Subadditivity inequality and power functions
Prove that $(p+q)^m \leq p^m+q^m$
Everybody knows :-) that in Windows plain text files lines are terminated with CR+LF, and in Unix&amp;Linux - with LF only. How can I quickly convert all my source code files from one format to another and back? Classifying whether a collection of objects is a set I'm wondering whether or not there is a definite criterion for determining whether a collection of objects is a set. In the literature, I've recently encountered some obscure examples (in Riemann Surface Theory, to be precise) of naturally-arising collections of objects which are not sets.   Here is some pseudo-rigor to make the question more precise:   Let $S$ be a collection of objects. Is there some property $P$ so that $S$ is a set iff $S$ has property $P$? Can EU citizens travel to UK after Brexit with just an identity card? What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters? What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters?  I believe the answer for this is 6. As we can write the group elements as below   (a)(b)(C) (ab)(c) (ac)(b) (bc)(a) (abc) (bac)   Can we generalize that for any $S_n$ onto $n$ the number of automorphisms will be $n!$ Also I cannot find this anywhere in my text, can we have a permutation $S_n$ onto $m$ where $n\neq m$? (for eg: is it possible to have a permutation group say $S_5$ on say 2 elements?) Available space not changing when resizing a partition In my computer I have several partitions. I have one partition with Fedora that had just below 40 GB of space, and which I wanted to make bigger. Therefore, using GParted, I moved 10 GB from another partition to the Fedora partition. Now, according to GParted, I should have just below 50 GB (see sda12):  However, from Fedora itself the available space looks different:  This was the same space that was available before I resized the partition. How do I make that space actually available to Fedora? Prove that $\cos\theta$ is root of equation $8x^3-4x^2-4x+1=0$, given $\theta=\frac{\pi}{7}$.   I put $\cos\theta$ in equation, but couldn't show the left-hand side to be zero. 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. Inductive proof that there are infinitely many pairs of consecutive powerful integers? I always used to open a new VLC window; go to "open file"...etcetera when I wanted to watch something because when I click on a file in Windows Explorer and chose "open with" or just clicked on the file or right-clicked to choose "play with VLC" it always opened in an old already used VLC window.  Is there any way to get VLC to use a new one without always resorting to: Open VLC, "open file", find file etcetera? Equivalent of "both" when referring to three or more items? What would be the correct word to use when referring to three or more items, in the same manner as the word both?  For example, using two words, with the word both:     "There are several recommendations I   have to further improve the sites —   both to improve their profit, and   decrease their cost."   Using three words, with a blank space in place of the correct word:     "There are several recommendations I   have to further improve the sites —   _ to improve their profit, decrease their cost and improve their   usability."   So, what would be the correct word to use in place of the __? External hard drive very slow to load after dropping it and can't be repaired with Disk Utility Today as I was using my WD HDD, it fell off my corner. After I fixed the thing, I plugged it into the Mac and it loads the HDD but it's very very very very slow. It also does not work sometimes. The entire laptop just hangs  Tried running Disk Utility First Aid but it won't work.  It says some error and hangs  Can someone advise me on what I can do in this case? How can I prevent URLDownloadToFile from retrieving from the cache? I am using URLDownloadToFile to retrieve a file from a website. Subsequent calls return the original file rather than an updated version.  I assume it is retrieving a cached version. I have 2 equation in terms of $a,b$ and $c$ .  $3a + 10b + 5c =0$ and $4a + 6b + 2c =0$  I need to find a:b:c and answer is $\dfrac a5 = \dfrac {b}{-7} = \dfrac {c}{11}$  I want to know how to get that?  My attempt:  Given equations can be written in form   $$\left ( \begin{matrix}           3 &amp; 10 &amp; 5 \\           4 &amp; 6 &amp;  2 \\           \end{matrix} \right )  \left ( \begin{matrix}           a\\         b\\         c\\         \end{matrix} \right ) =  \left ( \begin{matrix}            0 \\          0\\         \end{matrix} \right ) $$  But here I don't have any idea how to proceed. I can do for 3×3 matrix and I thought it can be done in same way.  Thanks. Updating list definition using features I have a feature that deploys content types, a list definition and template that uses these content types and finally a list instance. This feature is already in production.  Now we have a change request to add new views to this existing list. So I make the changes to schema.xml and upgrade the solution. But alas, the new views don't show up. If I create a new site, the list instance is created with the new views. I tried deactivating/reactivating, iisreset but still no success. Is there anything I'm missing? How to change the numbering of \part, \chapter, \section, ... to alphabetical, Roman numbers, etc Remove automatically added keyboard inputs and prevent them from coming back (Windows 10) I have 2 languages installed on my computer, both with a single input method.  I have 2 keyboards: CES-CSQ and ENG-US.    However lately (maybe after the last Win10 update) I started to see 2 additional keyboards in my systray  - namely CES-CS and ENG-CSQ.    Is there there a way to remove those 2 input options (CES-CS, ENG-CSQ) which I do not see in the Control panel's Language options?  Solution described at  question does not apply to my problem because I do not see input options that I want remove in Control panel's Language options. How to repeat a string a variable number of times in C++? I want to insert 'n' spaces (or any string) at the beginning of a string in C++. Is there any direct way to do this using either std::strings or char* strings?  E.g. in Python you could simply do  &gt;&gt;&gt; "." * 5 + "lolcat" '.....lolcat' Let $f$ be a holomorphic function in $H={\{z\in\mathbb{C}}:\Re(z)&gt;0\}$ such that it is continuous in $cl(H)$, $|f(z)|\leq1$ $\forall z\in \delta H$ and $\lim_{|z|\to\infty}f(z)=0 $. Prove that $|f(z)|\leq1$ $\forall z\in H$. I thought about taking the bounded set $H\cap D(0,R), R&gt;0$. This way we could use the maximum modulus principle to prove it but I do not really know how to relate it with the limit since I would need $|f(z)|\leq1$ $\forall z\in H\cap D(0,R)$, and I do not have it on $D(0,R)$. I have a matrix and need to highlight some elements in the matrix. I have found how to highlight a single element (I want to put the cell in the square):  $$ A = \begin{bmatrix} \fbox{0} &amp; \fbox{0} &amp; 0 \\  \fbox{0} &amp; \fbox{0} &amp; 0 \\ 1 &amp; 1 &amp; 1 \\  \end{bmatrix}$$   But how can I outline elements of the submatrix like in the picture below? I need just a frame where some elements are located. 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?