to forgive is a great value Forgiveness is a great value Forgiving is a great value  Does meaning change ? And why ? Grateful to your help
Could anyone explain when to use a noun or a gerund?  Are these sentences correct? What is the difference between usage of gerund and noun there?        I worked on the improvement of the article.   I worked on the article improving.   I worked on the improving of the article.                The investment idea was published.   Investing idea was published.
How can I use BibTeX to cite a web page? I'm looking to cite a number of web pages using bibtex and I was wondering if there was a specific template of the form @&lt;template name here&gt; for doing that. If you could use the following website as an example that would be great How can we find premade adventures for a virtual tabletop? Me and a couple of friends are just getting into P&amp;P rpgs and are really excited to try something new. However, we have a problem that we live quite far apart from each other. Therefore we'd like to use one of excellent virtual tabletops that are available. But none of us have any real experience with creating an adventure and would thus like to use a premade and beginner friendly adventure. But we're having a hard time finding one with premade story, maps etc in an online format. Most seem to be printed books and the Roll20 marketplace hasn't really gotten started yet. So what we're looking for a is online way to play a premade adventure to get us started in the RPG world.  How can we find these adventures for a VTT? Is there a way to add a timer to a Beamer presentation? I have seen presentations in Power Point which contain a timer. Can this be done in Beamer using a simple command, or maybe a package? If not a timer, is it possible to at least get a clock on your slides? How do I pass variables and data from PHP to JavaScript? Recommended way to initialize srand? Complete residue system proof I was given a proof of this in class, but it does not make sense to me, can someone provide a better proof, or explain the one I have provided, thanks.  Suppose $\gcd(a,n) = 1$, where $a$ and $n$ are natural numbers. Prove that $0$, $a$, $2a$, $3a,\ldots, (n-1)a$, is complete residue system modulo $n$.  Proof given in class:  \begin{align*} ka &amp;\equiv ra \pmod{n}\\ &amp;\Rightarrow  k \equiv r \pmod{n}\\ &amp;\Rightarrow  \text{$k-r$ divides $n$}\\ &amp;\Rightarrow \text{$k=r$ because $0\leq k\lt n$, $0\leq r\lt n$} \end{align*} Let $f(z)$ be entire function. Show that if $f(z)$ is real when $|z| = 1$, then $f(z)$ must be a constant function using Maximum Modulus theorem Let $f(z)$ be entire function. Consider the functions $e^{if(z)}$ and $e^{−if(z)}$ and applying the Maximum Modulus Theorem, show that if $f(z)$ is real when $|z| = 1$, then $f(z)$ must be a constant function.  (We take $f(z)=u(z)+iv(z)$)  I am confused as so far I have $|g(z)|=|e^{if(z)}|=|e^{-v(z)}|$ and then since $f(z)$ is real, $f(z)=u(z)$ and $v(z)=0$ so I assumed it would follow that $|g(z)|=|e^{v(z)}|=1$.  Similarly, $|g(z)|=|e^{-if(z)}|=|e^{v(z)}|=1$.  Using Liouville I assumed one could say that both $g(z)$ and $h(z)$ are bounded entire functions, they are constant and so it follows that $v(z)$ is constant, meaning that both its partial derivatives are equal to 0 and, due to Cauchy Riemann, both of the partial derivatives of $u(z)$ are equal to zero.  It would then follow that $f(z)$ is constant.  I don't know how to go about the question using the Maximum Modulus Theorem, also I feel I am overlooking the importance of $|z|=1$ perhaps?  Any help would be much appreciated!! I read an essay about prime numbers. In it the author suggests that a natural first question to ask is,      What is the probability of a random natural number being prime?   but proceeds to dismiss it as "not making sense". I wonder what's wrong with the question. Is its meaninglessness related to the fact that there is an infinite number of naturals? A great Python IDE for Ubuntu On iOS, while watching a video in YouTube app, when I go to the Home Screen, the video stops playing. I found no setting to enable it.  I know it is available for Android, but is there a way to do so in iOS? Is there any setting, or a 3rd party app that I can use? Problem in notation: $(\vec{v}\cdot\vec{\nabla})\vec{v}$ versus $L_v(\vec{v})$ About 0.999... = 1 I've just happened to read this  on MO (that of course has been closed) and some of the answers to a similar  on MSE.   I know almost nothing of nonstandard analysis and was asking myself if something like the sentence « $1- 0.999 \dots$ is a nonzero positive infinitesimal» could be easily expressed and proved in nonstandard analysis.  First of all, what is 0.999... ? If we take the usual definition as a series or as a limit of a sequence of rationals, then it will still be a real number and equal to $1$ (I guess by "transfer principle", but please correct me if I'm wrong).  Instead, let's define  $$0.9_N:=\sum_{i=1}^N 9\cdot 10^{-i} $$  where $N\in{}^*\mathbb{N}\setminus\mathbb{N}$ is an infinite nonstandard natural number. This $0.9_N$ is a legitimate element of ${}^*\mathbb{R}$, expressed as $0.$ followed by an infinite number of "$9$" digits.  What can be said about $\epsilon_N:=1-0.9_N$ ? Is there an elementary proof that $\epsilon_N$ is a positive infinitesimal of ${}^*\mathbb{R}$ ? (by "elementary" I mean just order and field axioms and the intuitive facts about infinitesimals, like that for $x$ infinite $1/x$ is infinitesimal etc.; no nonprincipal ultrafilters &amp; C). Google Chrome Address Bar Font has gone too large, how can we reduce it Running Unity on my desktop (2*20" LCD displays), I initiated a standard daily update on my Ubuntu 14.04 LTS today and Google Chrome updated itself to Version 35.0.1916.114.  The URL address bar input now shows IMO a too larger font size which then proceeds to auto show in green. I prefer the smaller font size and have no need for 'gooey slime green' auto complete font colours. Any advice on how to revert back to smaller, generic Address font styling.  I use both FF and Chrome for numerous tasks, Chrome being my primary browser and I've checked my system Unity 'default' theme (Ambiance! LOL.. yes I'm tired of that also).  Thanks for sharing. Is there any practical difference between saving at 300ppi or 72ppi? I often see statements in discussions about web displayed image quality that go something like this: "I only upload pictures at 72 dpi and 1200 pixels on the long edge, so if someone copies and prints the image it won't look as good as if it were 300 dpi."  What? Have I missed something here?  Does an image edited and saved/exported with 1200x800 pixels at 300 ppi look any different online than the same image saved/exported with 1200x800 pixels at 72 ppi? Other than the metadata regarding ppi, is there any difference in the two images at all? If so, what is the difference? If I tell my printer to print the images at 4R (4X6 inches) will there be any difference at all in how the printer creates a print from the 1200x800 @ 300 dpi image versus the 1200x800 @ 72 dpi image? Where did Hogwarts get money for salaries, food and other purchases? Show that $\int_0^\pi f(\sin x)\,\mathrm{d}x = 2\int_0^{\pi/2}f(\sin x) \, \mathrm{d}x$ multi-layer board copper pour I have a 6-layer board where the internal 4 planes are +15,GND,VCC,-15.  I was wondering if there was any advantage to doing a copper pour on the top and bottom layers?  I would probably leave them floating as I don't want to use micro-vias to say tie it to GND?    Is this actually a bad idea?  I.e. floating copper=antenna.  Would it be just as acceptable to have 4 layer board with the top layer having copper pour to VCC and the bottom having a pour to GND and keep the two internals as +-15?  Note that this is for a fairly low speed circuit which has some analog and digital parts. Urdu language not listed in my ubuntu 16.04 LTS I am a new user of Ubuntu 16.04 LTS. To my surprise it does not have Urdu Language in language support widow. Kindly help.   The given answer to  is not helping me. PHP validation/regex for URL I've been looking for a simple regex for URLs, does anybody have one handy that works well?  I didn't find one with the zend framework validation classes and have seen several implementations. How do I check the health of a SSD?