Identity Element and Identity Properties
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
How to send array with CURL? Should I `urlencode` it? How do I install Adobe Acrobat Reader from the repository? How do I install Adobe Acrobat Reader in Ubuntu 14.04 using a Trusty apt repository?  This is NOT a duplicate of . In Synaptic &gt; Repositories &gt; Other software I enabled "Canonical Partners", but I still cannot install acroread as it is not available on my 64-bit system.  Here's the output from the console:   root@liv-inspiron:/home/liv# apt-get install acroread Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package acroread root@liv-inspiron:/home/liv# apt-get install acroread:i386 Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package acroread property not working with getter AND setter Why do I have so many .Xauthority.* files in my home directory? What is the most elegant proof of the Pythagorean theorem? "I had my house [be] burned down" I have found out that using the verb be in passive constructions such as:      I had my house be burned down    is incorrect, therefore it should be      I had my house burned down.    But is it possible instead of be to use get? E.g.      The wire is passed through the pliers in a specific way to avoid having it get bent.   The rope had its surface wear.   The rope had its surface get worn.   The rope had its surface worn.   The first two sound very odd to me, but just for clarification could you please point out the errors and which ones are correct? Or is using get, be it in -ing or the to infinitive, in any situation along with have incorrect? Trig sum: $\tan ^21^\circ+\tan ^22^\circ+\cdots+\tan^2 89^\circ = \text{?}$ As the title suggests, I'm trying to find the sum $$\tan^21^\circ+\tan^2 2^\circ+\cdots+\tan^2 89^\circ$$ I'm looking for a solution that doesn't involve complex numbers, or any other advanced branch in maths. The solution can involve techniques such as induction, telecoping, etc, but preferably only ideas from precalculus, e.g. trig identities, polynomials, etc.  EDIT: I know that the sum is a rational number. How can I prevent data theft from a company?  Are there any solutions to this problem?  Is there any software that encrypts important data (.doc, .xls, etc.) and prevents it from copying?  I need a solution where employees can read/write documents but can not copy then to a USB drive or e-mail them. Are there any places to leave luggage in Brussels, for short and/or long periods of time? Is it (always) true that $$\mathrm{Var}\left(\sum\limits_{i=1}^m{X_i}\right) = \sum\limits_{i=1}^m{\mathrm{Var}(X_i)} \&gt;?$$ Typsetting the Ponny Today, once again, the  came to my attention and I have decided to try to  using XeLaTeX. The result is far from perfect, worse even than Chrome's rendering.  Is there a way I can improve the result? Is XeLaTeX and LuaLaTeX incapable of handling the Ponny?  :  \documentclass[]{article} \usepackage{lmodern} \usepackage{amssymb,amsmath} \usepackage{ifxetex,ifluatex} \usepackage{fontspec} \defaultfontfeatures{Mapping=tex-text,Scale=MatchLowercase} \IfFileExists{upquote.sty}{\usepackage{upquote}}{} \IfFileExists{microtype.sty}{\usepackage{microtype}}{} \usepackage[normalem]{ulem} \setmainfont{Doulos SIL}  \title{html - RegEx match open tags except XHTML self-contained tags - Stack Overflow} \date{} \author{StackOverflow}  \begin{document} \maketitle  Rege̿̔̉x-based HTML parsers are the cancer that is killing StackOverflow \emph{it is too late it is too late we cannot be saved} the trangession of a chi͡ld ensures regex will consume all living tissue (except for HTML which it cannot, as previously prophesied) \emph{dear lord help us how can anyone survive this scourge} using regex to parse HTML has doomed humanity to an eternity of dread torture and security holes \emph{using rege}x as a tool to process HTML establishes a brea\emph{ch between this world} and the dread realm of c͒ͪo͛ͫrrupt entities (like SGML entities, but \emph{more corrupt) a mere glimp}se of the world of reg​\textbf{ex parsers for HTML will ins}​tantly transport a p\emph{rogrammer's consciousness i}nto a w\emph{orl}d of ceaseless screaming, he comes\sout{, the pestilent sl}ithy regex-infection wil​\textbf{l devour your HT}​ML parser, application and existence for all time like Visual Basic only worse \emph{he comes he com}es \emph{do not fi}​ght h\textbf{e com̡e̶s, ̕h̵i}​s un̨ho͞ly radiańcé de\emph{stro҉ying all enli̍̈́̂̈́ghtenment, HTML tags \textbf{lea͠ki̧n͘g fr̶ǫm ̡yo​͟ur eye͢s̸ ̛l̕ik͏e liq}​uid p}ain, the song of re̸gular exp​re\sout{ssion parsing} will exti\emph{​nguish the voices of mor​\textbf{tal man from the sp}​here I can see it can you see ̲͚̖͔̙î̩́t̲͎̩̱͔́̋̀ it is beautiful t​}he f\texttt{inal snuf}fing o\emph{f the lie​\textbf{s of Man ALL IS LOŚ͖̩͇̗̪̏̈́T A}}\textbf{LL I​S L}OST th\emph{e pon̷y he come}s he c̶̮om\sout{es he co}\textbf{\sout{me}s t\emph{he} ich​}or permeat\emph{es al}l MY FAC\emph{E MY FACE ᵒh god n\textbf{o NO NOO̼}}\textbf{O​O N}Θ stop t\emph{he an​*̶͑̾̾​̅ͫ͏̙̤g͇̫͛͆̾ͫ̑͆l͖͉̗̩̳̟̍ͫͥͨ}e̠̅s\texttt{ ͎a̧͈͖r̽̾̈́͒͑e} n\textbf{​ot rè̑ͧ̌aͨl̘̝̙̃ͤ͂̾̆ ZA̡͊͠͝LGΌ ISͮ̂҉̯͈͕̹̘̱ T}O͇̹̺ͅƝ̴ȳ̳ TH̘\textbf{Ë͖́̉ ͠P̯͍̭O̚​N̐Y̡ H̸̡̪̯ͨ͊̽̅̾̎Ȩ̬̩̾͛ͪ̈́̀́͘ ̶̧̨̱̹̭̯ͧ̾ͬC̷̙̲̝͖ͭ̏ͥͮ͟Oͮ͏̮̪̝͍M̲̖͊̒ͪͩͬ̚̚͜Ȇ̴̟̟͙̞ͩ͌͝}S̨̥̫͎̭ͯ̿̔̀ͅ  \end{document}   UPDATE  Using the Doulos SIL font gets me something closer to what Firefox renders but still far from perfect. I want to use symbols from wasysym and marvosym packages:  \usepackage{wasysym} \usepackage{marvosym}   but it gives an errors as both packages have the command of \CheckedBox. I do not want to use this command, but since both packages have it, it makes confusion for latex. How can I ignore one command to have both packages? Approximation algorithms for min vector subset-sum over GF(2) In  vzn asked about the following problem, which I'll call Vector-Subset-Sum.     Given a set of vectors $v_i$ over GF(2) and a target vector $y$, is there a subset of the $v_i$ summing to $y$?   In the answers, comments, and referenced papers I noted   The decision problem is in P. The natural minimization problem (finding the smallest subset) is NP-hard. It's related to the problem of finding sparse codewords in a linear code.   My question is: are there any known polynomial-time approximation algorithms for the minimization problem in (2)? I know very little about coding theory, so there may be some obvious or well-known approximation-preserving reductions to (3) that I have not seen. When installing or booting from USB flash drive screen goes blank When I was installing Ubuntu 11.10 64-bit on my new PC from a flash drive since the only computers I have do not have disk drives, I ran into a problem.  After the ASUS logo when switching on the PC, and pressing F8 to select the USB flash drive, there was the options thing as normal that allows me to select to either boot form the flash drive or install on the HDD, when I do either of these, there is a bunch of text on a black background, as I would expect, but after a few seconds the screen goes blank and the monitor says No signal.  I have previously installed Ubuntu with a flash drive to fix issues caused my Windows and ran into no problems.  Is it a problem with the pen drive I am using? Or maybe a problem with the system? I tried it in my USB 3.0 ports at the back and the USB 2.0 ones as well.  My Specs are:   &nbsp;&nbsp;AMD Phenom II x4 965BE &nbsp;&nbsp;ASUS AMD Radeon HD 6670 &nbsp;&nbsp;ASUS M5-L75 USB3 (typing this from memory, it's an AM3+ ASUS board with USB3.0 in the AMD700 chipet or something) &nbsp;&nbsp;Corsair XMS3 DDR3 4GB(2x2GB) 1333MHz RAM    I ran the memtest program on the flash drive as well, and it came out clean. UV coordinates on a deformed plane Prepositions used with "inquire" Need Help Fixing Grub after Installing Ubuntu 13.04 x64 Alongside Windows 8 on a Lenovo IdeaPad Y400 with UEFI I have a Lenovo IdeaPad Y400 that came pre-installed with Windows 8. I would like to run Ubuntu alongside it in a dual-boot configuration. I've spent the past week fiddling around, re-installing both Windows and Linux in various configurations, and I've come awfully close to success, but seem to have hit a snag with Grub.  For my most recent attempt, I took the following steps:   Disabled Secure Boot Re-imaged Windows 8 from a hidden recovery partition, effectively restoring the machine to factory state Activated an option called Legacy Support in the BIOS (or is it UEFI now?) Booted Ubuntu 13.04 x64 from a USB stick, chose "install alongside Windows" and accepted all default options After a restart, found that I could boot Ubuntu, but could not boot Windows Once into Ubuntu, I ran Boot Repair with recommended settings and accepted all defaults. When Boot Repair finished, I was presented with the following message:      The boot files of [The OS now in use - Ubuntu 13.04] are far from the   start of the disk. Your BIOS may not detect them. You may want to   retry after creating a /boot partition (EXT4, >200MB, start of the   disk). This can be performed via tools such as gParted. Then select   this partition via the [Separate /boot partition:] option of [Boot   Repair]. ()    I followed the instructions at the url in the message, creating a 1GB EXT 4 partition near the start of the drive  when I tried to run Boot Repair again, the "Separate /boot partition" option on the "Grub Location" tab was disabled.  The new partition is /dev/sda11 and has the label GRUB. On restart, I get the following error message:      error: file '/boot/grub/i386-pc/normal.mod' not found.    grub rescue>    However, if I manually choose the boot partition by hitting F12, I can boot into Windows no problems. Selecting Ubuntu from the boot device menu gives me a Grub menu with the following options:      Ubuntu      Advanced options for Ubuntu       Windows UEFI recovery bootmgfw.efi      Windows Boot UEFI recovery       Windows UEFI recovery LrsBootmgr.efi      Windows Boot UEFI recovery bkpbootx64.efi       Windows Recovery Environment (loader) (on /dev/sda3)       Windows 8 (loader) (on /dev/sda5) System setup    Selecting Ubuntu from this menu allows me to get to my Ubuntu desktop. I haven't tried the other options yet for fear of losing the progress that I've made.   So it looks like I have successfully dual-booted the machine, but that Grub is broken for some reason or another.   My current partition scheme can be seen at:   Thanks in advance - Jonathan Given n distinct objects, there are $n!$ permutations of the objects and $n!/n$ "circular permutations" of the objects (orientation of the circle matters, but there is no starting point, so $1234$ and $2341$ are the same, but $4321$ is different).  Given $n$ objects of $k$ types (where the objects within each type are indistinguishable), $r_i$ of the $i^{th}$ type, there are   \begin{equation*} \frac{n!}{r_1!r_2!\cdots r_k!} \end{equation*}  permutations.  How many circular permutations are there of such a set? I am aware that, to use a Spell Scroll, you must have the related spell on (at least one of) your spell list(s). Then, if you have the spell slot to cast it, you succeed automatically; else, you must make an ability check in order to cast it (failure resulting in the scroll being wasted).  Consider this example : A Cleric 5 / Wizard 4 finds a Raise Dead Spell Scroll. The spell is on the Cleric List, but is a fifth level spell. Considering that the cleric-wizard has fifth level slots, but can only pick up to third level cleric spells, would he have to make the ability check to successfully cast the Raise Dead in the Spell Scroll, or would he succeed automatically ? How to "freeze" a cloth animation at X frame? How would one freeze a simulated body at frame X and use it as a static mesh?  Following a , I've been able to do a cloth animation to my model, now I'd like to have that made static, without the use of the timeline.   The thing is, I'm modelling something that's not going to be an animation, but a static object (something like a statue/figurine). So I don't need the animation, only the shape at a particular frame that I find convenient. I'd like eventually once this is done, to also modify that deformed grid.   I've tried to follow what was said , but couldn't figure out what chipmasque was saying. I'm quite new to blender (been using it on and off, just enough to forget everything).  I'm using blender 2.63, if it is of any relevance.