Show that if $r$ is nilpotent in a ring with identity, then $1-r$ is a unit in $R$
Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
Biber 2.14 - Puzzling repeated error : "Invalid format '2020-01-01' of date field 'date' - ignoring" Can't format / delete locked partition from GParted? Inequality $\left(a-1+\frac{1}b\right)\left(b-1+\frac{1}c\right)\left(c-1+\frac{1}a\right)\leq1$ Here are some tips for tagging questions. These guidelines will help you more accurately tag your questions, which in turn will help them get more attention and lead to better answers faster.     For more information, see "" in the . Based on newtons third law If an elephant can apply 250N force and a rabbit can apply 25N force , and if they are pulling each other , then elephant will pull with 250N force and according to newtons third law the rabbit should also pull the elephant with 250N force.then from where do the rabbit got the extra 225N i.e.(250-25=225) force??? can anyone please explain. I am trying to rotate a dual monitor which is attached to the VGA output of my laptop. My system is Ubuntu 15.10.  However, here is the outcome I get when I use xrandr:  xrandr --output VGA-1-0 --rotate right xrandr: output VGA-1-0 cannot use rotation "right" reflection "none"   I have seen other posts on this subject, which all recommend editing xorg.conf. I have tried that, too. Here's my current xorg.conf file:  Section "ServerLayout" Identifier "layout" Screen 0 "nvidia" Inactive "intel" EndSection  Section "Device" Identifier "intel" Driver "modesetting" BusID "PCI:0@0:2:0" Option "AccelMethod" "None" Option "RandRRotation" "True" EndSection  Section "Screen" Identifier "intel" Device "intel" EndSection  Section "Device" Identifier "nvidia" Driver "nvidia" BusID "PCI:1@0:0:0" Option "ConstrainCursor" "off" Option "RandRRotation" "True" EndSection  Section "Screen" Identifier "nvidia" Device "nvidia" Option "AllowEmptyInitialConfiguration" "on" Option "IgnoreDisplayDevices" "CRT" Option "RandRRotation" "True" EndSection   Still, I keep getting the same error when trying to use xrandr to rotate that screen.   Is there another way of doing so? Quantum mechanics and everyday nature Is there a phenomenon visible to the naked eye that requires quantum mechanics to be satisfactorily explained? I am looking for a sort of quantic Newtonian apple. Is there a way to set transparency of windows in GNOME? Chrome is unable to connect to the Internet I'm getting the error code: DNS_PROBE_FINISHED_NO_INTERNET in Google Chrome. The thing is, I have a working internet connection. I am posting this using that connection, using Internet Explorer. It's only Chrome doing this.  What happened was my laptop was refusing to go to sleep mode, so it ended up running out of battery power. I charged it, and when I subsequently booted the computer, Chrome stopped working. I don't see the connection...  I added Firewall rules (inbound/outbound) to allow Chrome to connect...so unless I'm missing something.  UPDATE: Chrome portable is working for me...just not the regular chrome.  UPDATE 2 Now I realize it had to do with Covenant Eyes which I have installed. See the accepted answer Cannot invoke method or retrieve property from null object. Object returned by the following call stack is null. \"File\r\n\" When to use icons vs. icons with text vs. just text links? This might seem like a very simple question, but what is the easiest way to turn a normal vertical list into a horizontal one? Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.) What is this sand covered insect? I have found in a wooden house, in the mountains of central Spain this very curious insect:    I was wondering if that was its skin or whether it's decomposition or sand or saw-dust.  That particular region of Spain does have stink-bugs ... but this one doesn't look like anything I've seen before.  A google image search returns mostly arachnids ... but it seems to have only 6 legs. Print lines between (and excluding) two patterns I'm going to submit form using cURL, where some of the contents is come from other file, selected using sed  If param1 is line matching pattern from other file using sed, below command will works fine:  curl -d param1="$(sed -n '/matchpattern/p' file.txt)" -d param2=value2 http://example.com/submit   Now, go to the problem. I want show only text between 2 matching pattern excluding the matching pattern itself.  Lets say file.txt contains:  Bla bla bla firstmatch It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout. secondmatch The point of using Lorem Ipsum is that it has a more-or-less normal distribution of letters, as opposed to using 'Content here, content here', making it look like readable English.   Currently, lots of "beetween 2 matching pattern" sed command won't remove firstmatch and secondmatch.  I want the result to become:  It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout. I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force holding a subatomic particle together? What keeps mass in it's state? I hope this is not a silly question but I am clueless. Thanks How do I hide Thunderbird from the launcher while running? I have a question for you all.  It's possible to "hide" thunderbird from the unity application bar when thunderbird is running?  For my is unhelpfull see thunderbird on the "mail" tray ( near shutdown button) and the unity "running" application.  If i close thunder with the close button, it don't notify me new email. How do I counter-knife an enemy? When you press down the right stick to counter the attack, do you just press it, repeatedly press it, or press and hold? I've been knifed a few times from the front and each time I try to counter I fail. Also, if you believe you are about to be knifed and hold down the right stick until you are knifed, will that counter an attack, or do you have to press it down just at the right time? Looking at the kids which - or that/who? We look at the kids which/that/who skillfully use tablets with the help of their small fingers and we understand that to surprise the younger generation will be more difficult each year.   Is the relative pronoun which acceptable here, or does it look totally out of place, because it befits a "non-restrictive relative clause" more?   It seems to me that the pronoun that looks best in the bolded position, with who an acceptable second choice. But it's hard to pin down why. How to write conditional equations with one-sided curly brackets I want to write a conditional expression such as the following.    What is the best way to express such conditional expressions in Latex?