Is there a name for an object $L$ that has an additive structure and a (not necessarily total) order such that for all $a,b,c \in $ L we have  $a+b = b+a$ $a+(b+c)= (a+b)+c $ $a+b \leq a+c \Leftrightarrow b \leq c$
I recently came across an algorithm that works on values assuming that they are draw from a monoid equipped with a total ordering relation.  I was wondering if there is a term for such a structure, since it seems related to concepts like Euclidean domains and fields (though the requirements are much less strict).  Does this entity have a name?  Or is it just "a monoid over totally ordered elements?"  Thanks!
Suppose $\lim \limits_{n \to ∞} a_n=L$. Prove that $\lim\limits_{n \to ∞} \frac{a_1+a_2+\cdots+a_n}{n}=L$ Integral of type $\displaystyle \int\frac{1}{\sqrt[4]{x^4+1}}dx$ How can I prevent SQL injection in PHP? Why is there a file called [ in my /usr/bin directory? Recently back to Linux from another operating system I noticed a file called [ which seems strange to me.  What is it for?  $ ls -l /usr/bin | head -2 -rwxr-xr-x 1 root root       39552 Nov  3 14:44 [   I'm using Ubuntu 15.04 You can't see the question owner's special color When the owner of a question comments on their question or an answer to their question or self-answers their question, they get a special color for the box around their username.  The problem is, you can't see the box:        Can you please make this not white on white? How can I modify title page so that it looks like it is in  video. Please seek to 16 seconds and watch title page. I do not have permission to post images. I liked this theme and I want to make a beamer theme that looks similar. I tried with beamercolorbox but I failed to position the box to the bottom.      Edit: Here is my minimum working example  \documentclass[xcolor=dvipsnames]{beamer} \defbeamertemplate*{title page}{customized}[1][] { \usebeamerfont{subtitle} \usebeamercolor[fg]{subtitle}  {\flushright \setbeamercolor{author}{bg=white,fg=Red} \usebeamerfont{author} \insertauthor\par \usebeamerfont{institute}\insertinstitute\par }  \vspace{0.2in}  \setbeamercolor{postit}{fg=white,bg=YellowOrange}  \begin{beamercolorbox}[sep=1em,wd=1.062\textwidth,ht=3cm,dp=3cm,right]{postit} \usebeamerfont{title} {\huge \inserttitle}\par \usebeamerfont{subtitle} {\insertsubtitle} \end{beamercolorbox} } \usecolortheme[named=YellowOrange]{structure} \useoutertheme{infolines} \setbeamertemplate{navigation symbols}{}  \institute{Harvard College Professor and\\ Johnstone Family Professor in Psychology, Harvard University}  \title{SAY WHAT?} \subtitle{Linguistics as a Window to\\ Understanding the Brain} \author{Steven Pinker}  \begin{document} { \setbeamertemplate{footline}{} \begin{frame} \titlepage \end{frame} } \end{document} What is the meaning of speed of light $c$ in $E=mc^2$? is the famous mass-energy equation of Albert Einstein. I know that it tells that mass can be converted to energy and vice versa. I know that $E$ is energy, $m$ is mass of a matter and $c$ is speed of light in vacuum.   What I didn't understood is how we will introduce speed of light?  Atom bomb is made using this principle which converts mass into energy; in that the mass is provided by uranium but where did speed of light comes into play? How can speed of light can be introduced in atom bomb? How to check the tasks that are running at different run levels in debian? Over the years I've written some libraries. These libraries sometimes depend on each other.  As a result, the "tex" directory is structured as follows:  tex ├── library |   ├── library1.sty |   ├── library2.sty |   └── library3.sty ├── project1 |   ├── master.tex |   ├── chapter1.tex |   └── chapter2.tex ├── project2 |   └── article.tex └── project3     └── paper.tex   The libraries depend on each other. As a result, in every library that depends on another library, this is part of the header:  %library2.sty \ProvidesPackage{library2} \RequirePackage{../library/library1}   In other words, the library is imported from the "root of every project". This is not a good design choice. What if someone copies the libraries in the folder of the root of a project, or what if the folder "library" is renamed...  It is however reasonable the "active directory" still remains in the project root.  What can be done to resolve such library dependencies? How to detect Windows 64-bit platform with .NET? In a  2.0 C# application I use the following code to detect the operating system platform:  string os_platform = System.Environment.OSVersion.Platform.ToString();   This returns "Win32NT". The problem is that it returns "Win32NT" even when running on Windows Vista 64-bit.  Is there any other method to know the correct platform (32&nbsp;or 64&nbsp;bit)?  Note that it should also detect 64&nbsp;bit when run as a 32&nbsp;bit application on Windows 64&nbsp;bit. 555 Monostable Timer delay I have built numerous 555 circuits over the years. I recently had to built a Monostable 555 cct. as per this site :    The cct. is used in a motor vehicle. When the remote control is pushed to open the doors, it sends positive 12V to this Monostable cct. to initiate it and a 3 Amp Power Transistor pulses the siren momentarily to indicatse "unlocking" by audible means.   The issue I have is that Rt and Ct used to time the output pulse is not short enough. I replaced these components to the smallest values I could get, but the output is still "too long". Teh siren makes a "chooow" sound instead of "chow". Sounmds too unprofessional or after-market.  Any ideas to get a short pulse (nearly a few micro seconds) out of this old 555 cct. ? How to understand the LaTeX warning “there were undefined references”? for loop in Java runs 3 times before taking next input Solve the integral $\int_0^\infty x/(x^3+1) dx$ I'm new here!  The problem: integrate from zero to infinity x over the quantity x cubed plus one dx. I checked on wolfram alpha and the answer is that the indefinite integral is this:  $$\int \frac{x}{1+x^3} dx = \frac{1}{6}\left(\log(x^2-x+1)-2 \log(x+1)+2 \sqrt{3} \arctan((2 x-1)/\sqrt{3})\right)+\text{constant}$$  and the definite integral is this:  $$\int_0^\infty \frac{x}{1+x^3} dx = \frac{2 \pi}{3 \sqrt{3}}\approx 1.2092$$  I am trying to figure out all the steps in between. I see that there are logs, which are equivalent to the ln variant that i am more familiar with, which means it was integrating $1/x$ at some point; I also see an inverse tangent in there.  I started with long division to simplify and I got (which could be wrong because I am very tired right now) $x/(x^3+1) = x^2+ 1/(x^3+1)$ which seems to be a step in the right direction. Wolfram Alpha thinks I definitely did that step wrong. The two equations do not evaluate as equal.  Then I cheated and took the wolfram alpha factorization of $(x^3+1) = (x+1)(x^2-x+1)$...I probably should have known that but didn't offhand. Now it is looking like $x^2$ plus the partial fraction decomposition $1/(x^3+1) = A/(x+1)+(Bx+C)/(x^2-x+1)$. Am I heading in the right direction with this? At this point do I just plug in and crunch? How did the Wampa freeze Luke's feet into the ceiling of the cave? Where to ask "subjective and argumentative" questions on programming? Recently  was "closed as subjective and argumentative".  I wonder, where would you recommend to ask such questions? Is there a way to get trig functions without a calculator? In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a calculator?  Sometimes I don't feel right when I can't do things out myself and let a machine do it when I can't.  Or, if you could redirect me to a place that explains how to do it, please do so.  My dad said there isn't, but I just had to make sure.  Thanks. Setting chain length My chain broke and in a moment of silliness (I was cold wet and slightly annoyed)  I threw the broken one away before thinking about measuring the new one.  Is there a guide to getting the chain length/tension correct ?  It's an 8 speed road bike (Shimano Sora back, double ring front) Why are there two Address lines in Address forms? Experience and a quick Google Images search suggests that it's standard to provide two fields for Address/Street. A colleague argues that it's perceived as two alternative addresses, and that the fact that there's only one country, state, zip, phone just makes it more confusing. I tried to think of a good explanation for having two fields but couldn't. To the reason of "there are some very long addresses" he replies "then why don't they use a multiline input field which would make it clearer that it's the same address".  So, what's the reason? And is it only standard for the US or for Europe as well? I know that it holds for $n=5$, so the first step is done.  For the second step, my IH is: $4^n &gt; n^4$, and I must show that $4^{n+1} &gt; (n+1)^4$. I did as follows:  $4^{n+1} = 4*4^n &gt; 4n^4$, and if I show that $4n^4 &gt; (n+1)^4$ holds for $n\geq 5$ I'm done, so I expand the right hand side and arrive to:  $$4n^4 &gt; n^4 + 4n^3 + 6n^2 + 4n + 1$$  And this holds iff: $$3n^4 - 4n^3 - 6n^2 - 4n - 1 &gt;0$$ And here I'm stuck, I don't really know how to show that the given inequality holds. Any hints?