I was wondering the following: Let's suppose that $G$ is a non-empty set, then, can we always find a binary operation $*$ such that $(G,*)$ is a group?  For example, if we fix $G=\mathbb{Q}$ the sum of rationals $+$ tell us that $(\mathbb{Q},+)$ is a group.  Another way to understand it: Is there a set for which we cannot find a binary operation such that is not a group?
I know that there is no vector space having precisely $6$ elements. Does every set have a group structure?
How to link data to a polygon ArcMap 10.3 I have a map with different polygons (118). Each of this polygons represent diferent vegetation types.  For each of those polygons I have data of which species there is and how abundant they are (the abundance is measured with a scale from 1 to 3).  I would like to "link" (I am sorry if its not the correct way of name it) the data of which species and abundance there is in each of those polygons.   I would like afterwards to be able of selecting the different polygons containing the same abundance and species.  In the polygons I created there is no atributes associated other than (FID, shape and Id. the 3 of them created alone by the program when I drew them) and the tables I have in excel with the data I want to "link" to the polygons contain a column called species and another abundance.  As you can see, I'm pretty new using the program...    As I have tried to do what you all suggest in the comments down here, and I couldn't achieve what I was wanting to do (provably because of my bad explanation before...)  I leave a picture:  As you can see in the attribute table, that is how every attribute table of each polygon (which represents one area) looks like. On the right there is how I have my data in excel. Could you please suggest something I could do in order to add to the polygons attribute table the data belonging of species and its abundances (polygon number 1 has to have all the species (Acer mons, Acer pseu, Acer repens….) and its abundance (which are the numbers of the row Area1). Possible Duplicate:          On Windows I am able to switch between keyboard layouts by pressing Alt+Shift. Is there a similar keyboard shortcut in Ubuntu? C# Structs: Unassigned local variable? OS X Yosemite brought support for recording iPhone/iPad screen natively without having to using AirPlay applications like AirServer or Reflector.   How do I record the iPhone screen on macOS ? How to deal with spaces in a variable When does a complex matrix have a square root? What is the neccessary and sufficient condition for a matri$A \in C^{n  \times n}$ so that it has a "square root" , that is there is a matrix $B \in C^{n \times n}$ such that $A=B^2$.  I am not quite sure but I was thinking that it would be that A and B are similar. In the construction of types of numbers, we have the following sequence:  $$\mathbb{R} \subset \mathbb{C} \subset \mathbb{H} \subset \mathbb{O} \subset \mathbb{S}$$  or:  $$2^0 \mathrm{-ions} \subset 2^1 \mathrm{-ions} \subset 2^2 \mathrm{-ions} \subset 2^3 \mathrm{-ions} \subset 2^4 \mathrm{-ions} $$  or:  "Reals" $\subset$ "Complex" $\subset$ "Quaternions" $\subset$ "Octonions" $\subset$ "Sedenions"  With the following "properties":   From $\mathbb{R}$ to $\mathbb{C}$ you gain "algebraic-closure"-ness (but you throw away ordering). From $\mathbb{C}$ to $\mathbb{H}$ we throw away commutativity. From $\mathbb{H}$ to $\mathbb{O}$ we throw away associativity. From $\mathbb{O}$ to $\mathbb{S}$ we throw away multiplicative normedness.   The question is, what lies on the right side of $\mathbb{S}$, and what do you lose when you go from $\mathbb{S}$ to one of these objects ? Why do Tcler suggest to brace your `expr`essions? How does the ternary operator work? A book on quantum mechanics supported by the high-level mathematics How do I remove a configuration object from the active configuration? I'm writing a custom module for Drupal 8. It defines a field storage configuration object, in a file called modules/mymod/config/install/field.storage.bloom_stem.bs_twitter_ac.yml.  The problem is that this is not removed when I uninstall the module; it is apparently left behind because, when I re-install the module, I get a crash.   drush -y pm-uninstall mymod drush cr drush -y en mymod      exception 'Drupal\Core\Config\PreExistingConfigException' with message 'Configuration objects (field.storage.bloom_stem.bs_twitter_ac) provided by mymod already exist in active configuration'   So it seems I need to some how manually remove this configuration object. Do I need to provide some more code that deletes it when the module is uninstalled? Why does the question's closed status disappear when clicking to load a new edit? Why does a free-falling body experience no force despite accelerating? Is there an easy way to get to www.stackexchange.com from any of the SE sites? One thing I've noticed about the relatively new sitewide layout is that I can't find a quick way to get back to www.stackexchange.com without finding StackExchange in the sites list. As a result, I am typing stackexchange in my toolbar a whole lot more often now. In particular, I tend to enjoy browsing the hot questions list and my own personal feed quite often so visit these pages on a daily basis. Is there an easy link to them that I'm missing?  (On the android app, there is a feed in the menu that I really appreciate, something like that on the desktop would be ideal!) Word for an event that will likely never happen again I've read , but none of them are what I am looking for. I once read a book that used a word to describe an event that has happened in the past, but the odds were so astronomical that it will likely never happen a second time. The context I read these words in were the creation of the first life on earth (without any theological ideas). Basically, the text said that the scenario for the creation of the first living organism happened on a planet where conditions were just right by complete chance, and that the odds of this were so astronomical that it would likely never happen again anywhere in the universe over any length of time.  Sample sentence: "The creation of the first organisms was incredibly unlikely, the event can be called a _________ event, or an event that will likely never happen again."   I can't pretend to understand the validity of the claims by the text, but the words they used to describe these events were quite clever (and scientific sounding) that it would make a fun hyperbole.  I thought it was something along the lines of singularity event, but that doesn't sound quite right. Windows 8 opens notepad on boot- no startup entry found I just upgraded from windows 7 to windows 8 and everything is working fine except notepad keeps opening on boot with a "access denied" window that comes up as well. I've ran MBAM and removed some junk, I've disabled every "file not found" item in autoruns as well as something that had a text/xml title in it and I've ran CCleaner a few times. Nothing is working, any help is much appreciated! Why are date-based hats awarded too early? Sorting hashmap based on keys Chapterwise page range in the TOC Can you give me some advice for how to obtain the following format of the TOC?        Chapter’s heading 1-7   Chapter’s heading 9-10   Chapter’s heading 11-15 Why does the humidifier make a stove's flame orange? Just like , the color of my stove's flames were affected by the humidifier as well.  Why does this happen? Is it a good thing or a bad thing ?