Can all finite groups be distinguished either by their order, or by number of their subgroups?
Groups with Same Number Of Elements and Subgroups
Can I use a Thunderbolt display for a macbook pro with a mini display port? Accessing System Databases/Tables using LINQ to SQL? How to create individual chapter PDFs from included TeXs? My document structure has   one file with preamble (i.e. MainTex) and around 75 individual .tex files (i.e. Chapter_01, Chapter_02, ..., Chapter_75) representing each chapter.   I am using \include command to create a one big PDF file, the output is MainTex.pdf. Life is all good up to this point.   If I have to create individual PDF for each chapter then do I need to run 75 times with each chapter name and rename the PDF manually to match to chapter name. Because if I include only Chapter_01 and run it creates PDF named as MainTex.pdf.  Is there a way I can automate this workflow? How to open a PDF file from terminal? I used to work on the Mac terminal before and I used:   open file2open.pdf   and the PDF file would be opened on preview or whatever my default viewer was. When I use it in the terminal in Ubuntu I get this error message:   Couldn't get a file descriptor referring to the console Down vote changed to up vote caused reputation meter to pass daily maximum I want to digitize my old family albums using a scanner and there are lots of photos in them. Thus far, my method has been to scan 4 images at a time and then manually cropping them in a simple editor like Picasa or Windows Live Photo Gallery. This has been pretty time consuming as each scan is followed by 4 crop operations. Scanning each image individually would possibly be even more time consuming.  Is there any software or simple plugin (preferably free) that does this job? The best solution I have found is in , but that's an overkill. Is there a similar feature for one of the free photo editors like Paint.NET or GIMP? Why does the road look like it's wet on hot days? Often, I'll be driving down the road on a summer day, and as I look ahead toward the horizon, I notice that the road looks like there's a puddle of water on it, or that it was somehow wet. Of course, as I get closer, the effect disappears.  I know that it is some kind of atmospheric effect. What is it called, and how does it work? Is $L^{p}$ space with alternate norm Banach? Why is "idea" sometimes pronounced as "idear"? I know that idea is pronounced as /aɪˈdiə/, but I've meet several people in real life who put an 'r' at the end of the word. How come? How do I check if a string contains a specific word? For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$? I have a vector space $V$ over a field of characteristic $0$. If $M_1,\dots,M_k$ are proper subspaces of $V$, and $N$ is a subspace of $V$ such that $N\subseteq M_1\cup\cdots\cup M_k$, how can you tell $N\subseteq M_i$ for some $i$?  I was first trying to show it just in the case $N\subseteq M_1\cup M_2$, and hoping to extend it to finitely many $M_i$. If either of the $M_i$ contains the other, the claim follows, so I suppose neither $M_i$ contains the other.   In hopes of a contradiction, I suppose $N\not\subseteq M_1$ and $N\not\subseteq M_2$, Picking $x_1\in N\setminus M_1$ and $x_2\in N\setminus M_2$, I'd have $x_1+x_2\in N\subseteq M_1\cup M_2$. The only thing I could conclude was that actually $x_1,x_2\notin M_1$ and $x_1,x_2\notin M_2$, which seems like a dead end. What's the right way to do this? Making a live USB with persistent storage $e^{i\theta}=\cos\theta + i\sin \theta$  $e^{i\sin^{-1}x}=\cos(\sin^{-1}x)+i\sin(\sin^{-1}x)$  $i\sin^{-1}x=\ln|\sqrt{1-x^2} + ix|$  $\sin^{-1}x=-i\ln|\sqrt{1-x^2} + ix|$  Now from here I'm kind of lost, since it seems like this should be the definition, but when I look it up, the definition of inverse hyperbolic sine is:  $\sinh^{-1}x=\ln(\sqrt{1+x^2} + x)$  So although they're very similar, I guess I just don't know how to handle the logarithm and anything to the ith power or drop off the absolute value. I will be writing scripts for ArcGIS Desktop in Python with ArcPy.   Is there a community or open source project where code and models can be shared? is that function must be constant under the following conditions I'm talking about complex function   $f$ is analytic function on a region $D$ that include the point $z=0$. for every $n\in N$ such $\frac{1}{n}$ is in $D$ , the function follows this condition $|f(\frac{1}{n})| \leq \dfrac{1}{2^n}$   is that function must be constant ? Cannot set LD_LIBRARY_PATH in /etc/profile.d Title of novel with girl who can read minds by observing body language, later communicates with a hive mind on an alien planet's surface As a kid I was greatly influenced by a book where a girl (I believe her name was Marlena) lived in a ship orbiting an alien planet.  The ship was intended to colonize the planet but the humans had encountered difficulty.  People on the surface early on had gone incurably mad.  The planet was covered with single cell organism, but no other life.  Other than the "bacteria" it was sterile.    The girl, along with most of the colonists, was still living on the orbiting ship for the foreseeable future.  The girl had an uncanny knack of reading people's minds by noting minute changes in behavior and body language, kind of like Sherlock Holmes' famous observations.  Eventually she got a chance to go to the surface, and found the planet trying to communicate with her.  In one memorable scene the swirls in the water of a stream formed a face and started trying to call her name, "Eeeena, Aaleeena, Aarleena, Marlena!"  It turns out that the single celled organisms on the planet comprised a hive mind which had tried to communicate telepathically with previous humans by altering their brains slightly, causing the madness.  The girls's brain was different, however, constantly modifying and changing itself so that it was not damaged by the hive mind's attempts to communicate with it. I am working on a proof about Dedekind cuts on the positive rational numbers. I have been stuck for a while on the following point and would appreciate any help.  Given $x\in \mathbb{Q}^+$ such that $x^2&lt;2$, how to find $y\in \mathbb{Q}^+$ such $y&gt;x$ and $y^2&lt;2$? How do I remove Ubuntu's password requirement? What is the difference between CentOS "DVD" vs "Everything" ISOs