Consider the following LaTeX manuscript featuring a TikZ picture of a matrix with a single cell.  \documentclass[tikz]{standalone} \begin{document} \begin{tikzpicture}   \matrix[draw,nodes=draw]   {     \node {*}; \\   }; \end{tikzpicture} \end{document}   The resulting image is  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;  How can I adjust the padding surrounding the cell? For instance, suppose I wish to get rid of the padding all together. I attempted to add inner sep=0pt to the matrix's option list, but then not only did the padding surrounding the cell collapse, but also the padding surrounding the asterisk inside the cell:  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  P.S. If the matrix has more than one cell, I don't wish to alter the spacing between the rows or the spacing between the columns; only the padding inside the matrix that surrounds the entire grid of cells.
I want to draw a TikZ matrix with its border and I would like to define the distance between most external matrix nodes and matrix border. Something like a matrix inner sep. If I change inner sep in matrix options declaration, all nodes inside the matrix also change its inner separation.      I know how to do it with fit library. I just want to know if its possible without it.
Prove $3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$ if $x,y,z$ are positive real numbers,Prove:$$3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$$ Additional info:$\sum_{cyc}$ denotes sums over cyclic permutations of the symbols $x,y,z$. I'm looking for solutions and hint that using Cauchy-Schwarz and AM-GM because I have background in them.  Things I have done: Writing Left hand side in expanded form:$$LHS=3(\sum_{cyc}x^3y^3+\sum_{cyc}xy^4z+3x^2y^2z^2)$$ Right now I don't have good idea were to start(Is expanding and looking for AM-GM is good?).So any hint is appreciated. Source : This inequality can be found as Problem 42, page 13, in the book &quot;Old and New inequalities&quot; by Titu Andreescu, where it is attributed to Manlio Marangelli. RSA when N=pq and p = q Is there a secular, non vulgar alternative to "for heaven's sake"? I know for heaven's sake, for Pete's sake, for God's sake and for Christ's sake. All of those, however are religious references. The only non-religious equivalent phrases I know are for fuck's sake and its variations. Are there any non-vulgar, non-religious alternatives? I am very used to the general construct of for X's sake and am looking for something along the same lines that I could use in cases like  C'mon, it's just a scratch for X's sake! That's not even true for X's sake!  It does not need to also be applicable as a general exclamation of frustration (Oh, for chrissake!) but that would be nice. Basically, I'm looking for a synonym for the &quot;Oh come on!&quot; sense of for fuck's sake rather than the Oh shit! one.  EDIT: Since this has gotten quite a bit of attention, I would like to urge those who answer to read the entire question, not just the title. I am not just looking for polite swearwords but for something that can be used in the example phrases above. The boundary of union is the union of boundaries when the sets have disjoint closures Assume $\bar A\cap\bar B=\emptyset$. Is $\partial (A \cup B)=\partial A\cup\partial B$, where $\partial A$ and $\bar A$ mean the boundary set and closure of set $A$?   I can prove that $\partial (A \cup B)\subset \partial A\cup\partial B$ but for proving $\partial A\cup\partial B\subset \partial (A \cup B)$ it seems not trivial. I tried to show that for $x\in \partial A\cup\partial B$ WLOG, $x\in \partial A$ so $B(x)\cap A$ and $B(x)\cap A^c$ not equal to $\emptyset$ but it seems not enough to show the result. What happens to the Windows 7 key when upgrading to Windows 8? Microsoft is offering "Microsoft Windows 8 Professional Upgrade" at a discounted price compared to the OEM version. However it states:     If you currently have a personal computer running Windows 7, Windows XP or Windows Vista then you can upgrade to Windows 8 Pro (Professional).   My question is what happens to the Windows 7 key that I use to upgrade? Will it become the Windows 8 key or will it generate a new Windows 8 key?  Basically if I upgrade using my Windows 7 key from my laptop for my desktop will I be able to continue using the laptop on Windows 7 while concurrently using Windows 8 upgrade on my Desktop? Why do you need explicitly have the "self" argument in a Python method? Do I need a UK or Ireland transit visa when flying from the US to a Schengen country? Show that product of primes, $\prod_{k=1}^{\pi(n)} p_k < 4^n$ This an interesting problem my friend has been working on for a while now (I just saw it an hour ago, but could not come up with anything substantial besides some PMI attempts).  Here's the full problem:  Let $x_{1}, x_{2}, x_{3}, \cdots x_{y}$ be all the primes that are less than a given $n&gt;1,n \in \mathbb{N}$.   Prove that $$x_{1}x_{2}x_{3}\cdots x_{y} &lt; 4^n$$  Any ideas very much appreciated! What are Zombies and what causes them? Are there Zombie processes and Zombie objects? What the pointer size in 64 bits computer in C++? Would you please tell me which of the following terms is correct? If both are correct, are they equal?     I have no [...] I don't have any [...] How to burn or mount an ISO file? Would you take a share in Stack Overflow? Joel Spolsky has just posted  where he talks about seeking venture capital for Stack Overflow.  If instead they opted to seek shareholders from the StackOverflow community along the lines of the , but at a larger scale, would you be interested?  I'm asking this because I suspect there might be enough fanatics willing to invest $500 or so in a product they love to raise a considerable sum. People also often talk about the motivation for high rep users. It seems to me having an actual stake in the product might be a decent incentive (especially if you also get a gold badge for buying shares). How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$? Proof of this result related to Fibonacci numbers: $\begin{pmatrix}1&1\\1&0\end{pmatrix}^n=\begin{pmatrix}F_{n+1}&F_n\\F_n&F_{n-1}\end{pmatrix}$? $$\begin{pmatrix}1&amp;1\\1&amp;0\end{pmatrix}^n=\begin{pmatrix}F_{n+1}&amp;F_n\\F_n&amp;F_{n-1}\end{pmatrix}$$  Somebody has any idea how to go about proving this result? I know a proof by mathematical induction, but that, in my opinion, will be a verification of this result only. I tried to find through the net, but in vain, if someone has some link or pointer to its proof, please provide, I'll appreciate that.  Thanks a lot! How to iterate over arguments in a Bash script I have a complex command that I'd like to make a shell/bash script of.  I can write it in terms of $1 easily:  foo $1 args -o $1.ext   I want to be able to pass multiple input names to the script. What's the right way to do it?    And, of course, I want to handle filenames with spaces in them. What's the most popular way to encrypt individual files or folders? I'm an elected diamond moderator on one site, and a user of several others. I think it would be extremely helpful for our flagging process if users had the option to enter freeform text explaining their flag on types of flags other than the "in need of moderator attention" flag.  An example of when this is relevant: Sometimes posts have had rude/abusive flags, but the rude/abusive part might be difficult to notice, or it might be a single word or sentence buried somewhere in the middle of the post. Users have to choose between "flag it as rude with no explanation" or "flag it as misc and explain what's going on". Often they'll pick the first because of course it seems like what they should do (e.g. they know the system has special handling attached to rude/abusive flags) but it means they can't explain what's going on to us, so we have to reach out directly in private to find out.  Sometimes it also helps to be able to explain why a comment is no longer needed, because past experience tells me the "no longer needed" flag on its own might be declined on a particular site -- so I pick the custom reason instead of "no longer needed" just so I can provide explanation.  I'd prefer users be able to understand they can pick the appropriate reason and be able to attach any explanation they deem necessary to further direct moderators to the issue. If not for all kinds of flags, then at least for spam or rude/abusive flags. $X_n\leq Y_n$ implies $\liminf X_n \leq \liminf Y_n$ and $\limsup X_n \leq \limsup Y_n$ Can anyone prove this question? I tried but I didn't get any I idea, so I hope someone can solve it.     Let $X_n\leq Y_n$ for each $n\in \Bbb N$. Show that $\liminf X_n \leq \liminf Y_n$ and $\limsup X_n \leq \limsup Y_n$.   Please prove this question - thanks.  The definition I have:     Let $X_n$ be a sequence in real number and let $$E=\{x\in \Bbb R^\sharp:(X_{n_k}) \rightarrow x \text{ for some subsequence }(X_{n_k})\text{ of }(X_n)\}$$ for all $n \in \Bbb N$ and $k$ from $1$ to $\infty$. Then by definition $\lim\sup X_n = \sup E$ and $\lim\inf X_n = \inf E$. I am new to Salesforce and hence a lot of silly questions. What is the rational behind defining future methods as Static? I mean has these methods been not static what harm would have they caused?