Does $\langle ( 1 ,3), (1, 2 ... ,10)\rangle$ generate the group $S_{10}?$
Prove or disprove: $S_{10} = \langle (1,3),(1,2, ... ,10) \rangle$
Not flying the first leg of the journey – Company cancels the second-leg ticket I've a friend that booked a round-trip journey. He booked A-to-B and B-to-A. Somehow he needed to be earlier at location B, so he took a train and did not take the flight from A to B.  When he went to the airport to take the "back home" flight (B-to-A), he was informed that his ticket was canceled because he did not take the A-to-B flight. They canceled the ticket and sold it to someone else.  Is this normal? The company said it was their right to do so, and he could not get the flight back. The company was Iberia. Blackboard bold characters The blackboard bold font in the AMSFonts package only has capital letters.  I sometimes wish to use a blackboard bold "1", for which I can use \usepackage{bbold}. But this changes the entire blackboard bold font, and I like the original AMSFonts versions of the capital letters better.  Is there a simple way for me to get \mathbb{1} from one package and the blackboard bold capitals from another? I'm using PostGIS 1.5.2, with geometries in SRID:900913. I need create a circles using a list of points as centre, with a radius of 600 kilometers. I'm using this query:  INSERT INTO circles (geom) (    SELECT ST_Buffer(point, 600000, 'quad_segs=8')     FROM points );   But circles created have not 600 kilometers of radius (radius is near this length, but not exactly).  Are there other methods to create circles in PostGIS?  NOTE: Information represented is from Spain. Correct projection is 4326, but client use Google rasters, so I am storing data in 900913 to avoid reprojections and increase performance. How would you explain covariance to someone who understands only the mean? ...assuming that I'm able to augment their knowledge about variance in an intuitive fashion (  ) or by saying: It's the average distance of the data values from the 'mean' - and since variance is in square units, we take the square root to keep the units same and that is called standard deviation.  Let's assume this much is articulated and (hopefully) understood by the 'receiver'. Now what is covariance and how would one explain it in simple English without the use of any mathematical terms/formulae? (I.e., intuitive explanation. ;)  Please note: I do know the formulae and the math behind the concept. I want to be able to 'explain' the same in an easy to understand fashion, without including the math; i.e., what does 'covariance' even mean? Can Cycles use multiple UV layers? How to handle ordinal categorical variable as independent variable I am using a logit model. My dependent variable is binary. However I have an independent variable which is categorical and contains the responses: 1.very good, 2.good, 3.average, 4.poor and 5.very poor. So, it is ordinal ("quantitative categorical"). I am not sure how to handle this in the model. I am using gretl.  [Note from @ttnphns: Although the question says the model is logit (because the dependent is categorical), the crucial issue - ordinal independent variables - is basically alike, be the dependent categorical or quantitative. Therefore the question is equally relevant to, say, linear regression too - as it is to logistic regression or other logit model.] I'm looking into developing an ordering app for a potential client. The main part that I'm concerned about in this question is the payment mechanism. I would assume that there are already multiple plugins or similar programs out there, but I'm not sure where (or if) I should be asking for recommendations. Finding volume of a segment What's interesting in latus rectum? I'm a maths teacher in Italian secondary school and I've been spending some time trying to construct "meaningful" problems about conic sections. I particularly like problems which focus on practical applications of the curves (in engineering, physics, finance, etc.), on their geometric properties, or both.  I know there's this really easy formula to find the latus rectum of a conic from its key parameters. It's quite nice and straightforward to derive it, but...  ... What's its use? Why should anyone be interested in knowing the latus rectum of a curve? Is there any physical phenomenon, any architectural trick, or anything else where its position and/or length plays a key role?   I know just the relation between angular momentum, standard gravitational parameter and latus rectum in an astronomical orbit ($l=\frac{h^2}{GM}$, where $l$ is half the latus rectum, and $h$ is the ratio between the angular momentum associated to the orbiting body and its mass). It's cool, but a bit tricky, and probably too far-fetched for secondary school students... Is there anything simpler? Or just anything else, at any difficulty level?  Many thanks! How do I disable auto-maximizing of newly launched windows in GNOME? Each time I open any application, it zooms to fill-up the entire desktop and so I am always forced to use "Unmaximize" using Alt+Space menu. Option clash for package xcolor I'm writing a report, and have a rather large table in my appendix. I'd like to emphasize some specific values by coloring some single cells. I'm trying to do it with xcolor. But receiving the error:  ! LaTeX Error: Option clash for package xcolor. See the LaTeX manual or LaTeX Companion for explanation. Type H &lt;return&gt; for immediate help. ... l.17 The package xcolor has already been loaded with options: [] There has now been an attempt to load it with options [table]   My preamble looks as follows  \documentclass[a4paper,oneside,article]{memoir} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage[danish]{babel} \usepackage{lmodern} \usepackage{graphicx}     \graphicspath{{Figures/}} \usepackage{fullpage} \usepackage{modroman} \usepackage{float} \usepackage{caption} \usepackage[numbers]{natbib} \usepackage{url} \usepackage{pgfplots} \usepackage{mathtools} \usepackage[table]{xcolor}   And take out of my table  \begin{table}  \centering   \begin{tabular}{|c|c|c|}        \hline    \cellcolor{green!25}D &amp; x &amp; D/$L_0$ \\        \hline    65 &amp; 2600 &amp; 0,417\\        \hline    60 &amp; 2400 &amp; 0,385\\   \end{tabular}  \caption{Bestemmelse af bølgehøjde}  \label{tab:Q1} \end{table}   Read some other questions asking more or less the same. And the answer to them seems to be a "collision" between packages. I have no idea how to find the problem. So my question is:   Where is the "collision"? How on earth would I have found it without help ? How can I see flags I cast from all sites? If $n^c\in\mathbb N$ for every $n\in\mathbb N$, then $c$ is a non-negative integer? Supposing that a real number $c$ is given, is the following true?  "If $n^c$ is a natural number for every natural number $n$, then $c$ is a non-negative integer."  Though this seems true, I can't prove that. Can anyone help? We hold an L1 visa (Citizens of India) and are planning a cruise to the Bahamas this summer. Are there any Visa requirements to enter Bahamas. I am trying to remove the Facebook and Messenger apps from my Asus Zenphone Laser 2.  Unfortunately, in both cases, I seem to be unable to find the option to fully delete them from the device. I have disabled them, but the app management screen now shows the following:     How can I fully delete/uninstall them? Mothballs in the pantry: is it safe to keep food there? My roommate put some mothballs in the pantry and when I came home and saw them, I took them out.  They were probably only there for a few hours, but is it safe to store food in there?  Should I throw out the food that was in there together with the mothballs?  I'm leaning towards 'when in doubt throw it out' but I'm unsure whether that is overkill in this case. Determine all of the accumulation points of the following sets in $\mathbb{R}^1$ and decide whether the sets are open or closed or neither.  The set $X$ of all numbers of the form $2^{-n} + 5^{-m}$ where $m,n = 1,2,\ldots$.   Claim: The set of accumulation points is the following: $$\left\{\frac{1}{2^n}: n \in \mathbb{N} \right\} \cup \left\{\frac{1}{5^n}: n \in \mathbb{N}\right\} \cup \{0\}.$$ Let $n \in \Bbb{N}$ and $r&gt;0$, and consider the open neighbourhood $B\left(\frac{1}{2^n},r\right) = \left(\frac{1}{2^n} - r,\frac{1}{2^n} + r\right)$. For the given $r$ we can find $m$ large enough such that $5^{-m} &lt; r \implies \frac{1}{2^n} + \frac{1}{5^m} &lt; \frac{1}{2^n} + r$, and $\frac{1}{2^n} - \frac{1}{5^m} &gt; \frac{1}{2^n} - r$; therefore $5^{-m} + 2^{-n} \in B\left(\frac{1}{2^n},r\right)$. A similar argument shows that each element of $\{5^{-m}: m \in \mathbb{N}\} \cup \{0\}$ is an accumulation point of $X$. Now consider $y \in X$. $B(y,r)$ isn't a subset of $X$ since for all $r &gt; 0$, $B(y,r) \subset (\mathbb{R} - \mathbb{Q}) \not\subset \Bbb{Q}$, hence $B(y,r) \not\subset X$. How to download Bootcamp drivers without Bootcamp assistant? Detect if program is running with full administrator rights Are logs kept for past at jobs?