Commands in math I have some commands as follows, but it doesn't work to run my LaTeX file. Is there any wrong order in these commands?   \documentclass[12pt,a4paper]{amsart} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{array,arydshln} \usepackage{arydshln} \usepackage{amsfonts,amssymb,amsrefs,mathtools} \usepackage{mathtools} %\usepackage{kbordermatrix,amsthm,rotating,array} %\usepackage{amsmath,kbordermatrix,blkarray} %\renewcommand{\kbldelim}{(} %\renewcommand{\kbrdelim}{)} %\usepackage{amsmath} \usepackage{tikz} \usepackage{pgf,tikz} \usetikzlibrary{arrows, automata} \usepackage{graphicx} \usepackage[pdftex]{graphicx} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} \hypersetup{colorlinks=true,linkcolor=red, anchorcolor=green, citecolor=cyan, urlcolor=red, filecolor=magenta, pdftoolbar=true} \usepackage[demo]{graphicx}  \usepackage{placeins} \usepackage{float} \usepackage{subfig} \usepackage{subcaption} %\usepackage{array} %\renewcommand{\arraystretch}{1.6}  %Me \renewcommand{\arraystretch}{1.4} \newcommand\bigzero{\makebox(0,0){\text{\huge0}}} %%%%%%%%% \usepackage{tabularx,rotating} \usepackage{multirow} \usepackage{rotating} \usepackage[graphicx]{realboxes} \usepackage{booktabs} \usepackage[margin=1in]{geometry} \usepackage{ragged2e} \usepackage{xcolor} \usepackage{adjustbox} %%%%%%%%%%%%%%%%%%%%%%%%% \theoremstyle{plain} \newtheorem{thm}{Theorem}[section] \newtheorem{lem}[thm]{Lemma} \newtheorem{prop}[thm]{Proposition} \newtheorem{cor}{Corollary}  \theoremstyle{definition} \newtheorem{defn}{Definition}[section] \newtheorem{conj}{Conjecture}[section] \newtheorem{exmp}{Example}[section]  \theoremstyle{remark} \newtheorem{rem}{Remark}[section] \newtheorem{note}{Note}[section]
Option clash when using graphicx and tikz packages The following code fails Option clash for package graphicx, it seems to be an incompatibility between the package graphicx (when the option pdftex is used) and the package tikz.  \documentclass[a4paper,10pt]{book} \usepackage[T1]{fontenc} \usepackage[utf8x]{inputenc} \usepackage{tikz} \usepackage[pdftex]{graphicx}  \begin{document}      The lazy dog...  \end{document}   I am currently working with Debian wheezy (updated as of 10th November 2012), and the latest TeXLive LaTeX distribution included.  Any ideas?
Activity has leaked window com.android.internal.policy.impl.PhoneWindow$DecorView@44f72ff0 that was originally added here Proof of an inequality by induction: $(1 + x_1)(1 + x_2)...(1 + x_n) \ge 1 + x_1 + x_2 + ... + x_n$ Let $n \in \mathbb N^+$. Show that if $x_1, x_2, ... , x_n$ are $n$ real numbers such that $-1 \le x_i \le 0$ for each $1 \le i \le n$, then $$(1 + x_1)(1 + x_2)...(1 + x_n) \ge 1 + x_1 + x_2 + ... + x_n$$  I am using a proof by induction, but I am unable to complete it. I would appreciate any tips on how I could finish the proof.   Incomplete Proof Let $P(n)$ be the proposition that $(1 + x_1)(1 + x_2)...(1 + x_n) \ge 1 + \sum_{i = 1} ^ n x_i$. When $n = 1$, LHS = RHS = $1 + x_i$. Clearly $1 + x_i \ge 1 + x_i$ and so $P(1)$ is true. Assume that $P(k)$ is true, i.e. $(1 + x_1)(1 + x_2)...(1 + x_k) \ge 1 + \sum_{i=1}^k x_i$. Case 1 Suppose $x_{k + 1}  = -1$. Then $1 + x_{k + 1} = 0$, hence LHS = $(1 + x_1)(1 + x_2)...(1 + x_k)(1 + x_{k+1}) = 0$. RHS = $1 + x_1 + x_2 + ... + x_k - 1 = x_1 + x_2 + ... + x_k$ which is always nonpositive since each $x_i$ is nonpositive. Hence RHS $\le 0$ and so LHS $\ge$ RHS. Case 2 Suppose $x_{k+1} = 0$. Then $1 + x_{k+1} = 1$, hence multiplying it to LHS does not change anything. Also, adding $x_{k+1}$ to RHS does not change anything. Therefore, LHS $\ge$ RHS still holds. Case 3 Suppose $-1 &lt; x_{k+1} &lt; 0$. Then $0 &lt; 1 + x_{k+1} &lt; 1$. Adding $x_{k+1}$ to RHS makes the RHS smaller since $x_{k+1}$ is negative. If LHS $= 0$, then multiplying $1 + x_{k+1}$ to LHS does not change anything, and so LHS $\ge$ RHS holds. If LHS > $0$, then multiplying $1 + x_{k+1}$ to LHS makes the LHS smaller since $0 &lt; 1 + x_{k+1} &lt; 1$. In this case LHS $\ge$ RHS does not necessarily hold? ... Figuring out algorithm/formula for item scaling in WoW What are the left and right ideals of matrix ring? How about the two sided ideals? Chrome not asking to remember passwords Prefer composition over inheritance? Proof of property of abelian group I would like to close some view windows that I opened accidentally.  See the image below:    Edit: another note: I tried searching for the solution, but only found things like "Join Area", which don't seem to work in this situation. I am working on a large C++ project in Visual Studio 2008, and there are a lot of files with unnecessary #include directives. Sometimes the #includes are just artifacts and everything will compile fine with them removed, and in other cases classes could be forward declared and the #include could be moved to the .cpp file.  Are there any good tools for detecting both of these cases? List of lists changes reflected across sublists unexpectedly I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it? What are PATH and other environment variables, and how can I set or use them? Questions about    setting environment variables the PATH   are very common here, and in most cases the answers are very similar to each other. In the future it would be nice to have a good Q/A for this.  So the question is: What are environment variables, like the executable PATH, and how can I change and use them on major operating systems?  A good answer would include a simple explanation of what environment variables and especially PATH mean to the OS, as well as simple guidelines on how to set and read them accordingly. I am thinking about buying a new lens specifically to take photos of distant targets (birds, bears, etc). I currently own the Canon 70-300 IS USM, which is a nice lens, but I find that if I want to take a photo of anything further away than about 10 meters, the target does not fill a large amount of the frame (meaning I have to significantly crop in post production).  I am currently looking at the Canon prime 400mm, however I would like to determine at what distance an object will fill a reasonable proportion of the frame.  Is there a formula or rule of thumb I can apply that will help me in this situation? I realise the size of the target I am shooting will play a role here, so if we need to make an assumption about the size of the target please let me know. I'm a Canadian citizen with a Canadian passport. I booked a flight with American Airlines to Mexico City From Toronto Pearson and it says that "Passenger details are needed to check in".  Flight 1: YYZ -> DFW -> MEX Flight 2: MEX -> DFW -> YYZ     They already took my name, gender and such. It is now asking for my passport number and expiry date. That all seems reasonable. However, when I enter that I am a Canadian resident it asks for:  1) Street or hotel in US 2) City in US 3) State in US    My trip to DFW is only for a connecting flight. The fields are required so I can't submit my passport information without filling this in.    Is there something I'm missing? Stopping all automatic updates Windows 10 ionice without effect I want to clear a element from a vector using the erase method. But the problem here is that the element is not guaranteed to occur only once in the vector. It may be present multiple times and I need to clear all of them. My code is something like this:  void erase(std::vector&lt;int&gt;&amp; myNumbers_in, int number_in) {     std::vector&lt;int&gt;::iterator iter = myNumbers_in.begin();     std::vector&lt;int&gt;::iterator endIter = myNumbers_in.end();     for(; iter != endIter; ++iter)     {         if(*iter == number_in)         {             myNumbers_in.erase(iter);         }     } }  int main(int argc, char* argv[]) {     std::vector&lt;int&gt; myNmbers;     for(int i = 0; i &lt; 2; ++i)     {         myNmbers.push_back(i);         myNmbers.push_back(i);     }      erase(myNmbers, 1);      return 0; }   This code obviously crashes because I am changing the end of the vector while iterating through it. What is the best way to achieve this? I.e. is there any way to do this without iterating through the vector multiple times or creating one more copy of the vector? HP Spectre x360 disable trackpad in tablet mode I have the HP Spectre x360 and when I bend the laptop back into tablet mode (360 hinges), usually the keyboard and mouse disables in Windows.   In Ubuntu 15.04 the keyboard successfully disables, but not the trackpad.   What wizardry can I perform to rectify this issue?   Hopefully I could create an actively running script where it listens for particular events (activation of tablet mode) and then disable the track pad once boolean value equals True or something. I could probably get the ball rolling if there was a command out there that would display what component is being used / activated, so I could capture the event ID or something (not sure if this is even possible, just speculating...) I've had my HTC Desire for a couple of months now and it is awesome! (A huge improvement to my previous phone... Nokia 3315)  Though recently, I've realised that the phone semi-freezes more and more often - ie. when swiping between homescreens it will either pause/freeze and I will have to re-swipe to get it to change screens. Or worse, it just won't respond to any further swipes and I have to lock the screen then unlock to get the phone back into action.  Got quite annoyed at this (was probably happening once or twice a day) so I thought it might help to turn it off and on again. So I did - not sure if it was a placebo effect but it seems to have helped a bit?  So given that this is my first smartphone, I was wondering if it is 'normal' to need to restart the phone every so often. If so, how often is 'normal'? If not, what can I do to diagnose/fix this problem? extended stars-and-bars problem(where the upper limit of the variable is bounded) PlotRange precision limit?