Ingress hacking streak back to '0' despite definite hacking within 24 hrs
What is the logic behind the timer of the Sojourner Badge?
This week I saw the definition of a measurable set for an outer measure.     Let $\mu^*$ be an outer measure on a set $X$. We call $A \subseteq X$ measurable if $$\mu^*(E) = \mu^*(A\cap E) + \mu^*(A^c\cap E)$$ for every $E \subseteq X$.   This is not the first time I've seen this definition. Unlike most other things in mathematics, over time I have gained absolutely no intuition as to why this is the definition.   The only explanation I've ever seen is that a set is measurable if it 'breaks up' other sets in the way you'd want. I don't really see why this is the motivation though. One reason I am not comfortable with it is that you require a measurable set to break up sets which, according to this definition, are non-measurable; why would you require that? Of course, you can't say what a non-measurable set is without first defining what it means to be measurable so I suppose no matter what your condition is, it will have to apply to all subsets of $X$.     Is there an intuitive way to think about the definition of measurable sets? Is there a good reason why we should use this definition, aside from "it works"? author not appearing in \maketitle in amsart I am new to the amsart document class. For some reasons \author (etc..) is not showing after I use \maketitle. This is my tex:  \documentclass[12pt,reqno,a4paper]{amsart}  \usepackage{amsmath} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{mathrsfs}  \usepackage{amsthm}  \usepackage{latexsym}  \usepackage{pictexwd} \usepackage{pdftricks} \usepackage{natbib} \usepackage{setspace} \usepackage{color} \usepackage[affil-it]{authblk}  \begin{document}  \title{Temptation, Asymmetric information and Committment}  \author{Mark}  \affil{University of Leicester}  \date{February 2014}  \maketitle  \begin{abstract} To be written \end{abstract}  \section{introduction}  ...  \end{document}   and this is the output:   can anybody help me out? What do you call the grouping of numbers based on the cardinality of digits in the square they produce? Inequality Proof in Real Numbers: If $p+q=1$ then $pq\le\frac14$ Let $p,q \in \mathbb R$, and $p+q=1$. Prove that $$pq \le \frac{1}{4}.$$   The first thing I did was define 3 possibilities that we can have from $p+q=1$:  1º  $p$ or $q$ is negative. Example:   $p=-10$, $q=11$   $-10+11=1$  $(-10)(11)=-110$  So if $p$ or $q$ are negative the inequality $pq$ $\le$ $\frac14$ holds.  2º $p$ or $q$ is $0$, that makes the inequality $pq$ $\le$ $\frac14$ be $0$ $\le$ $\frac14$, the inequality holds.  3º The final possibility I saw  was $0$ $\lt$ $p,q$ $\lt 1$, here i just see that the max value from $p,q$ can be $p,q = 1/2$ making $\frac12 + \frac12 = 1$ and $(\frac12) (\frac12) \le \frac14$, but i do not see the elegant way of proving that with other values the inequality holds.  I apologize in advance if I made any mistake or missed something. How can I modify the size of swap with LVM partitions? I have searched this for hours but still no luck, obviously doing something wrong.  The journal (Risk Analysis) wants "Reference style is based on the National Library of Medicine (NLM) style guide. In-text citations are numbered, superscripted and in parentheses, and the reference list is numbered in order of appearance within the manuscript. Footnotes are superscripted without parentheses".  Could someone please suggest an appropriate .bst file to use that will produce this? Thanks, J Monotone functions and non-vanishing of derivative I am trying to run an executable file from a network drive on Windows 7 Professional (64-bit) in order to install a program, but, each time I try, it doesn't run and the following message appears:  {path-name} The specified path does not exist. Check the path, and then try again.   I am definitely connected to the network drive as I can see all of the directories and files, and can even open non-executable file types. Also, I am fairly confident that this is neither a firewall nor a permissions issue. If $|G| = pq$,  $p,q$ primes, $p \gt q, q \nmid p-1 $, then how do I prove $G$ is cyclic without using Sylow's theorems? Footnotes in tables? Thats my . I loaded this to PostgreSQL DB using PostGIS shape file loader. I ran pgr_anlayzeGraph() on it and found it had a lot of isolated segments.  Next I ran pgr_nodeNetwork() to create a new table 'ways_ways'. I made the topology  for it and ran the following query in Qgis sql window.   SELECT * FROM ways_ways JOIN (SELECT seq, id1 AS node, id2 AS edge, cost FROM  pgr_astar('SELECT id, source, target, cost, x1, y1, x2, y2 FROM ways_ways',  1, 108, false, false) )AS route ON ways_ways.id = route.node;   Given below are the screenshots: Original floorplan and the prescribed route  query ouput   Clearly , I don't have a continuous output. I ran pgr_analyseGraph on ways_ways to find that it has no more isolated segments . It has 51 deadends, which is acceptable.   Did I miss any step in pgrouting? Is there anyway to see which node has id 1 and id 108 in qgis?  i ran the same query in another map(which i downloaded) and got output for all possible source and target ids. So how can i create a way(a route) that is completely noded? Where is Jon going? Circular polarizing filter - slim or regular? I have a Canon EOS 550D. Right now I only have some standard lenses, and I'm looking to buy a Tokina AT-X 116 Pro DX II 11-16mm F/2.8. (I love landscape photography and photography in nature in general.) I want to try using a circular polarizing filter, and I've been looking at the Hoya Filter Circ Pol DMC Pro1 77mm. I can see that the "slim" version is cheaper than the regular one, however, I'm not sure what the difference is. Can any of you tell me which would one be preferable for landscape photography? (I found a thread posted about this some years ago but I would like to hear what you guys think, knowing what camera, lens and filter I'm thinking about combining.)  All feedback would be very much appreciated! :-) I am non-EU citizen working in Germany. Can I travel to UK without a visa? How to build Blender as a Python module? I have seen this question now many times and every question here and on other forum points to  experimental tutorial by . Now sadly a lot of answers are invalid right now because this central link is down. I couldn't find anything by Googling so if anybody has a fork of the tutorial or a second source that would be great? The link can't be gone for too long, I saw an answer with it 4 months ago.  The only other thing I have found is , but it also references the now missing tutorial. Any ideas how to find it? $\DeclareMathOperator{\card}{card}$From Problem-Solvers Topology  Prove the following: CANTOR'S THEOREM If $A$ is a set, then $$\card A &lt; \card \mathcal{P}(A)$$ where $\card A$ stands for the cardinality of set $A$.  My Answer If $A = \emptyset$, then $\card A =0$ and $\card \mathcal{P}(A)=1$. If $A = \{a\}$, then $\card A=1$ and $\card \mathcal{P}(A)=2$. So suppose that $A$ has at least two elements. Define a function $f: A \rightarrow \mathcal{P}(A)$ such that $f(x) = \{x\}$ for all $x \in A$. Then $f$ is injective. But it cannot be surjective, because for any two distinct elements $a,b \in A$, there is no element in $A$ that is sent to the set $\{a,b\}$ in $\mathcal{P}(A)$. Therefore, there is no bijection, and $\card A &lt; \card\mathcal{P}(A)$. Do you think my answer is correct? Thanks in advance Get the title instead of the number of a referenced chapter/section? Splitting a string into words and punctuation I lost my house in minecraft. How can I find it? I was in creative mode on minecraft PE. I made this really awesome house plus a hotel! I was finishing up my house but decided to explore first. I explored for about 10 minutes and then stopped. Suddenly, I started worrying because I didn't know where I was. I couldn't find my house on a map, a compass, and I didn't make a beacon or keep track of what side of the sun it was on either. How can I find my house again??? How to reinstall default packages In an attempt to uninstall wine I ran the command sudo apt-get purge wine* which as you may have guessed removed many of the default packages. I am wondering if there is a way to use the installation disk to reinstall the default packages without overwriting the file system. Not sure if it makes a difference or not, but I am duel booting Windows 8 and Ubuntu 14.04 which was updated from Ubuntu 12.04.  Thanks in advance.