Infinite series with e and pi
Gosper's unusual formula connecting $e$ and $\pi$
Ubuntu boots on terminal only, how do I recover the GUI desktop? Custom URL Hack - anybody know how can i find the fields IDs from "User" object? I'm new in custom URL hacking.  I am trying to write a custom URL in a custom button. It is suppose to clone the User record, and while doing so, I want some user fields to be cleared. However, I need help identifying those fields IDs (e.g. Email, Name, etc).  How can i refer these fields when writing the custom URL code? Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$ Problem  Suppose $f$ is a non-negative integrable function on a measure space $(X,\mathcal{A},\mu).$ Prove that $$\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$$  Attempt  Let $E_t=\{x:f(x)\geq t\}$ Note that $f\chi_{E_t}\leq f$. Since $f$ is integrable, the Lebesgue dominated convergence theorem tells us that $$\lim_{t\to\infty} \int f\chi_{E_t}\rightarrow \int \lim_{t\to\infty} f\chi_{E_t}=0,$$ since $\lim_{t\to\infty} f\chi_{E_t}=0$ a.e. $\ ^{(1)}$ The result follows from the fact that $$t\mu(E_t)\leq\int f\chi_{E_t}.$$  Question  I am having trouble proving $(1)$. That is, how can I show that $f\chi_{E_t}\rightarrow 0$ a.e? Partial adb restore ICS devices support creating backups using adb backup, and restoring them using adb restore. Using adb backup, one can select that everything should be backed up, or only a certain package.  However, adb restore lacks all the options of adb backup. When I call adb restore backup.ab, where backup.ab is only the backup of a single package, the phone shows me a warning dialog saying that all settings are going to be lost after restoring the backup. Is it true that restoring a single package backup wipes all data on the phone? If yes, is it somehow possible to restore a single package using adb restore? How do you transition from 1-page dungeon map to battle mat? I have a bunch of different ways I use to make maps for my tabletop game.  Sometimes I draw one on graph paper.  Sometimes I use .  Sometimes I copy a map from a published adventure or use the  random generators.  These all have the same output:  a piece of paper (or maybe two) with a map on it, and the map is usually quarter inch squares, or so.  When it's time to put minis on a mat, though, I need to copy over the relevant details of the map to our battle mat.  (We use Tact-Tiles.)  This is fine when most of our map is overland detail and I'm just copying down one or two rooms in which combat will occur.  For dungeon crawls, where there are more random encounters or where combat can chase through many rooms, it can lead to a pretty tedious drawing of the whole dungeon as we go.  I feel foolish for having to ask, but is there some trick, technique, or something to make it less tedious to transcribe maps from printed pages to the battle mat?  EDIT:  Answers in general are great, but I should note that the best answers, for me, will be informed by this previously-unmentioned fact:  the game venue is not my house, so I have limited prep time on site. Is $0\,\mathrm{m}$ dimensionless? Is $0 \, \mathrm m = 0 \, \mathrm s = 0 \,\mathrm {kg} = 0$? How do we define $[0 \, \mathrm m]$?  I once was given an assignment where I was asked to deduce and write down some physical quantity. It turned out that this quantity was $0$ in one unit or another, so I decided to drop the physical units because I figured that it didn't matter anyhow.  But I got to thinking:  If $0 \, \mathrm m = 0$, then we could add units of different dimensions (an operation not normally defined) like so: $5 + 0 \,\mathrm m = 5$.   Does $[ \cdot ]$ map $0 \, \mathrm m$ to both $0$ and $L$? Is there an established regime of thinking about physical quantities as an abstract algebra? Perhaps as a vector space where formal sums such as $5 \, \mathrm m + 10 \, \mathrm s$ are allowed? Would it be improper to drop the units of measurement of $0 \,\mathrm m$ like this in an academic paper? How can I make a copy of a material? Did this character lose a limb in “The Force Awakens?” Inspired by  which states limb loss as a recurring theme, I started thinking about the final lightsaber battle. After watching The Force Awakens the second time, I was not sure if      Kylo Ren   lost a limb or just lost his lightsaber. We definitely see      Rey slash at Ren’s right hand.   So knowing that context:      Did Kylo Ren actually lose his arm/hand? Prove F test is equal to T test squared I need to show that F test is equal to T test squared, when the T test is for 2 independent groups and assuming variances are equal.  I know that $F=\frac{MSB}{MSW}=\frac{SSB/k-1}{SSW/N-K}$ and I know that $T=\frac{X-Y}{S_p \sqrt{\frac{1}{n}+\frac{1}{m}}}$,   so $T^2=\frac{(X-Y)^2}{S_p^2 ({\frac{1}{n}+\frac{1}{m}})}$  I've seen this proof in Regression but here we're not using MSE and MSR, so i'm not sure how to connect between the two. How far can/should one press philosophical doubt? Should we keep on questioning until nothing is left to question or is there a point on which we need to stand (which we often tend to do)? Descartes used 'I think' as this fixed point where the skepticism abates, there may be others. But what is a rational way to find one, if any? How is this question addressed in modern philosophy? Windows Server 2008 R2: User account set to not show on login This afternoon I set up a Win Server 2008 R2 system for use with Team Foundation source code control. In order to give my team-mates the right to connect, I had to create a user account for each person, 10 in total. (I can't, and I don't want to create a domain).  Now, after doing this, all user accounts are displayed in the login screen.  What can I do so that all the accounts are not displayed there? Is it possible to do a cross page POST to an ASP.NET, from a static HTML form? Check and fix SD card errors within Android itself? I want to create a DEB file manually. I would like to just provide a folder which contains data to install, and a script to be executed after installation.  Is this possible? steam fatal error "steam needs to be online to update, but was set to offline movies." I tried re-installing  it but it simply keeps giving me this error in a little window. When I close it, an identical error pops up some 3 seconds later without any new provocation. I have an Excel file containing data collected over many years as latitude and longitude coordinates for archaeological sites. How can I import it into QGIS as a new layer? Boggle: What is the dice configuration for Boggle in various languages? This is the dice configuration for the English Boggle:  Other variants and discussions concerning letter distributions for English can be found here:  , , ,  (Wikipedia).  I am interested in the 16 dice configurations for also other languages (Spanish in particular) and I am unable to find it anywhere online.  Versions I have managed to find so far:  ,  English 25 dice version:   Spanish 25 dice version:   Italian 25 dice version: I realised, reading another Phys.SE question about  that I don't really understand how  works. Particularly concerning, for a SCUBA diver.  The top answers to that question seem to claim that balloons get their "sense of down" from a pressure differential. They continue: when a car accelerates, the air at the back of the car becomes more dense, and at the front less dense, changing the plane of the pressure differential and so also, the balloon's sense of up. I find that extremely hard to credit. However, I realised that I don't really know why less dense things float in more dense things.  I'm fairly sure it's something to do with displacement of heavier things by lighter things, and I think pressure acting on the lighter thing's surface has something to do with it, but that's about it. When I have .txt files or .py files, I can Quick Look those files in Finder. I have .jl files that are codes written in the Julia Language. Of course they are text files. They will open in a text editor like Sublime Text. How can I Quick Look these .jl files in Finder? Install Java JDK and JRE on Debian 8