How to create a directory for everybody?
How can I share a directory with an another user?
I'm trying to prove commutativity of addition for vector spaces, using the axioms for vector spaces. Apparently commutativity can be proven! Im having trouble getting a good feel for what is allowed and what is not. Here's my work so far:  $u+v+u+v = 2(u+v) = 2u + 2v = u+u+v+v = u+(u+v)+v$  Here I just wanna claim that $u+(v+u)+v = u+(u+v)+v$   $\Rightarrow -u+u+(v+u)+v+(-v) = -u+u+(u+v)+v+(-v)$ : here im just adding -u to the right, and -v to the left. Question: is this "adding to both sides" really legit in this context? Why?   Quick help proof: $-v+v = (-1)v+(1)v = (-1+1)v = 0v = 0 = v-v$  And another: $ 0+v = v+(-v) + v = (1)v + (-1)v + v = (1-1)v + v = v = v+0$  We have $0 + (u+v) + 0 = 0+(v+u)+0 \Rightarrow u+v = v+u$  This feels ugly and not at all elegant, especially the great leap "add -u to both sides" feels completely out of place. Do I need more lemmas? Is there a more elegant way?   //not homework or anything, just for my own pleasure, feel free to provide theory, as it is more insightful than solutions. :) Thanks!   EDIT: corrected notation a little. How to prevent click events on the document body (maybe a bug in Cordova?) How to dismiss the Windows 8.1 Upgrade banner? As of today, my Windows 8 system is displaying a large banner covering about a quarter of the screen, demanding that I upgrade to Windows 8.1 for free.  The banner helpfully informs me that that I can continue to use the computer while the upgrade is downloading.  There's a button to go to the store for the upgrade, but no other choices, such as No Thanks, Maybe Later, or Absolutely Not.    I can't find a way to dismiss the banner, and I can start programs but can't give them focus while the banner is present.  So I'm dead in the water.  How can I fix this?  Bringing up Task Manager doesn't give me any options.    My employer doesn't yet support Windows 8.1 (which is also an issue, but beyond my control) so I won't be able to connect to work if install the upgrade.  So there is no way on God's green earth that I'm going to install this upgrade now.    UPDATE: The banner went away after the second restart and I was able to run regedit as @magicandre suggested.  The banner hasn't reappeared.  So far, so good. Storing two kinds of point geometry in shapefile or creating multipoint shapefiles? Following , can I have a mixture of two kinds of geometry in a shapefile of type point. Just like I have about shapefiles of type polygon or I should always create a shapefile of type multipoint in order to support multipoints in my layer?    My problem is as you see at , I can't use ogrinfo in order to understand that the geometry type of a multipoint shapefile will be known as wkbMultipoint or wkbPointwhen I use this line of code:    OGRwkbGeometryType GeometryType = poLayer -&gt;GetGeomType();     for a layer of type multipoint before programming.     Will OGR know a layer of type multipoint as wkbpoint or wkbmultipoint?   When we create a shapefile in ArcCatalog, we have point and multipoint, but not multipolyline or multipolygon for polyline and polygon.Why? What is the correct output of cat /etc/apt/sources.list? Is there ever a time to create a user for a company? I'm wondering if there's ever a reason or time when a company should have its own user (like say, Stack Overflow), instead of users that make it up (like, Jeff Atwood).   I figure this is kind of a bad idea as someone with access to multiple accounts could upvote himself over and over.... but is there any point this is okay and/or a good idea? What is color temperature and how does it affect my photography? In indirect speech we generally backshift the tense. For ex - Direct speech : "I am the most powerful person." Indirect speech : "He said that he was the most powerful person."  What if someone reports like -  He denied the charges claiming that he is/was the most powerful person. So here which is correct- is or was ?  Thanks in advance. Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A I ran across this problem in my Analysis class and can't seem to come up with a good solution. Here's the question: Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals $A$. $f$ is continuous on $[a,b]$ and differentiable on $(a,b)$.  I tried applying the Mean Value theorem like this: There exists a $c \in (a, x)$ st $f(x)-f(a)=f'(c)(x-a) \implies \frac{f(x)-f(a)}{x-a}=f'(c) \implies f'(a)=\lim_{x\to a}\frac{f(x)-f(a)}{x-a}=\lim_{c\to a}f'(c)=A$  However, I think this is wrong. I am pretty sure the Mean Value theorem is needed, but my application of it seems to be incorrect. Would somebody be able to point me in the right direction? Conjugate Variables, Noether's Theorem and QM How to show this property of $\mathbb{RP}^{n}$. To prove that: The $n$-dimensional projective space can be presented as:  $\mathbb{RP}^n=\bigcup_{i=0}^{n} A^{i}$.  (The intersection of each two $A^{i}$ is empty)، $A^{i}$ is isomorphic to $\mathbb R^{i}$ ($A^{0}$ includes only one point). The definition of $\mathbb{RP}^n$ is: $\mathbb{RP}^n= (\mathbb R^{n+1} \setminus \{0\})/ \sim$ , $\sim$ is defined as: $x \sim \lambda x$for all $\lambda\in \mathbb R^\times$ and $x\in \mathbb R^{n+1} \setminus \{0\}$. $\mathbb R^\times $ is the productive group of scalars $\ne0$ in the field $\mathbb R$. I'm just a beginner in this field so any help would be appreciated. How does Intel Turbo Boost work? I just got a new Intel CPU, and the specifications say 3.5GHz but with turbo boost to 3.9GHz. What does Intel Turbo Boost do? From the description it sounds like they are saying "The road's speed limit is 100 km/hr, but if you get to that speed then the new speed limit is 140 km/hr". Why not just set the clock speed to 3.9GHz to start with? So what is Intel Turbo Boost actually doing? Is $n^{th}$ root of $2$ an irrational number? Possible Duplicate:          Will every $n^{th}$ root of $2$ be an irrational number? If yes, how can I prove that? php function for collating external variables into a single object regardless of GET or POST I recall reviewing someone else's PHP code once and he had a function or class method that rolled all GET and POST variables into a single plain old object that could then be passed around. If the same name-value pair appeared in both GET and POST, POST would win.  Is there a well-coded PHP add-on out there of any sort that does exactly this? Recently, I was doing my homework and I found out that Torque can be calculated using $\tau = rF$. This means the units of torque are Newton meters. Work &amp; Energy are also measured in Newton meters which are Joules.  However, torque isn't a measure of energy. I am really confused as why it isn't measured in Joules. Converting ArcGIS (*.mxd) file to QGIS (*.qgs) file? My wireless has suddenly became disabled by hardware switch, BIOS, rfkill, fn+f8 do nothing Using Regular Expressions to Extract a Value in Java I have several strings in the rough form:  [some text] [some number] [some more text]   I want to extract the text in [some number] using the Java Regex classes.  I know roughly what regular expression I want to use (though all suggestions are welcome). What I'm really interested in are the Java calls to take the regex string and use it on the source data to produce the value of [some number].  EDIT: I should add that I'm only interested in a single [some number] (basically, the first instance). The source strings are short and I'm not going to be looking for multiple occurrences of [some number]. When abstract logic circuits get translated to the electrical equivilant, how are conversions from 0 to 1 handled? I've searched around and there's lots of good information out there, but I'm a bit of a n00b when it comes to the precise meanings of words like current, voltage, amplify, resistor, diode etc. So what at first presents itself as a simple explanation quickly turns into a wikipedia tabfest of ever increasing complexity. With that in mind please forgive my probably inaccurate use of these terms in this post.  The basic problem for me is that gates on a logic circuit appear to be creating power from nothing, which is impossible. For example imagine two NOT gates connected in sequence: To my uninitiated mind what seems to be happening is that the first NOT gate cuts the power to the second NOT gate, which responds by magically conjuring new power out of thin air and sending it on it's way. The only explanation I can come up with feels a bit redundant and absurd (That every single gate on the diagram is implied to be directly connected to a power source)  The closest I've come to an answer is something to do with changing the "signal" from "high" to "low" but again, I'm not familiar enough with the language. It still suffers from the same problem, if you've got a low signal how is it that a NOT gate can turn it into a high one without directly drawing on a power source?  To wrap up and present the question in all it's rookie glory: How do logic gates physically convert 0 to 1 without violating the law of conservation of energy? I install virtualBox on Ubuntu 16.04, but after install and create new virtual Host shows this error:     Kernel driver not installed (rc=-1908)      The VirtualBox Linux kernel driver (vboxdrv) is either not loaded or there is a permission problem with /dev/vboxdrv. Please install virtualbox-dkms package and load the kernel module by executing  modprobe vboxdrv       as root. If it is available in your distribution, you should install the     DKMS package first. This package keeps track of Linux kernel changes and   recompiles the vboxdrv kernel module if necessary.  where: suplibOsInit what: 3 VERR_VM_DRIVER_NOT_INSTALLED (-1908) - The support driver is not installed. On linux, open returned ENOENT.     How to address this modprobe vboxdrv error?