So, I heard that all speed is relative. And that nothing can travel faster than light. Then I guess it is OK for a spaceship to leave Earth at 0.6c constant speed. And what if an other spaceship were to leave Earth at 0.6c in the opposite spacial direction. Then the relative speed between the two ships would be 1.2c, which is greater than c. How would that work out? Maybe something with time dilation?
Let's say I fire a bus through space at (almost) the speed of light in vacuum. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus toward the front, does that mean I'm traveling faster than the speed of light? (Relative to Earth that I just took off from.)
Joint distribution of a Normal and Truncated Normal I have a random variable $X\sim \text{Normal}(\mu,\sigma)$ and have the transformation $Y=\max\{0,X\}$.  Is the distribution of $Y$ a truncated normal where it is truncated to live on the positive half of the real line?  Secondly, is there a closed form solution for the joint distribution of a Normal random variable and a truncated Normal random variable? How can I access the "Open command window here" option in Windows without holding shift? Cannot install Ubuntu in VirtualBox due to "this kernel requires an x86-64 CPU, but only detects an i686 CPU, unable to boot" error I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space of state functions, from where this arises? and why 2-order space that assumes the following inner product:  $\langle\phi|\psi\rangle =\int\phi^{*}\psi\,dx$  While there is many ways to define the inner product.  In Physics books, this always assumed as given, never explains it, also I tried to read some abstract math books on this things, and found some concepts like "Metric weight" that will be minimized in such spaces, even so I don't really understand what is behind that, so why $L_2$? what special about them? Who and how physicists understood that those are the one we need to use? If $a_1, a_2, ..., a_n$ is a reduced residue system $\mod p$ and $a_1', a_2', ..., a_n'$ is another reduced residue system $\mod p$ then $a_1 a_1', a_2 a_2', ..., a_n a_n'$  is not a reduced modulo system $\mod p$.  Not able to show a counter to it. Help Needed. The sum $\sum_{k=1}^nk(k!)$ can be easily calculated by noting $k(k!)=(k+1)!-k!$. Is there a way to calculate the sum nicely using a combinatorial argument. Is it possible to notice it is $(n+1)!-1$ combinatorially? On iPhone it's very easy to clone an app (running multiple copies of the app on the same device); e.g.:    Is it possible to do this on Android? About the structure of ''There are/is'' I want to discuss the structure of ''There are/is''. First of all, what is the difference between:  There are three children.  and  Three children exist.  Do they have the same meaning? And secondly, In my native language, we would say that  Üç çocuk vardır.  &quot;Üç çocuk&quot; = Three children, &quot;var&quot; = existence (something  that exists, a being), and &quot;dır&quot; is a copula. So basically, this structure is not different from -for example- ''three children is a car''. ''a car'' and ''existence'' have the same function. But ın English, that structure that I have mentioned is confusing for me. I know that you are all used to it. Some can say ''What's the problem with that? It is just ''there are'' and ''there is.'' ''. I realize that I still did not ask a question. Well, let me try to ask a good one, I guess. Normally, ''there'' means a place where I am not in that place. Is there any relevance between ''there'' that means a place where I am not in that place AND ''There'' that is used in the structure of ''There are/is''? What kind of structure is this? By the way, I am new in English. Please excuse my naive usage of language. What do you think about it? How to prove this inequality $\left|x\sin{\frac{1}{x}}-y\sin{\frac{1}{y}}\right|<2\sqrt{|x-y|}$? For any real numbers $x,y\neq 0$,show that $$\left|x\sin{\dfrac{1}{x}}-y\sin{\dfrac{1}{y}}\right|&lt;2\sqrt{|x-y|}$$ I found this problem when I dealt with . But I can't prove it. Maybe the constant $2$ on the right hand side can be replaced by the better constant $\sqrt{2}$? Thank you. I use the code below to produce handouts of my presentations.  When I open the resulting pdf with any pdf viewer, it is viewed correctly, but when I print it, it is always printed very small, no matter the program I use (Okular, Evince, Acrobat...). Bonus to anyone that can make the pdf be printed correctly by Okular under Ubuntu! Thanks!  MWE here:  \documentclass[handout]{beamer} \usepackage{pgfpages} \pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm] \setbeameroption{show notes on second screen=bottom}  \setbeamercolor{background canvas}{bg=pink}  \mode&lt;presentation&gt; {     \usetheme{Singapore} } \begin{document}   \begin{frame}[plain]     \titlepage   \note{     Notes for the title page } \end{frame}   \section*{Outline} \begin{frame}[plain] \frametitle{Outline}     \tableofcontents  \note{     Notes for the table of contents } \end{frame}   EDIT:   If I place the line "\pgfpagesuselayout{2 on 1}" after the line "\setbeameroption{show notes}" I do not experience the printing problem anymore!! However, the slide preview and notes that appear at the bottom belong to the NEXT SLIDE, instead of to the CURRENT SLIDE!! What is going on with that? Notify close voters when a closed question gets edited As mentioned in , a question closed because it was not well-phrased is currently very unlikely to be reopened after an edit clarifying the issues. Those who voted to close should at least be asked to reconsider and reopen the question after such an edit. Customize feed on stack exchange android app QGLWidget appears black in Windows 7 C++ single template specialisation with multiple template parameters Prove that $\bigcap_{k = 1}^\infty C_k$ is also compact and connected. Let $X$ be a Hausdorff space and let $C_0 \supset C_1 \supset ...$ be a decreasing sequence of compact connected subsets of $X$.  Prove that $\bigcap_{k = 1}^\infty C_k$ is also compact and connected.  I have the compact part.  Just don't know how to show it is connected. Show that any prime divisor of $x^4+x^3+x^2+x+1$, with $x\in\mathbb{N}$, is $5$ or $1$ mod $5$ We can write the "polynomial" as follows: $$x^4+x^3+x^2+x+1=\frac{x^5-1}{x-1}.$$ For even $x=2y$, we have that $x^5-1=(2y)^5-1=32y^5-1\equiv1$ mod $5$.  For odd $x=2y+1$, we have that $(2y+1)^5-1\equiv_532y^5\equiv2$ mod $5$.  I find it hard to believe my computations above. I guess this makes me rather clueless. I was hoping there was some way out with Legendre symbols. Any help is appreciated. With the last update of Fallout Shelter, Bethesda has added these "limited time" quests.  Question is, how limited is that time exactly? What happens when the quests "end", will it still be possible to get the benefits? IS or ARE? "The only thing that I want you to hit right now IS/ARE the books" The use of nominative "whom" (as in “persons whom it is foreseeable are likely to...”) From  page 48 of Law: A Very Short Introduction, by Raymond Wacks:     In other words, you owe a duty to persons whom it is foreseeable are likely to be harmed by your conduct.   To try to parse this, temporarily overlook 'it is foreseeable'. Then persons is the subject of the verb phrase are likely to be harmed. So , should the relative pronoun for persons be who instead? Is my parse wrong?   Are the (deleted) comments right: that this style predominates in law texts? If this is correct grammar, what is the general rule? Is it commonly used in other contexts? Exporting 2D vector graphic from ArcScene to Illustrator How can I export 2d vector graphic from ArcScene so I can edit it with Adobe Illustrator? I've tried changing the options when I export 2D scene as AI file or PDF file, but they always remain as a unique image that does not allow me to edit the lines and polygons.