Are there any differences between Gnu sed's "i text" and "i\ ...." commands?
Extra Backslash Required in First Appended Newline in sed
Why does a minimal prime ideal consist of zerodivisors? Let $A$ be a commutative ring. Suppose $P \subset A$ is a minimal prime ideal. Then it is a theorem that $P$ consists of zero-divisors.  This can be proved using localization, when $A$ is noetherian: $A_P$ is local artinian, so every element of $PA_P$ is nilpotent.  Hence every element of $P$ is a zero-divisor. (As Matt E has observed, when $A$ is nonnoetherian, one can still use a similar argument: $PA_P$ is the only prime in $A_P$, hence is the radical of $A_P$ by elementary commutative algebra.)  Can this be proved without using localization? Here is what I tried doing:  #!/bin/sh res=`df | awk 'FNR == 2 { print $5 }'` res2=$((res+0))   Here is my error:     -bash: 53%: syntax error: operand expected (error token is "%")   I Googled 'string to int bash' which showed me $((res+0)) but it doesn't work due to the % in the string (53%). How do I convert it in such a way I can do an if statement such as the one below (but that works)?  if [ "$res2" -ge 50 ] then     echo "Your disk &gt;=50% full!" fi Is it correct to use "their" instead of "his or her"? Is this sentence grammatically correct?  Anyone who loves the English language should have a copy of this book in their bookcase.  or should it be:  Anyone who loves the English language should have a copy of this book in his or her bookcase. Show that $n$ lines separate the plane into $\frac{n^2+n+2}{2}$ regions Show that $n$ lines separate the plane into  $\frac{n^2+n+2}{2}$ regions if no two of these lines are parallel and no three pass through a common point.   I know we start with the base case, where, if we call the above equation P(n), P(0), for 0 lines would be 0.  But I really have no idea how to begin the inductive step.  How do we know what k+1 we're supposed to arrive at?  Thanks! How can I search an Excel spreadsheet in SharePoint? Looking to be able to search an Excel spreadsheet from the SharePoint mobile app.  I have a spreadsheet with Postal Codes/Zip Codes with corresponding information. I would like to be able to search as you would in Excel.  When I upload a test spreadsheet, it opens as like a PDF. User has "Read" permissions for the document library the spreadsheet is located in.  Thanks in advance, Schengen Visa for both business and tourism Why does the loss/accuracy fluctuate during the training? (Keras, LSTM) I have to design a circuit in which I have to transfer data through lasers (serial transmission of data). Now what I was thinking was to check if the laser light is on then '1' is passed and when the laser is off '0' would be passed. Now I need to check if a 1 or a 0 was passed.   How would I check for this and another problem I'm facing is if it's on it may keep on passing 1's. How would I check for this? I though of using LDR's (Light Dependent Resistors)? Would this be okay or it there a better method? How is canonicity of derivative works determined for Star Wars? Upgrade to the specific php 7.1/7.2 from php 7.0 in Ubuntu 16.04 How can I upgrade to php 7.1 from php 7.0 in ubuntu 16.04 ?  If I do a php -v I get this message:  PHP 7.0.8-0ubuntu0.16.04.3 (cli) ( NTS ) Copyright (c) 1997-2016 The PHP Group Zend Engine v3.0.0, Copyright (c) 1998-2016 Zend Technologies     with Zend OPcache v7.0.8-0ubuntu0.16.04.3, Copyright (c) 1999-2016, by Zend Technologies Is there a word for four times as much, analogous to once, twice, and thrice? Is there a word for 'four times as much', analogous to once, twice, and thrice? Injectivity of Homomorphism in Localization Let $\alpha:A\to B$ be a ring homomorphism, $Q\subset B$ a prime ideal, $P=\alpha^{-1}(Q)\subset A$ a prime ideal. Consider the natural map $\alpha_Q:A_P\to B_Q$ defined by $\alpha_Q(a/b)=\alpha(a)/\alpha(b)$. Suppose that $\alpha$ is injective. Then is $\alpha_Q$ always injective?    I think so, but I'm clearly being too dense to prove it! My argument goes as follows.  Let $\alpha(a)/\alpha(b)=0$. Then $\exists c \in B\setminus Q$ s.t. $c\alpha(a)=0$. If $B$ is a domain we are done. If not we must exhibit some $d\in A\setminus P$ s.t. $da=0$. Obviously this is true if $c =\alpha(d)$. But I don't see how I have any information to prove this!  Am I wrong and this is actually false? If so could someone show me the trivial counterexample I must be missing?   Many thanks! How can I resize an ext root partition at runtime? How can I increase the size of the root partition of a system at runtime?   I have a partition that is not allocated after the root partition (which is also ext4), how can I add that unallocated space to the space allocated to the root partition without having to shutdown the server? How many attacks can a fighter with two-weapon fighting make at 5th level? strtok segmentation fault Show that $f$ is differentiable on $(−1, 1)$. Let $f$ be a function defined on the interval $(−1, 1)$ such that for all $x, y \in (−1, 1)$, $$f(x + y) = \frac{{f(x) + f(y)}}{{1 - f(x)f(y)}}.$$ Suppose that $f$ is differentiable at $x = 0$, show that $f$ is differentiable on $(−1, 1)$.  Need your kind guidance and help. Thanks in advance! How would I go about identifying a port, card or connector on my system which I am unfamiliar with?  Where would I find information on what these parts are? What would be the steps I would take in identifying a unknown port or cable?   This question comes up frequently, and the suggested solutions are usually the same. This community wiki is an attempt to serve as the definitive, most comprehensive answer possible. Feel free to add your contributions via edits. Equation of a rectangle I need to graph a rectangle on the Cartesian coordinate system. Is there an equation for a rectangle? I can't find it anywhere. Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant I want to show that if a function $f:[a,b]\rightarrow \mathbb R$ satisfies a Hölder condition of order $\alpha &gt; 1 $ then it is constant.  The way I think of it is as follows:  $$|f(x) - f(y)| &lt; K|x-y|^\alpha$$  $$\frac{|f(x) - f(y)|} {|x-y]}  &lt; K|x-y|^{\alpha -1}$$  $$\lim_{y\rightarrow x} \frac{|f(x) - f(y)|} {|x-y]} \le \lim_{y\rightarrow x}  K|x-y|^{\alpha -1} =0 $$ As the limit is $0$, we can remove the modulus, so we get:  $$\lim_{y\rightarrow x} \frac{f(x) - f(y)} {x-y} = 0$$ So $f$ is derivable and $f'(x) = 0$ for all $x$ in $[a,b]$. Note that the reason we can add the limit $y\rightarrow x$ is because $[a,b]$ is closed in $\mathbb R$.  However, the question gives as a hint using the mean value theorem. I am not sure why one should do that. You would first have to prove that $f$ is derivable in a similar manner to what I did, and then prove that $f$ is constant. Or is there a simpler way to do it and I am missing it?  Also please inform me of any mistakes I did in the proof (if any)/ Thank you! There's a way to safely try KDE on top of an Ubuntu installation, keeping the possibility to revert the changes in case I dislike how it runs?