In the end, the table should look like     How to make the top row with "Team sheet" span more than one column? This is how far I came:
I want to create a table like this using Latex        ---------------------------------       |               sets            |       ---------------------------------       | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | --------------------------------------- | I1  | * |   | * | * |   | * |   | * | ---------------------------------------   Here is what I wrote  \begin{table} \caption{Multiprogram sets} \label{multiprogram}  \begin{tabular}{| c | c | c | c | c | c | c | c | c |}   \cline{3-9}   \multicolumn{8}{}{}    &amp;   Sets  \\   \hline   \multicolumn{1}{}{}   &amp; 1 &amp; 2 &amp;  3 &amp; 4 &amp; 5 &amp;  6 &amp; 7  &amp; 8 \\   \hline    astar         &amp;  &amp; * &amp;  &amp; * &amp;  &amp;  &amp; * &amp;   \\   \hline  \end{tabular} \end{table}   But it doesn't work! The output look like            -----------------------------                                  sets | ---------------------------------------         1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | --------------------------------------- | I1  | * |   | * | * |   | * |   | * | ---------------------------------------   Any way to fix that?
SEO preference: does a site with WWW rank better than without WWW? After having read various articles on this site about WWW or Non-WWW website setup, ,  and , and after having setup a correct redirection rule in .Htaccess to at least eliminate duplicate contents (currently the non-www solution (e.g. http://example.com) I have a feeling that my site rank less since I changed this.   My confusion was strengthened by these two opponents:     &amp;     Could the change of www.example.com >> http://example.com have a factual impact on ranking?  say either is better or worse. Are they holding information back?  I am confused fellow folks...  As much as I would like to separate facts from fiction, I am aware that not all the good valid information is written. Not on google webmaster site and perhaps not elsewhere. If so it seems out of date!  Does or does not a WWW domain impact SEO/rank better than its NON-WWW version? (Given that you have setup a proper redirect to avoid duplicates and go with one) 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! How do I find out the user name and password for an existing account? Which characters are valid in CSS class names/selectors? What characters/symbols are allowed within the CSS class selectors? I know that the following characters are invalid, but what characters are valid?  ~ ! @ $ % ^ &amp; * ( ) + = , . / ' ; : " ? &gt; &lt; [ ] \ { } | ` # What are the limits of house-elf apparition? I know Wizards can't apparate where they want on the Earth, except if they are very powerful but what about a house-elf ? Their magic is different so I was wondering if they can apparate wherever they want or if they have a limit too. Up arrow under a sequence Is there a single word to describe a solution that hasn't been optimized? What functionality do 'marks' offer in the El Capitan Terminal? Since upgrading to OS X El Capitan, I've noticed a change in the Terminal: Executed lines show an opening bracket on the left, and a closing bracket on the right, as shown in this screenshot:    Similar questions have been asked here:          Some of the questions are referring to these brackets as marks, and the Terminal's Edit menu has a couple of entries related to marks, for example:   Edit > Marks > Mark as Prompt and Send Return Edit > Clear to Previous Mark Edit > Navigate > Jump to Previous Mark     Is there a summary of what these marks can be used for? I have not seen any reference to this new feature in any of the El Capitan feature overviews. What does the explicit keyword mean? What does the explicit keyword mean in C++? How to fix "Headers already sent" error in PHP Comparison theorem for ODE Here is something I'm trying to prove:     Conjecture: Suppose $f'(x) \leq \phi(f(x), x)$ and $f(a)=\alpha$. Suppose $g'(x)=\phi(g(x),x)$ and $g(a)\geq \alpha$. Then $f(x)\leq  g(x)\,\,\forall x$.   It definitely seems like it should be true, and I don't think we even need continuity of $\phi$.  (Edit: a user has correctly pointed out that we should require $\phi$ be locally Lipshitz in the first variable, uniformly with respect to the second variable. Let's add that assumption.)   I can prove it in the case that the inequality is strict. I'll place my proof below the fold. How can I extend it to weak inequality?  If it's wrong, I'd love to see a counterexample. A reference is fine; I have the book by Teschl, for example.  A similar question with stronger assumptions was asked .     Proposition: Suppose Suppose $f'(x) &lt; \phi(f(x), x)$ and $f(a)=\alpha$. Suppose $g'(x)=\phi(g(x),x)$ and $g(a)\geq \alpha$. Then $f(x)\leq  g(x)\,\,\forall x$.  Proof: Suppose not. Suppose WLOG there is a $b&gt;a$ such that $f(b)&gt;g(b)$. Let $c:=\inf \{x&gt;a:f(x)&gt;g(x)\}$. By definition of the derivative we have $f'(c)\geq g'(c)$, a contradiction, since $f'(c)&lt;\phi(f(c),c)=\phi(g(c),c))=g'(c)$. RSA: Fast factorization of N if d and e are known Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials? Let $ A, B $ be two square matrices of order $n$. Do $ AB $ and $ BA $ have same minimal and characteristic polynomials?   I have a proof only if $ A$ or $ B $ is invertible. Is it true for all cases? Convert particle system to animated meshes How to implement Enums in Ruby? What's the best way to implement the enum idiom in Ruby? I'm looking for something which I can use (almost) like the Java/C# enums. If $f(x)$ is continuous on $[a,b]$ and $M=\max \; |f(x)|$, is $M=\lim \limits_{n\to\infty} \left(\int_a^b|f(x)|^n\,\mathrm dx\right)^{1/n}$? Auto increment filename I have a need to collect some duplicate files and want to avoid name collisions. The problem is that this collection of files might be added to by another execution of my script before the files are cleaned out and just want to continue to increment the number.  I decided on a simple until loop to increment the number like so.  until [[ ! -f ${PWD}/DUPES/${num}-$1 ]]; do num=$((num +1)) done mv --no-clobber $1 ${PWD}/DUPES/${num}-$1   I can't imagine ever exceeding 1k files in an extreme example, so my questions are...  Is this a terribly inefficient way to achieve this? Should I be parsing the existing files to get the highest leading number to start incrementing from there, or is this ok for the extreme example I put forth?  Or is there a better way all together? Extract URLs from text in PHP Tools to get a pictorial function call graph of code The special linear group $\text{SL}_n(\mathbb{R})$ is its own commutator Let $SL_n(\mathbb{R})$ be the set of $n\times n$ matrix with determinant one. Where can I find a proof that $[SL_n(\mathbb{R}),SL_n(\mathbb{R})]=SL_n(\mathbb{R})$? I've seen this result mentioned in several places, but couldn't find a proof.  For reference, the commutator $[SL_n(\mathbb{R}),SL_n(\mathbb{R})]$ is defined as the group generated by the set of all elements of the form $a^{-1}b^{-1}ab$, with $a,b\in SL_n(\mathbb{R})$.