Unable to install lxde on ubuntu 18.04
Unable to correct problems, you have held broken packages
Suppose $\sqrt6 = \frac pq$ where $p$ and $q$ have no common factors.  $$6 = \frac {p^2}{q^2}$$  $$6p^2 = q^2$$  So $q^2$ and therefore $q$ is divisible by $6$.   $$p^2 = \frac {q^2}{6}$$  So $p^2$ and therefore $p$ is divisible by $6$.   S0, $p$ and $q$ have a common factor $6$. Contradiction.  Therefore $\sqrt6$ is irrational.  Does the proof work? Is there a difference between copy initialization and direct initialization? Very good linear algebra book. I plan to self-study linear algebra this summer. I am sorta already familiar with vectors, vector spaces and subspaces and I am really interested in everything about matrices (diagonalization, ...), linear maps and their matrix representation and eigenvectors and eigenvalues. I am looking for a book that handles every of the aforementioned topics in details. I also want to build a solid basis of the mathematical way of thinking to get ready to an exciting abstract algebra next semester, so my main aim is to work on proofs for somehow hard problems. I got Lang's "Intro. to Linear Algebra" and it is too easy, superficial.  Can you advise me a good book for all of the above? Please take into consideration that it is for self-study, so that it' gotta work on its own. Thanks. Is there any way to specify a suggested filename when using data: URI? If for example you follow the link:  data:application/octet-stream;base64,SGVsbG8=  The browser will prompt you to download a file consisting of the data held as base64 in the hyperlink itself.  Is there any way of suggesting a default name in the markup?  If not, is there a JavaScript solution? Can unconscious characters be willing? This situation came up last week during our session. The party was facing a pretty difficult mob of enemies and one of the party members was knocked unconscious. Seeing the situation worsening, one of the players decided to use the  (DMG p. 197). In the text, it says:     The rod then instantly transports you and up to 199 other willing creatures you can see to a paradise that exists in an extraplanar space.   At first glance I thought this was actually a pretty good time to use the rod. The question came up though, what about the party member who is unconscious? In the end I made the call that the character went with them to keep things moving and more fun.  However, I'm feeling like back pedaling a bit and notifying my players that for future uses, the line "... willing creatures..." will be more strictly enforced as I don't feel like an unconscious creature could be willing.  Did I handle this the right way? Office 2016 Advanced Setup Display keyboard without animation Are airlines in the EU obligated to provide water for passengers? curlicue letters with mathptmx package How to show letters like  with mathptmx package?  I'm using pdfLaTeX with mathptmx package becasue its gooding looking normal math font letters a-z, A-Z. However, if only with this package, \mathsrc{...} is reported as "undefiend sequence" and \mathcal{...} is curlicue style like the following:  \mathcal{F} shows . If I add \usepackage{mathrsfs}, \mathcal{F} and \mathscr{F} are the same as .  What I expect is \mathcal{F} shows  and \mathscr{F} show the one in previous line.   What should I adjust? I hope mathptmx package is still being used.  Minimal code script goes like that:  % using PdfLaTeX \documentclass[journal]{IEEEtran} \usepackage{amssymb,amsmath,amsfonts} \usepackage{mathptmx}  \usepackage{mathrsfs} \begin{document} $$\mathcal{F}$$ $$\mathscr{F}$$ they are the same \end{document} Image with axis Ping faster than light I just discovered very strange thing while testing my internet connection. My ping is smaller than it should be. For example ping time to Arizona State University is about 14ms.  eryk@eryk-pc:~$ ping www.asu.edu PING www.asu.edu.cdn.cloudflare.net (104.16.51.14) 56(84) bytes of data. 64 bytes from 104.16.51.14: icmp_seq=1 ttl=60 time=13.8 ms   I'm living in Poznań in Poland so my distance to Arizona State University in a straight line (very optimistic assumption) is about 10000 km. Considering the fact that ping time is a time for two directions (to the target and back to home). So my ping packet have to cross 20000 km distance. Speed of light is 300 000 km per second that is 300km per millisecond. So the smallest possible time to ping Arizona State University with my packet travelling at a speed of light is  20000/300=67ms   I have noticed similar results for servers located in Australia and some other States of America. Is my internet connection five times faster than light? Evaluate $\lim_{n \to \infty} \int_{0}^1 [x^n + (1-x)^n ]^{1/n} \ \mathrm{d}x$ Explaining Horizontal Shifting and Scaling I always find myself wanting for a clear explanation (to a college algebra student) for the fact that horizontal transformations of graphs work in the opposite way that one might expect.  For example, $f(x+1)$ is a horizontal shift to the left (a shift toward the negative side of the $x$-axis), whereas a cursory glance would cause one to suspect that adding a positive amount should shift in the positive direction. Similarly, $f(2x)$ causes the graph to shrink horizontally, not expand.  I generally explain this by saying $x$ is getting a "head start". For example, suppose $f(x)$ has a root at $x = 5$. The graph of $f(x+1)$ is getting a unit for free, and so we only need $x = 4$ to get the same output before as before (i.e. a root). Thus, the root that used to be at $x=5$ is now at $x=4$, which is a shift to the left.  My explanation seems to help some students and mystify others. I was hoping someone else in the community had an enlightening way to explain these phenomena. Again, I emphasize that the purpose is to strengthen the student's intuition; a rigorous algebraic approach is not what I'm looking for. Korea: Visa required to go to the city while in transit in Seoul for a Philippine citizen? Simple georeferenced 3D data format for building models it can not access popup.js file after creating a chrome extension Expected number of hamiltonian paths in a tournament The following theorem is from Alon&amp;Spencer's The probabilistic method, in the beginning of chapter 2:  Theorem 2.1.1: There is a tournament $T$ with $n$ vertices and at least $\frac{n!}{2^{n-1}}$ Hamiltonian paths.  Briefly the theorem is proved by looking at $X_\sigma$ the indicator random variable for a permutation $\sigma$ giving a Hamiltonian path, that is, satisfying $(\sigma(i),\sigma(i+1))\in T$ for $1\leq i \lt n$. Then   $\sum \mathbb{E}\left[X_\sigma\right] = \frac{n!}{2^{n-1}}$.  I don't understand where did this value ($\frac{n!}{2^{n-1}}$) came from! could someone explain it please? I keep hearing about tandem breakers, and how they won't work with 240V loads and how they should never be used for a multi-wire branch circuit.  Aside from those issues...  What is a tandem breaker?     (note: they can be thrown independently). Cannot see pictures on Stack Overflow In the 70's I had a stack of old Amateur Radio magazines (50s-60s), and for a long time I saved an article about using the  to combine a number of resistors to achieve a specific value. Does anyone recall and have a copy of this article, or know how the Euclidean algorithm is applied to solve this problem?