Writing List To Text File
Writing a list to a file with Python
Assume $f:A\to A'$ is a function, $B\subset A'$, $C\subset A'$, and $f^{-1}(B\cap C)=\emptyset$  How can we see that $f^{-1}(B)\cap f^{-1}(C)=\emptyset$? for any ring $A$ the matrix ring $M_n(A)$ is simple if and only if $A$ is simple Let integer $n\geq 1$. I have obtained that for any field $k$, the matrix ring $M_n(k)$ is simple, i.e., $M_n(k)$ contains no nonzero proper two sided ideals. Now I want to prove that: for any ring $A$ (not necessarily commutative), the matrix ring $M_n(A)$ is simple if and only if $A$ is simple.   How to prove? Which damage dice exactly does the Great Weapon Fighting fighting style allow you to reroll? Get the name of an object's type "Within" and "in" when referring to time I know that both can mean "inside" but what I don't have clear is whether both mean the same when talking about time. For example:   The party is in two days = The party is within two days ??   According to this link  within means a limit that can be exceeded, so I'm wondering too if say "the party is within two days max" is correct or redundant. I would like to make cross references to own defined counter on environments. So far I have tried the following,   \documentclass{book} \newcounter{entryc}[subsection] \newcommand{\thetheorem}{\thesubsection.\arabic{entryc}} \newenvironment{qd}[1]{\refstepcounter{entryc}\noindent\textbf{Quasi Definition \thetheorem.}\begin{itshape}} {\end{itshape}} % \begin{document}  \chapter{First chapter} This is the first chapter.  \section{First section} This is the first section.  \subsection{First subsection} This is the first subsection.  \begin{qd}{}\label{qd:emp} This is my environment. \end{qd}  \noindent In quasi definition \ref{qd:emp} it \dots  \end{document}   What happens is that     But I would prefer "...In quasi definition 1.1.1.1". Do anyone have some suggestions of how solve this? and How to avoid the          \noindent  thing before the continuation of the text?   Additional information: if possible I would try to not use ntheorem. When I open the file in Vim, I see strange ^M characters.  Unfortunately, the world's favorite search engine does not do well with special characters in queries, so I'm asking here:   What is this ^M character? How could it have got there? How do I get rid of it? Trying to run , embedded Tomcat instance fails.  Error seems to appear here:    Apr 17, 2015 2:13:47 AM org.apache.catalina.startup.HostConfig deployDescriptor  INFO: Deploying configuration descriptor /opt/OpenForisCalc/calc-server/tomcat/conf/Catalina/localhost/calc.xml  Apr 17, 2015 2:13:58 AM org.apache.catalina.core.StandardContext startInternal   SEVERE: Error listenerStart   Then if messes up with the rest (this repeats a lot):  Apr 17, 2015 2:13:58 AM org.apache.catalina.core.StandardContext startInternal  SEVERE: Context [/calc] startup failed due to previous errors Print floating point values without leading zero How to recover a deleted NTFS partition with data I am on Ubuntu 12.04 64-bits  I accidentally deleted a NTFS 255 GB partition using Gparted, and yes it contains LOTS of important data.  Upon realizing the deletion I haven't yet created any file-system on it. So it still shows Unallocated.    I tried Testdisk , but it shows entire partitions created from the beginning.  This sdb is my secondary drive with Xubuntu and Kubuntu on it. And that 255 GB NTFS  partition was cross platform storage drive.  I am currently in sda with Ubuntu and Win7 in dual boot, which enables me to use it as Safe recovery option rather then Live USB drive.   First ,  should i allocate it to ? file-System for better recovery .  Second , i really need to recover data from this drive so please give me possible  suggestions and proven methods of data recovery.  Third ,does Testdisk requires deleted partition to be allocated for its recovery .  I am currently trying the answer seen here  with Testdisk scanning for partition second time, hoping to recover it.   It looks a duplicate but i can't confirm if the OP got it right. Since my first doubt is to allocate it or not.  If any clarification required please do comment ,i will add it.  Edit: TestDisk deeper search results.      The following partitions can't be recovered:          Partition               Start        End    Size in sectors     &gt;  HPFS - NTFS          22241 107 11 55592   3 27  535777280        FAT32 LBA            274460 158 19 460576 228 16 2989957948  NTFS, 274 GB / 255 GiB &amp; for FAT32 LBA 1530 GB / 1425 GiB How do you prove a number is prime? I am a software engineer but try to keep up with maths as I really enjoyed the subject at school. I just saw a great TED talk:   The talk states that the current largest known prime is $2^{57885161}-1$  This got me thinking - how does one actually prove whether a number this large is prime or not?  Is it just done by brute force via a computer algorithm or are there any well known mathematical techniques for doing so?  I would be really grateful for any pointers as I am eager to learn about these techniques (if they exist). Throwing errors on a standard page layout using Apex! Scenario: I have a custom button on a standard layout, which will call an apex class to do some validation on a record. If not validated, it needs to throw out some errors on that page. What are the best UX options to achieve this?  I am not too sure how to achieve this. Within a trigger, you can use the addError method to add the custom errors.  Can my Apex class reference the fields of a standard object? The ideal approach would be to do the following:  Contact.Email.addError('Please enter the right format here');   How can I achieve this via an apex class that the custom button will call?  What I have thought: Having a VF Page popup on the screen so that user can see all the errors, but that's not the best approach as UX is a big deal for this application  Thanks. Why is you subjective? (Catchy title, eh?)  I am asking the following on the photo.SE site:     How do you change from portrait to landscape in Lightroom   DANGER! DANGER! This appears to be subjective and is likely to be closed.  If I ask the following radically different question:     How do I change from portrait to landscape in Lightroom   ... there is no problem.  So, like the title says: Why is "you" subjective?  (And  where Jeff spills the regex) Pre-image of a measurable set A is always measurable? Let $f$ be a continuous function on a set $E$.  Is it always true that $f^{-1}(A)$ is always measurable if $A$ is measurable?  I say no.  We know that $\bar{\psi(x)}:=\frac{\phi(x)+x}{2}$ where $\phi$ is the Cantor (or Cantor-Lebesgue) function and $\bar{\psi}:[0,1] \rightarrow [0,1]$.  We know this function maps a measurable subset of $C$ (the Cantor set) into a non-measurable set $W$.  A few observations about $\bar{\psi(x)}$.  It is strictly increasing and continuous, so it has a continuous inverse $\bar{\psi(x)}^{-1}$.  Thus $\bar{\psi(x)}^{-1}(W)=c \subset C$; that is, $\bar{\psi(x)}^{-1}(W)$ is non-measurable, but c is.  Is this correct? How to deal with downvotes without any explanation When I try to delete the file, using the GUI it says      The action cannot be completed because the file is open in another   program   And using the del /f /q command line it says     Access is denied   I have tried unlocking the file with Unlocker, as well as trying to locate which process is using the file with the Resource Monitor or the Process Explorer, but no locking handle was found in either case.  I am able to rename or move the file, but not to delete it or change its content. Looking for succinct way of describing the act of solidifying an idea into reality Looking for a succinct way of describing the act of solidifying an idea into reality. "Building [idea] out" seems too generic but I'm trying to avoid a long winded, step by step explanation of the process.  Any ideas would be greatly appreciated. Thanks! I am on a MacBook Pro 13 running latest Sierra. I have an external Seagate solid state hard drive that was working and out of the blue stopped working. The only thing on it was my Adobe Lightroom images/videos. Not the LR DB files. I'm sure you have all heard this woe before, so I won't dwell on that. And yes, I back up to the cloud. AWS S3 specifically. Though I am traveling South East Asia for the last year, and staying in cheap hostels. So good internet is hard to come by sometimes. I can't back it up after every export. While most of it is backed up, there is some that is not.  Moving on. The symptoms seems to change every time I plug it in. The first sign was it ejected on it's own. I plugged it in again, and it wouldn't mount. Disk Utility recognized it, so did the command line diskutil list but it wouldn't mount. I rebooted and it worked for a second. Then I could only get to it from the command line. Then trying to frantically back up to my local what was not backed up to the cloud, it all failed. Basically just a cp -R [directory] [local-directory] command.  After some more frantic unplugging and re-plugging plus some command line manual mounts, I finally got it to where the Disk Utility would be able to run first aid on it. It failed. I don't recall the error. So I put it in a freezer. After a few hours I tried again. It is not any better. It still will not mount. Now Disk Utility sees it, but with no partition. I can't even give me information about how much space is used on it.  I have also tried it from a Windows machine. It did not mount. I have tried other cables. No success. As well as tried my other USB port. I also have another working external hard drive exactly like the one giving me issues. It works on all cables and USB ports.  I do have Docker running with a Ubuntu container, I'm trying to think of a way to see if I can try to get to the USB from there. I also have a USB that I have thought about running a live Ubuntu on there to see if I can mount and retrieve the data or fix the HDD that way. But if it will not mount, I doubt these will work.  Can anyone else think of any other tricks I can try myself to see if I can repair this or at least retrieve the data without paying for a service or software? If not, those suggestions are also welcome.  Update   I made the mistake in original post that it was a Solid State Drive. This is my mistake, it is actually a spinning disk hard drive. I bought them long ago and have been traveling with them for so long I just forgot. Question is updated to reflect this. Now diskutil list does not show it at all. The Disk Utility app also does not see it. Based on suggestion from @Allen I seeked out the USB to SATA cable. I did not quite find it, as my options are extremely limited where I am at. Though a local expat on a facebook group was able to help me with a empty 2.5 casing that I was able to extract the drive from original casing and put it in his blank case. It now mounts. Though it has the "click of death" sound to it. And data is not really reachable. While I can ls the directories and Adobe Lightroom does not have the exclamation mark when it can not reach the actual external files. Right clicking on the images and clicking on "Show in Finder" or any other variation of trying to get to the files through Finder or terminal, I have no success. It usually hangs and I get the spinning wheel. Since Adobe Lightroom imports these images into directories named by date, I am going to send the drive off to a data recovery service and ask to recover just unbacked up directories i.e. dates. Next time I will make harder efforts to backup and probably get an actual SSD.   I think this can be closed, due to my low reputation points I can not close this myself. How do I find the length of an array? Is the Ubuntu Phone available anywhere yet? I want start developing apps.  I am very impatient to start to develop on real ubuntu phone.