If a group $G$ has no nontrival proper subgroups, prove that $G$ is a cyclic group with order $p$, where $p$ is a prime number.
If $G$ has no proper subgroup, prove that $G$ is cyclic of order $p$, where $p$ is a prime number.     I know that since $G $is a group with no proper subgroups, $g \in G$ is not just the identity. I don't know where to go from there.
Control custom properties How can I add remove and create a callback/event for a custom property using bpy. I have a scene, called scene, and I want to add a custom property named x, defulat value 2 (as intereger), and a callback foo, to run when it is changed. I also need to be able to read the value from it, and delete it. How do I do this? so i have a 30A disconnect available for use at a customer site for running 2 5HP motors ( at 480V)  the only question i have though is if the line is sized for a 10HP motor would both the 5HP motors need additional fuse protection?   Or could i get away without having addtional fuses protecting the motors ? If $x$ and $y$ are irrational, is $x + y$ irrational? Is $x - y$ irrational? Migrated questions don't have a user action label in the question list Adding Arabic text to an English document Can I delete user directory after deleting user? The reason I ask is because I recently made the mistake of installing Oracle 12c on my sub-performance laptop. Noticing the excessive amount of resources this added up to on startup, I decided to uninstall it.  What I failed to see through, however, was the fact that it created a new Windows user account in order for the initial installation to work out. In my case, it was mandatory because I only had an administrator account and I didn't see the need to use the built-in account. So, after failing to successfully install 12c twice, I wound up creating not just one, but two Windows user accounts. This had to do with something in regards to how Oracle sets up the Oracle Home business and whatnot, but I have no idea what any of that detailed, so I just went ahead and did it.  After uninstalling what I could in regards to Oracle and the database, I decided the next thing to do would be to remove the created users.  Having Windows 10 Home installed, I couldn't use the local users &amp; groups view/tool to delete these from the GUI. SO, I did the next best thing and Googled a solution. In my case, I used the following command:  net user username /DELETE   When I executed the command, the console gave the response of having successfully deleted the account for both accounts specified.  To verify that this had worked, I went to the users directory located in %SYSTEMROOT%/Users/ and came to find that the user directories were still there.  What does this mean and if I should delete them, will anything bad happen?  Can I even delete these directories?  Regards,  --T.R.G Node access based on view mode How to avoid NoMethodError for nil elements when accessing nested hashes? I built a simple bridge rectifier.         &ndash; Schematic created using   I connected the output of the function generator with CH1 of my oscilloscope and  with the input of the rectifier (using a T-Piece). The output goes into CH2.   The original wave looks like this:    After connecting CH2 the picture looks like this:   While CH2 looks good,  CH1 now shows the wave I would expect without capacitator but not the expected original wave.   Could somebody explain why? I'm using a Gwinstek GDS-1072A-U Oscilloscope and a Gwinstek SFG-1003 function generator. nameref (hyperref) evaluating counter instead of section name What's the proper way to reference a section with a counter in the title? The TOC generates correctly, but the cross references aren't so lucky.  MWE:  \documentclass[letterpaper, 12pt, twoside]{exam}  \usepackage{hyperref}  \newcounter{KSRLessonNumberCounter} \setcounter{KSRLessonNumberCounter}{1} \newcommand{\KSRSection}[2][\value{KSRLessonNumberCounter}]{         \setcounter{KSRLessonNumberCounter}{#1}         \section*{Lesson \arabic{KSRLessonNumberCounter}: #2}         \addcontentsline{toc}{section}{Lesson \arabic{KSRLessonNumberCounter}: {#2}}         \stepcounter{KSRLessonNumberCounter} } \newcommand{\KSRSubsection}[1]{         \subsection*{#1}         \addcontentsline{toc}{subsection}{#1} } \newcommand{\KSRLessonNumber}{ }  \begin{document}  \KSRSection{Sample}  This is the first lesson. The second lesson is \nameref{sec:blah}.  \KSRSection{Blah} \label{sec:blah}  This is the second section  \KSRSection{Lorem Ipsum}  Dollars are Set in \nameref{sec:blah}.  \end{document} I want to work on a small app that will use Telegram from within Ubuntu but wanted to first know if there was already a work in progress for this since I noticed that, for example, pidgin has support for WhatsApp. With this in mind, is there a messenger app that has support (even basic support) for Telegram from within Ubuntu. Applying graduated renderer in PyQGIS? Just trying to run the following code already given in the pyqgis cookbook to create graduated colors symbology (as in example with 2 classes)  I define the source info for the shapefile but when I run execute the code within my test-plugin, it just adds the layer without classifiying. Just adds as usual, all polylines appear same.  Any solution or working code/method?  link to code in cookbook   from qgis.core import  (QgsVectorLayer, QgsMapLayerRegistry, QgsGraduatedSymbolRendererV2, QgsSymbolV2,QgsRendererRangeV2)  myVectorLayer = QgsVectorLayer('C:/my_test_shape_file.shp', 'test_shp_file', 'ogr')  myTargetField = 'target_field' myRangeList = [] myOpacity = 1  # Make our first symbol and range... myMin = 0.0 myMax = 50.0 myLabel = 'Group 1' myColour = QtGui.QColor('#ffee00') mySymbol1 = QgsSymbolV2.defaultSymbol(myVectorLayer.geometryType()) mySymbol1.setColor(myColour) mySymbol1.setAlpha(myOpacity) myRange1 = QgsRendererRangeV2(myMin, myMax, mySymbol1, myLabel) myRangeList.append(myRange1)  #now make another symbol and range... myMin = 50.1 myMax = 100 myLabel = 'Group 2' myColour = QtGui.QColor('#00eeff') mySymbol2 = QgsSymbolV2.defaultSymbol(myVectorLayer.geometryType()) mySymbol2.setColor(myColour) mySymbol2.setAlpha(myOpacity) myRange2 = QgsRendererRangeV2( myMin, myMax, mySymbol2, myLabel) myRangeList.append(myRange2)  myRenderer = QgsGraduatedSymbolRendererV2('', myRangeList) myRenderer.setMode(QgsGraduatedSymbolRendererV2.EqualInterval) myRenderer.setClassAttribute(myTargetField) myVectorLayer.setRendererV2(myRenderer) QgsMapLayerRegistry.instance().addMapLayer(myVectorLayer)      @Kelly's code works perfectly.   However I noticed that both the code (one I have typed in my first message and yours in the 2nd message) DO NOT work in QGIS v1.7.3 but WORKS in QGIS v1.8.0. I think this was a bug(?) that already resolved in v1.8.0  And one more question;  Do you have any sample code for (natural breaks, Jenks) classification of the "numeric_attribute_field" based on given number of classes (i.e. no of classes will be a variable in the code, say "n", and I will pass that from the plugin GUI i.e. n = spinBox.value() ) I was wondering if there is an easy way to trigger an e-mail alert on Windows Server 2008 when any logical disk partitions become low on space.  I have 2 SQL servers that have come close to running out of disk space because of the DB log files.  Thanks, Ryan How to set the command prompt's color in Bash? After swapping the positions of the hour and the minute hand, when will a clock still give a valid time? At 12 o'clock, the hour hand and minute hand of the clock can be swapped, and the clock still gives the same time, but at 6 o'clock, it can not be swapped. So in what cases when we swap the hour and the minute hand position does a clock still give a valid time? How to test for minimum amount of items in inventory and execute a command if true I am using the AmazingKit plugin on my Minecraft server to make inventory kits for players. In a command block I have the following command:  /tellraw @p ["",{"text":"Iron","clickEvent":{"action":"run_command","value":"_____"}},{"text":" / "},{"text":"Gold","clickEvent":{"action":"run_command","value":"_____"}}]   Which prints the following result: Iron / Gold.  When a player clicks on Iron, what command should I write where the empty space is _____ in order to check if the player has at least (>=) 20 iron ingots in his inventory and if he/she does, remove 20 iron ingots and execute /kit Basic. If the player has less than 20 iron ingots in inventory, the command won't be executed. Instead, Insufficient amount of iron ingots will be printed out.   Same applies when a player clicks on "Gold".  I'm on 1.14 version Boolean b1 = true; Boolean b2 = true; String b3 = 'b1 &amp;&amp; b2'; Boolean b4 = Boolean.valueOf(b3); system.debug('test Bool '+ b4);   Given a string how can you convert into expression without breaking the sting. I am looking for a textbook that treats the subject of Special Relativity from a geometric point of view, i.e. a textbook that introduces the theory right from the start in terms of 4-vectors and Minkowski tensors, instead of the more traditional "beginners" approach. Would anyone have a recommendation for such a textbook ?  I already have decent knowledge of the physics and maths of both SR and GR ( including vector and tensor calculus ), but would like to take a step back and expand and broaden my intuition of the geometry underlying SR, as described by 4-vectors and tensors. What I do not need is another "and here is the formula for time dilation..." type of text, of which there are thousands out there, but something much more geometric and in-depth.  Thanks in advance. Possible to perform cross-database queries with PostgreSQL? I just finished taking my first year of calculus in college and I passed with an A.  I don't think, however, that I ever really understood the entire $\frac{dy}{dx}$ notation (so I just focused on using $u'$), and now that I'm going to be starting calculus 2 and learning newer integration techniques, I feel that understanding the differential in an integral is important. Take this problem for an example: $$ \int 2x (x^2+4)^{100}dx $$ So solving this... $$u = x^2 + 4 \implies du = 2x dx \longleftarrow \text{why $dx$ here?}$$ And so now I'd have: $\displaystyle \int (u)^{100}du$ which is $\displaystyle \frac{u^{101}}{101} + C$ and then I'd just substitute back in my $u$. I'm so confused by all of this.  I know how to do it from practice, but I don't understand what is really happening here.  What happens to the $du$ between rewriting the integral and taking the anti-derivative?  Why is writing the $dx$ so important?  How should I be viewing this in when seeing an integral?