Would forcing a photon to travel under $c$ even after it leaves a medium break Relativity?
Does slowing light violate relativity?
Why aren't search engines indexing my content? This is a general, community wiki  question and answer pair intended to address any questions   concerning the reasons a site or specific site contents do not appear   in search engine results.      If your question was closed as a duplicate of this question and you   feel that the information provided here does not provide a sufficient   answer, please open a discussion on .   My site (or specific pages on my site) is not appearing in search engine results.  Why isn't my content indexed and what can I do about it? Simple enough question: is there some shell command (or GUI method) I can use that, given the path to a file on my system, tells me what package put it there? Assuming the file did in fact come from a package, that is.  Bonus question: what if it's a file that isn't installed on my system? Is there, say, a website that will let me look up a file and see what packages, if any, provide it? How to wait in bash for several subprocesses to finish and return exit code !=0 when any subprocess ends with code !=0? How to wait in a bash script for several subprocesses spawned from that script to finish and return exit code !=0 when any of the subprocesses ends with code !=0 ?  Simple script:  #!/bin/bash for i in `seq 0 9`; do   doCalculations $i &amp; done wait   The above script will wait for all 10 spawned subprocesses, but it will always give exit status 0 (see help wait). How can I modify this script so it will discover exit statuses of spawned subprocesses and return exit code 1 when any of subprocesses ends with code !=0?  Is there any better solution for that than collecting PIDs of the subprocesses, wait for them in order and sum exit statuses? Finishing a proof: $f$ is injective if and only if it has a left inverse I've already done a lot of searching (in particular: ) to try to prove this statement:      $f: A \to B$ is injective if and only if it has a left inverse. [I'm going to also assume $A$ and $B$ are nonempty.]   My attempt so far:     $\Leftarrow$ Suppose $f$ has a left inverse and $f(a_1) = f(a_2)$ for    $a_1, a_2 \in A$. Then there is a function $g: B \to A$ such that   $g\left(f(a_1)\right) = a_1$ and $g\left(f(a_2)\right) = a_2$. Since   $g$ is well-defined, it follows that $g\left(f(a_1)\right) =  g\left(f(a_2)\right)$, and hence $a_1 = a_2$.         $\Rightarrow$Now   suppose $f$ is injective. Then $f(a_1) = f(a_2) \implies a_1 = a_2$.   Furthermore, since $A$ is nonempty, there is an element $x \in A$.   Define $g: B \to A$ by  \begin{equation*} g(b) = \begin{cases}  f^{-1}(b), &amp; b \in \text{Im}(f) \\ x, &amp; b \in A \setminus  \text{Im}(f)\text{.} \end{cases} \end{equation*} This mapping is   well-defined, since if $f$ is injective, $f^{-1}(b)$ is unique.   My main question: does this imply that if $f: A \to B$ is injective that any mapping $g: \text{Im}(f) \to A$ is bijective? Otherwise, I don't understand why we can even use $f^{-1}$ on an element. [Please read the link above for more details - in proof 1.] Wayne Dalton Garage So I recent had a Garage door "professional" come out to my house and look at my garage. I originally thought I was having a motor problem because it would only lift door sporadically. After performing a 25 point inspection he believed he located the problem, which was the spring system from my Wayne Dalton Garage (torquemaster). He told me how horrible of a system they are and they don't fix them because of that they only replace the entire system and would cost me $700 or more. So now I'm left trying to figure out what I need, torquemaster springs, bracket assembly, both or if I need something completely else. I need some experience Wayne Dalton experience. Live USB "Check disk for defects” finds defects but doesn't list them I downloaded the iso file for XUbuntu. I created a live usb using Pen Drive Linux. I turned on my computer, booted to the XUbuntu installation screen, and selected "check disk for defects".  A minute later, it says that it found one defect. How do I figure out what this defect is? Mean absolute error OR root mean squared error? Why use Root Mean Squared Error (RMSE) instead of Mean Absolute Error (MAE)??    Hi  I've been investigating the error generated in a calculation - I initially calculated the error as a Root Mean Normalised Squared Error.  Looking a little closer, I see the effects of squaring the error gives more weight to larger errors than smaller ones, skewing the error estimate towards the odd outlier. This is quite obvious in retrospect.   So my question - in what instance would the Root Mean Squared Error be a more appropriate measure of error than the Mean Absolute Error? The latter seems more appropriate to me or am I missing something?  To illustrate this I have attached an example below:                    The scatter plot shows two variables with a good correlation,  the two histograms to the right chart the error between Y(observed ) and Y(predicted) using normalised RMSE (top) and MAE (bottom).     There are no significant outliers in this data and MAE gives a lower error than RMSE. Is there any rational, other than MAE being preferable, for using one measure of error over the other? For example, if I have a lens that is 16mm-50mm, which focal length would be the closest to the human eye's view? (I don't have a camera yet, so I'm just curious.)   Would 50mm be more zoomed in than "normal"?  I imagine 16mm would be wider than the normal human point of view? Toggle Switch to swap the connections of two buttons A bold plus symbol in math mode How to get the file name and a line number of a function call? Calculating distance of sites to riverways using ArcGIS Desktop? How do you calculate the distance of about 10 sites scattered across a region to bodies of water (rivers and lakes) using ArcGIS 10.1?  I have the lat/lon coordinates of the 10 sites as a point feature class and I have downloaded the Surface Water Area (polygon shapefile) for the study  area from the UK Ordnance Survey webpage.  I want to determine the easiest route-ways that are available in the study area by taking into account slope and proximity to rivers. I understand that I can achieve this by running a cost path analysis if I have a dem raster, slope raster and distance rasters to rivers and valley floors. But I am not sure how to create distance rasters to rivers and valley floors using Spatial analyst tools. The official currency of Hungary is the Forint but so far everything I have looked for prices online, such as trains, buses and taxis, are quoted in Euros and Forints. Hotel reservation asked that I pay in Euros at the hotel. Considering that I will only spend a few days in Budapest, are Forints necessary? Or can I pay for transport, admissions and food in Euros? In such a case, how is the conversion rate set? Cite_key instead of a number, what is going on? I have the following problem: I correctly obtain a numbered bibliography at the end but along the text the cite_key appear instead of a number. How to fix this problem?   \documentclass[11pt]{book}  \usepackage[]{biblatex} \begin{document} %some text  ... \cite{ABKM2015}... %some text  \begin{thebibliography}{99} \bibitem{ABKM2015} Arroja, F. and Bartolo, N. and Karmakar P. and Matarrese, S. (2015). \newblock The Two Faces of Mimetic Horndeski Gravity             \newblock {\em ArXiV}, 1506.08575 (2015). \end{thebibliography} \end{document}   After compiling I get ... [ABKM2015] ... while I want for example  [1]. What item bonuses apply to my follower? There are a lot of different side effects an item can have, and I assume that things like magic find have no influence on any of "our" found items at all.  However, I'm not sure about other things. For example:   Do followers get life-steal on weapons, too? Does increased orb healing make any difference? What about +experience after kills? Will my follower level up faster?   and probably a lot more.  Is there some general rule as to what effects of an item apply to followers, and which don't? Why must a final variable be initialized before constructor completes? When should you use WP_Query vs query_posts() vs get_posts()? It seems like half the tutorials in the  and around the blogosphere use  and half use . They all do similar things, so when should I use one over the others? What does "Could not find or load main class" mean? Let $x\in \mathbb{R}$ an irrational number. Define $X=\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$. Prove that $X$ is dense on $[0,1)$.    Can anyone give some hint to solve this problem? I tried contradiction but could not reach a proof.  I spend part of the day studying this question   and its answers. Only one answer is clear and give clues to solve the problem. This answer is the first one. However, this answer does not answer the question nor directly, nor the proof follows from this answer.   This answer has some mistakes, he use that $[(k_1-k_2)\alpha]=[k_1\alpha]-[k_2\alpha]$ which is not true. Consider $k_1=3, k_2=1, \alpha=\sqrt{2}$ we have $[(k_1-k_2)\alpha]=2\not= 3=[k_1\alpha]-[k_2\alpha] $. We only can assure that $[k_2\alpha]-[k_1\alpha]-1\leq [(k_2-k_1)\alpha]\leq[k_2\alpha]-[k_1\alpha]$.   Who answered said something interesting about additive subgroups of $\mathbb{R}$, but unfortunately the set $X=\{nx-[nx] : n\in \mathbb{N} \}$ is not a subgroup. Considering the additive subgroup $G=\langle X \rangle$, if we prove the part (a) of the link, we get that indeed $G$ is dense on $\mathbb{R}$ but we can not conclude that $X$ is dense on $[0,1)$.  I think this problem has not been solved.  Thanks! Do cards with abilities that target trigger heroic?