I was given a solution to include "Chapter" before my section entries in the ToC, however the number of the section does not get transferred to the ToC! For instance, in the MWE below, the sections are called "Chapter 1 \break Section One" and "Chapter One \break Section Two", however in the ToC, the sections are listed as "Chapter Section One" and "Chapter Section Two", and thus omitting the section numbers. I'd like to include these section numbers in the ToC.  Thanks!  \documentclass[12pt]{article} \usepackage[utf8]{inputenc} \usepackage[english]{babel} \usepackage[showframe]{geometry} \usepackage{titlesec} \usepackage{titletoc}  \addto\captionsenglish{ \renewcommand*\contentsname{\centerline{TABLE OF CONTENTS}}}  \titleformat{\section}[display]% {\null\vskip1em\sffamily\bfseries\filcenter}{Chapter \thesection}{0em}{}[] \titleformat{name = \section, numberless}[block]% {\null\vskip1em\sffamily\bfseries\filcenter}{}{0em}{} \titlespacing*{\section}{0em}{1em}{1em}  \titlecontents{section} [7em] % ie, width of contentslabel + 0.5em {\medskip} {\contentslabel[\MakeUppercase\chaptername~]{6.5em}}%\thecontentslabel {\hspace*{-6.5em}} {\titlerule*[0.5pc]{.}\contentspage}  \begin{document}  \tableofcontents \newpage  \section*{An Unnumbered Section} \addcontentsline{toc}{section}{An Unnumbered Section} \section{Section One} \subsection{A first subsection} \section{Section Two} Content  \end{document}
Basically, here's my MWE, and I need to include "Chapter" before every section title in the ToC (without changing anything else).      \documentclass[12pt]{article} \usepackage[utf8]{inputenc}  \usepackage[english]{babel} \usepackage[titles]{tocloft} \usepackage{titlesec} \usepackage{titletoc}  \addto\captionsenglish{ \renewcommand*\contentsname{\centerline{TABLE OF CONTENTS}}}  %\renewcommand{\thesection}{CHAPTER} %\renewcommand{\cftsecpresnum}{Chapter \thesection} \titleformat{\section}[display]% {\null\vskip1em\sffamily\bfseries\filcenter}{Chapter \thesection}{0em}{}[] \titlespacing*{\section}{0em}{1em}{1em}  \titlecontents{section} [1.5em] % ie, 1.5em (chapter) + 2.3em {} {\contentslabel{1em}} {\hspace*{-1.5em}} {\titlerule*[0.5pc]{.}\contentspage}  \begin{document} \newpage \tableofcontents \newpage  \section{Section One} \section{Section Two} Content \end{document}   The commented out code is what I've already tried. The first one just changes the number to "CHAPTER" and doesn't move the text in the ToC (so it just overlays on top of the name of the section), and if I include "\thesection" after "CHAPTER" it creates an infinite loop definition error. The second one causes no differences, and the code still compiles.  Thanks!
Let $X$ be a normed vector space.   Show that if a subsequence of a Cauchy sequence converges, then the whole sequence converges. Use the part 1 to show that $S = \{x\in X : \|x\| = 1\}$ is complete if and only if $X$ is Banach.     I have found the first part in a book, but I do not how to prove part 2. Thanx regards Can you please check my Cesaro means proof I wanted to prove the following:  if $x_n \to x$ then $y_n \to x$ where $$ y_n = {x_1 + \dots + x_n \over n}$$  Please can you tell me if my proof is correct? My proof is this:  Let $\varepsilon &gt; 0$. Fix $N$ such that $n &gt; N$ implies $|x_n - x| &lt; {\varepsilon \over 2}$.   Then $\left |{1 \over n} \sum_{k=N+1}^{N + n} x_k - x \right | &lt; {\varepsilon \over 2}$. Now let $M$ be such that ${|x_1 + \dots + x_N | \over M} &lt; {\varepsilon \over 2}$ and $M &gt; N$. Then  $$ \left | \sum_{k=1}^M {x_k \over M} - x   \right | \le  \left | \sum_{k=1}^N {x_k \over M}   \right | +  \left | \sum_{k=N+1}^M {x_k \over |M-N|}  - x   \right | &lt; \varepsilon $$ Here the proof is finished. But one can observe:  It is possible that $y_n$ converges even if $x_n$ doesn't: If $x_{2n} = 0$ and $x_{2n + 1} = 1$ then $x_n$ does not converge but $y_n \to {1 \over 2}$. Friend was brainwashed by MLM-/ponzi investment scam. What can I do? Recently a friend of mine invited me to hear about “an interesting chance to simply earn money.” Basically we and other invited people drove to a meeting room where a speaker told us about a growing startup where you could invest money in a field where similar investments had an ROI of apparently 1000 times the investment in 6 years. Afterwards there was coffee and small talk together, during which they also indoctrinated people saying, they should avoid talking to people talking bad about the investment (or saying it is scam) because you can't gain money from them and they just want to destroy your business.  You earn money if you invest money and if you refer friends who invest money up to multiple levels. The more you invest yourself the greater percentage you earn for your referrals.  Since I had already seen other ponzi-/MLM-schemes and I am from the field it is based in, I recognized that there is no real product and it is a ponzi-/MLM-scheme. Later I found its name on the official scam warning list of multiple countries.  From what I understand, my friend has already invested multiple months or years worth of income; and is earning an amount of money through referrals that would mean scamming other people directly or indirectly through referrals for possibly several $100,000's per month to earn an additional bonus. He also wants to use his position as a respected member of multiple local youth groups and other community groups to get their members as referrals or in his words “…to give them the opportunity to also simply earn money.”  I tried to convince him that it is just a ponzi scam with my knowledge in this field but he answered with the indoctrinated speech “You don’t need to know the details if it makes you rich or use it. You also don't know how every detail of a smartphone works?”/“My sponsor already earned $x with this” or “If you don't believe in this, just stop talking about it to me and other people or do you want to ruin me, my business and my investments?.” So basically this means I can either make his investment worthless/let him lose everything (he also quit his job) or let him scam other people and motivate them to scam other people.  At the moment you can only withdraw small amounts of money out of it because the company invented some reason but you will be able to withdraw all of it “soon” (=most likely never).  What is the best way to resolve this situation (best meaning with lowest loss of money for everybody)?  Edit: The founders are known names in Ponzi schemes or convicted for crimes like fraudulent bankruptcy and many of their claims are technically impossible or proven to not exist with very high probability according to sites about ponzi schemes. But of course they say "Every bigger company has their scandals".  You can't trade the bought virtual coins outside the company and the only product you can buy can be bought anywhere else for less than 10% of the price without the logo.  When I met other friends they mentioned that they got invitations for the same meeting. I just stated to them that I already went to one and told them the name of the company (which was not stated on the invitation) and that I will not invest in it because there are official warnings that this is a scam. I'd say Microsoft have a way of bending the rules and I know that McLaren have won the championship. While this sounds strange, I believe it is correct English (sorry, I'm not native).   But when it's a small company, would you still use it this way? Is a company always plural, or are small companies singular? I.e., would you say Bakery Johnson makes fine bread or Bakery Johnson make fine bread? Is it My book seller, Woody's, have moved or is it has moved? How to efficiently count the number of keys/properties of an object in JavaScript? Idea behind proof that $\frac{21n+4}{14n+3}$ is irreducible for all $n$ Why does camera this tracking fail completely even when the solution value is very low? The attached animated gif shows some frames of a video with a mesh box placed at each tracking marker used to successfully track (solution error &lt;.4) an 800 frame chunk of video.   The point is to illustrate just how poorly the camera tracker calculated: when the box is at a marker placed at the top of a faraway building on the left, it is actually visually much larger than when it is at the tracking marker closest to where the real camera was. I went to great lengths to be sure that the camera's sensor size and focal length are correct, and manually placed and followed all markers to be sure they were accurately tracking.   There is not a lot of parallax motion over the 800 frames, but there should have been enough to at least know that the point closest to the camera moved more than the point furthest away. Sometimes it seems to work, sometimes it doesn't. Does anybody know how to improve this? $4x^2+1$ factors only into $4y+1$ primes Reason of existense of the extra space in align environment and removal of it between two align environments This is a follow-up question regarding the extra vertical space in amsmath's align environment. Why when in use align uses so much vertical space in contrast with other environments like for example tabular or itemize?  \documentclass[12pt]{article} \usepackage[top=0.3in, bottom=1.2in, left=0.8in, right=0.8in]{geometry}   \usepackage[fleqn]{amsmath} \usepackage{unicode-math}  \setlength{\mathindent}{0cm} \newcommand{\3}{\vspace{0.3cm}}  \title{} \author{} \date{}  \begin{document}  70  \begin{align*} &amp;e^{jz}=\cos z+j\sin z\\ &amp;\cos z=(1/2)(2\cos z)=\\ &amp;=(1/2)(2\cos z+j\sin z-j\sin z)=\\ &amp;=(1/2)(\cos z+j\sin z+\cos z-j\sin z)=\\ &amp;=(1/2)(e^{jz}+e^{-jz}) \end{align*}  80  \begin{itemize} \item Item 1  \item Item 2  \end{itemize}  90  \begin{tabular}{c|c}  Entry 1&amp; Entry 2  \\  Entry 3&amp; Entry 4 \end{tabular}  \end{document}     Also another image of the huge space between two align environments. Even without the blank lines the space is a lot.    \begin{document}  \begin{multicols*}{2}   \begin{align*} &amp;\text{70}\\ &amp;e^{jz}=\cos z+j\sin z\\ &amp;\cos z=(1/2)(2\cos z)=\\ &amp;=(1/2)(2\cos z+j\sin z-j\sin z)=\\ &amp;=(1/2)(\cos z+j\sin z+\cos z-j\sin z)=\\ &amp;=(1/2)(e^{jz}+e^{-jz}) \end{align*}    \begin{align*} &amp;\text{207}\\ &amp;x(t)=A_{c}\cos \theta(t)\\ &amp;\theta(t)=2\pi f_{c}t+\phi(t)\\ &amp;\phi(t)=K_{p}m(t)\\ &amp;x(t)=A_{c}\cos[2\pi f_{c}t+K_{p}m(t)] \end{align*}   Edit I:  As I mention in a comment I have tried the following code and there is no difference between two align environments, only between text and an align environment. Why doesn't work in the case of the two environments and how can I fix it so to work? Also what is the reason that this space exists?  \setlength{\abovedisplayskip}{0pt} \setlength{\belowdisplayskip}{0pt} \setlength{\abovedisplayshortskip}{0pt} \setlength{\belowdisplayshortskip}{0pt} What is the distinction between "among" and "amongst"? Problem  The sequence $(a_n)_{n=1}^\infty$ is given by recurrence relation:   $a_1=\sqrt2$, $a_{n+1}=\sqrt{2+a_n}$.   Evaluate the limit $\lim_{n\to\infty} a_n$.  Solution   Show that the sequence $(a_n)_{n=1}^\infty$ is monotonic. The statement $$V(n): a_n &lt; a_{n+1}$$ holds for $n = 1$, that is $\sqrt2 &lt; \sqrt{2+\sqrt2}$. Let us assume the statement holds for $n$ and show that $V(n) \implies V(n+1)$. We have that $$a_n &lt; a_{n+1}.$$ Adding 2 to both sides and taking square roots, we have that $$\sqrt{2+a_n} &lt; \sqrt{2+a_{n+1}},$$ that is $a_{n+1} &lt; a_{n+2}$ by definition. Find bounds for $a_n$. The statement $$W(n): 0 &lt; a_n &lt; 2$$ holds for $n=1$, that is $0 &lt; \sqrt2 &lt; 2$. Let us assume the statement holds for $n$ and show that $W(n) \implies W(n+1)$. We have that $$0 &lt; a_n &lt; 2.$$ Adding two and taking square roots, we have that $$0 &lt; \sqrt2 &lt; \sqrt{2+a_n} &lt; \sqrt4 = 2.$$ The limit $\lim_{n\to\infty} a_n$ exists, because $(a_n)_{n=1}^\infty$ is a bounded monotonic sequence. Let $A = \lim_{n\to\infty} a_n$. Therefore the limit $\lim_{n \to\infty} a_{n+1}$ exists as well and $\lim_{n \to\infty} a_{n+1} = A$. (For $(n_k)_{k=1}^\infty = (2,3,4, \dots)$, we have that $(a_{n_k})_{k=1}^\infty$ is a subsequence of $(a_n)_{n=1}^\infty$, from which the statement follows.) We have that $a_{n+1} = f(a_n)$. That means that $A = \lim_{n\to\infty} a_n = \lim_{n \to\infty} {f(a_n)} = f(\lim_{n \to\infty} a_n) = f(A) = \sqrt{2 + A}$. Solving the equation $A = \sqrt{2 + A}$, we get $A = -1 \lor A = 2$. Putting it all together, we get that $A = 2$, because the terms of the sequence are increasing and $a_1 &gt; 0$.   Is my solution correct? Evaluate the integral $\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x dxdy}{\sqrt{4a^2x^2-(x^2+y^2)^2}}$ Change the order of integration in:  $$\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x }{\sqrt{4a^2x^2-(x^2+y^2)^2}}dxdy$$ and hence evaluate it.    I changed the order of integration and got the limits $y=0$ to $a$ and $x=a-\sqrt{a^2-y^2}$ to $a+\sqrt{a^2-y^2}$. I then tried changing to polar coordinates, but it is only making the integrand more complex. Choosing OpenLayers or Leaflet? I was debating with one of my collegues on OpenLayers v/s Leaflet. I made a point that OpenLayers is much better API if we wish to build a project, where you need direct connectivity to the Geoserver and PostGIS.  Then I found , which looks pretty new but has the features of connectivity with the Geoserver and PostGIS.  So my project details are as follows,   Use the map interface to fetch Feature Info Create a customized tool that takes the lat/lon from user as to where he/she clicks on the map and then fetches the Climate Data from the raster (which is handled by a py script on the server) Allows user to upload excel, which is sent to the py script, which returns a GeoJSON, which creates Vector Features on the map Allow user to create vector polygons, which will fetch the Features it intersects from the WFS Layer. Fetches Layer from the PostGIS Datastore on GeoServer and displays the layers on the map.   So now I am confused on which is better and why using OpenLayers over Leaflet makes more sense or not? I need font size = 14 in article document, but when I change  \documentclass[a4paper,11pt]{article}   to  \documentclass[a4paper,14pt]{article}   font becomes even smaller. How to change font size? Converting/using ArcGIS *.style file for/in QGIS (QML or SLD)? I have downloaded a dataset from a government organisation. it comes with a .style file.  I use QGIS 1.8 on windows 7.    Is there a way to use the .style file as a qml or sld? I have tried simply changing the extension but to no avail. Windows 8 OEM Reinstalling I know this question is a repetition but I didn't find any solution of my problem from any of the previous questions. Recently I formatted my Laptop HDD and now I want to re install windows 8 I've a Windows 8 OEM license but the problem is I don't have a disc , I downloaded en_windows_8_x64_dvd_915440 from msdn , but when I boot the windows it shows the error that the current version is not suitable with my serial key, so where I can find an OEM Windows 8 and also I've a retail windows 8 disc so if I install that windows 8 in my pc and is there any way to activate it using my OEM key What command do I need to unzip/extract a .tar.gz file? I received a huge .tar.gz file from a client that contains about 800 mb of image files (when uncompressed.) Our hosting company's ftp is seriously slow, so extracting all the files locally and sending them up via ftp isn't practical. I was able to ftp the .tar.gz file to our hosting site, but when I ssh into my directory and try using unzip, it gives me this error:  [esthers@clients locations]$ unzip community_images.tar.gz Archive:  community_images.tar.gz   End-of-central-directory signature not found.  Either this file is not a zipfile, or it constitutes one disk of a multi-part archive.  In the latter case the central directory and zipfile comment will be found on the last disk(s) of this archive. note:  community_images.tar.gz may be a plain executable, not an archive unzip:  cannot find zipfile directory in one of community_images.tar.gz or community_images.tar.gz.zip, and cannot find community_images.tar.gz.ZIP, period.   What command do I need to use to extract all the files in a .tar.gz file? Are there surface-mount pin header footprints for KiCAD? Convert String to Integer in QGIS tables Displaying multiple fields as labels if one field is null in QGIS? I am having some issues trying to show multiple fields for a single label in QGIS. In QGIS2.6, attempting to display labels for a feature consisting of multiple fields results in an empty label if one of the fields is null. So for example, in the label expression dialog:  concat("Temp Site",'\n',"Notes",'\n',"Function")   will function normally unless one of the fields is null, then it results in no label being shown. Using the '||' operator instead in the expression dialog also results in the same behaviour:  "Temp Site" || '\n'  ||  "Notes" || '\n'  ||  "Function"   Is there a way to display the labels even if one of the fields is null?