Is GRP a subcategory of SET, or not?
Category of Grp is not a subcategory of Set
Can you Start Skyrim 'silent' without the launcher showing up? Is there a way to view Google Chrome browsing history past three months ago? I'm trying to find a page I looked at months ago but it looks like it's disappeared off the face of the planet. I thought I would have better luck looking through my Google Chrome browsing history, but I can't see history past September. Can I force Google Chrome to display history further into the past? Can I retrieve the history manually from a directory? Is the history data gone? Cron Job not working in plugin I have written a plugin that will convert posts to excel format and then email the .xls to an email id. I can make it work with when function is declared in functions.php but does not work with function defined in plugin file.   if ( ! wp_next_scheduled( 'xls_func_hook1' ) ) {   wp_schedule_event( time(), 'hourly', 'xls_func_hook1' ); }  add_action( 'xls_func_hook1', 'sendxls1' ); //senxls1 is a function in functions.php if ( ! wp_next_scheduled( 'xls_func_hook2' ) ) {    wp_schedule_event( time(), 'hourly', 'xls_func_hook2' ); } add_action( 'xls_func_hook2', 'export2excel' );   The full code is at Why an abstract class implementing an interface can miss the declaration/implementation of one of the interface's methods? It's not like there's anything else to do.   Shouldn't the speaker say: "There's something else to do." ? so what's the meaning of the sentence and what's the difference between the two of them? Thank you, Find a plane that passes through a point and is perpendicular to 2 planes Tasks in custom Environment I need to wrap a tasks environment inside a custom \NewEnviron. Apparently, tasks chokes on code besides its \task or \item due to the , presumably causing it to do so on \BODY. Any way to get around this? Exact error given is "Something's wrong--perhaps a missing \item", as per:  \documentclass[a4paper]{book} \usepackage{environ} \usepackage[more]{tasks}  \NewTasks[style=enumerate,counter-format=tsk[1]),label-width=2ex]{mytaskenum}[\item](3) \NewEnviron{mytaskenv}[1][Exercises]{   % Misc. stuff to precede the tasks env here   \begin{mytaskenum}   \BODY   \end{mytaskenum}   % Misc. stuff to follow }{}  \begin{document}  \begin{mytaskenv}   \item item 1   \item item 2   \item item 3 \end{mytaskenv}  \end{document} Let $S=\{1,2,3,4,\dotsc,N\}$ and $X=\{ f: S \rightarrow S \mid x < y \Rightarrow f(x)\leqslant f(y)\}$. Then $|X|$ is equal to what? How to install World of Warcraft? C++ template typedef Footnote to an item in a description environment It seems like it's not possible to put footnote inside a description list item.  For example in the following code first footnote appears at the bottom of the page, but the second - doesn't:  \documentclass[a4paper,12pt]{article}  \begin{document}     Text text text.\footnote{This footnote is working}     \begin{description}         \item[Label\footnote{This footnote is not working}] Some description     \end{description} \end{document}   Why it's not working this way? And is there any way to put footnote to a list item? There have been a few questions regarding installing this package in the past, but they now seem to be out of date. I'm using MiKTeX 2.9 and TexMaker. When I try \usepackage{mathtools} in TexMaker it will try to install the package for me but will fail. I took the advice given in this thread:   As suggested I tried installing the mh package using the MiKTeX Package Manager, unfortunately I get the "unknown archive size" error, which I have read means that the package no longer exists. Another thread (lost the link) said you can use the MiKTeX Package Manager to directly install mathtools, however I do not see mathtools listed anywhere in the MiKTeX Package Manager...   So I ask, is the package under a different name? Are there any other ways to install this package? 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. Extended Rigid Bodies in Special Relativity I was reading Landau &amp; Lifshitz's Classical Theory of Fields and I noticed that they mention that an extended rigid body isn't "relativistically correct".   For example, if you consider a rigid rod and apply a torque at one end, by definition of being rigid, the whole body must start rotating at the same instant. But the information about the force being applied cannot travel faster than the speed of light.   The book hasn't mentioned how to resolve this paradox, and after thinking about it for a while, I'm wondering if one can even define a rigid body in a relativistically correct manner.  To summarize: How does one define a rigid body in special relativity? I'm aware that this one is far from yes or no question, but I'd like to know which techniques do you prefer in categorical data analysis - i.e. cross tabulation with two categorical variables.  I've come up with:    &chi;2 test - well, this is quite self-explanatory  Fisher's exact test - when n &lt; 40, Yates' continuity correction - when n > 40,  Cramer's V - measure of association for tables which have more than 2 x 2 cells, &Phi; coefficient - measure of association for 2 x 2 tables, contingency coefficient (C) - measure of association for n x n tables, odds ratio - independence of two categorical variables, McNemar marginal homogeniety test,   And my question here is: Which statistical techniques for cross-tabulated data (two categorical variables) do you consider relevant (and why)? Equation of the locus of the foot of perpendicular from any focus upon any tangent to the ellipse ${x^2\over a^2}+{y^2\over b^2}=1$ Find the equation of the locus of the foot of perpendicular from any focus upon any tangent to the ellipse ${x^2\over a^2}+{y^2\over b^2}=1$. will it also be an ellipse? I have three displays, a 4K display flanked by two 1080p displays. Physically, these monitors are roughly the same size. Furthermore, Windows 10 handles the DPI scaling of the 4K monitor separately from the 1080p monitors just fine. So while it appears as such to Windows    the real layout is three monitors of equal size side by side.  The problem is that the mouse keeps getting caught on the edges of display 2 and three when dragging from display 1. I would like the mouse to continue onto display 2 or 3 regardless of which part of the left or right edge of display 1 the mouse touches.  This question has been asked before (e.g. ) and a common answer is to suggest that this behaviour is intentional on the basis that mouse movement should reflect different size displays. Such an answer is not appropriate as it doesn't consider DPI and scaling. Finding a formula to sum natural numbers up to $n$ Possible Duplicate:          I got this question in homework:  Find an expression for the sum ‫‪     $\sum k = 1 +\cdots + n‬‬$.    and prove it using an induction.   I'm not even near finding the expression. What I did notice is that if $n$ is (for example) 5 then the sum would be   $5^2 - 4^2 + 3^2 - 2^2 + 1^2$  So the first number is always positive and from there on the sign changes.  Any tips on how do I contintue from this point on, assuming I'm in the right direction?  Thanks! I got a integrated GD, which is Intel, and another discrete GD, AMD Radeon 6490 HD I am using ubuntu 11.10  1st, when I boot into Windows, my GD is indeed AMD Radeon 6490 HD, but when I boot into Ubuntu, it shows that I have AMD Radeon 6470 instead.  2nd, I try most methods only to install driver for my AMD/ATI graphic card. First by jockey(fail, boot with unity 2D instead) and install manually (fail, boot into blank screen).   3rd, I give up using the AMD/ATI graphic card. Then I got a new problem. Both my graphic cards are powered on on startup, which causes my laptop to over heat.   I view the content of /sys/kernel/debug/vgaswitcheroo/switch  0:DIS: :Pwr:0000:01:00.0 1:IGD:+:Pwr:0000:00:02.0   Then I switch off IGD using echo OFF &gt; /sys/kernel/debug/vgaswitcheroo/switch and I get  0:DIS: :Off:0000:01:00.0 1:IGD:+:Pwr:0000:00:02.0   But after I reboot, the discrete graphic card is powered on again. How to solve this? List of generally believed conjectures which cannot all be true There are some conjectures which most leading experts believe in albeit no one can prove it yet. For example: $\mathcal{P} \neq \mathcal{NP}$, the Riemann hypothesis or the Collatz conjecture.  My question is whether there is a set of such conjectures which cannot all be true, eg. is a statement such as "Either $\mathcal{P} = \mathcal{NP}$ or the Riemann hypothesis is wrong" true?