Administration → StartUp Disk Creator -- no, that's not what I'm talking about.   I want to try Ubuntu 11.04's Unity without touching my existing Ubuntu install.  To do this, I need to install the nVidia drivers first (sigh).  To do this, I need changes to persist a reboot.  To do this, I need to really install Ubuntu on a USB key.  How do you do that?    What I tried   I tried to make a USB key from , then boot from it, then choose "Install Ubuntu." The installer refused to install to the installation media itself. I tried, from my installed copy of Ubuntu:  sudo kvm /dev/sdb --cdrom .cache/testdrive/iso/ubuntu_natty-desktop-i386.iso   ...but the installer didn't detect the disk properly. Calculate which day of the week a date falls in using modular arithmetic In  the main character (he is a mathematician) calculates the day of the week of someone's birthday (19/07/1992 is Sunday). I know (very) basic modular arithmetic but I can't figure out how to do it. Can someone point me to the right direction? It seems fun to do. I currently have a Yongnuo YN560-TX trigger and a Yongnuo YN-560 Mark III. I would like to get a iTTL flash that also works with remote triggering.  How compatible are are different flash brands (Neewer, Yongnuo, etc.) when it comes to things like setting zoom, etc. ? Does there exist a function such that $\lim_{x \to a} f(x) = L$ for all $a \in \mathbb R$ but $f(x)$ is never $L$? A book about explorers stranded on a planet with two computers I have been looking for a book that I read in the 80's but it's probably older. It was about a spaceship from Earth in a very long mission to discover life? I don't remember, but they had been far too long in space without any results, so the crew was on the verge of mutiny.  They land on a planet, home of two super-computers called...? Alpha? Beta? One seemed more advanced than the other, the planet was void of any other life, and supposedly it was forseen that the planet would be struck by a comet, and the computers see the ship as a way to save or abandon the planet before the impact.  At some point one member of the crew is captured by the computers, and it's vivisected in an attempt to get data about humans. Then they "reassemble" the crew member before returning it to the ship, hoping that the humans could "reactivate it" since the computers were unable to do so. Which of course enrages the ship's crew.  The ship was unable to take off for reason that I don't remember and they must fight the computers to save themselves.  Does anyone know what this is?  Thanks, as soon as I read the names, they did ring a bell on my memory. The case it's closed then. How does a Pokémon gain CP when evolving?