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How we can show every permutation is either even or odd,but not both......I can't arrive at a proof for this ..... Can anybody give me the proof...  Thanks in advance... Nested indenting issue How to get correct indentation after entering a nested list? I am writing a code review and I could not figure this out by googling. Here is an example of the three formatting styles I tried to use (but none of them works as I would like):  Case 1  The task is to align the last line (see below) "In the first line you use camelCase..." with the last line above the numbered list. In my first attempt, I added a new line (empty line) after the second numbered list item, and then indented by 4 spaces:     Variable name casing: See  on "Snake Case". In Perl, we use "snake_case" instead of "camelCase", and be consistent. Example:   Line 14: my $testType  Line 18: my $right_frame   In the first line you use camelCase, whereas in the second you use     snake_case.     As you can see, this gives the correct indentation but it introduces a blank line above the first numbered item.  Case 2  In this case I do not add the blank line after the second numbered list item ( but still indent by 4 spaces ):     Variable name casing: See  on "Snake Case". In Perl, we use "snake_case" instead of "camelCase", and be consistent. Example:   Line 14: my $testType  Line 18: my $right_frame In the first line you use camelCase, whereas in the second you use     snake_case.      In this case the line is considered as part of the last list item  Case 3  In this case, I try to add two blank spaces (invisible) at the end of the second list item:     Variable name casing: See  on "Snake Case". In Perl, we use "snake_case" instead of "camelCase", and be consistent. Example:   Line 14: my $testType  Line 18: my $right_frame In the first line you use camelCase, whereas in the second you use     snake_case.      In this case the line is considered part of the second item, and hence not correctly indented.  How to achieve the correct indentation? What software can I use to view epub documents? What software can I use to view .epub documents? How would one write object-oriented code in C? I want to get user input in one page, store that in a php variable and use it in another php page. I have tried using 'sessions' but it doesn't seem to be working. Is there another safe alternative? This information is likely to be usernames and passwords. when EditText is empty and click calculateButton, app crashes Overview of basic facts about Cauchy functional equation The  asks about functions $f \colon \mathbb R \to \mathbb R$ such that $$f(x+y)=f(x)+f(y).$$ It is a very well-known functional equation, which appears in various areas of mathematics ranging from exercises in freshman classes to constructing useful counterexamples for some advanced questions. Solutions of this equation are often called . Also a few other equations related to this equation are often studied. (Equations which can be easily transformed to Cauchy functional equation or can be solved by using similar methods.) Is there some overview of basic facts about Cauchy equation and related functional equations - preferably available online? How to convert URL parameters to a JavaScript object? From time to time I lose all edits because of undo in Object Mode. If I enter immediately after Undo in Edit Mode I can't redo, and switching again in Object results in losing all edit history.  How can I resolve this? Separating undo history by mode or linear/unified will both be acceptable.  Edit:I think the most preferable solution will be to disable/skip edit undos when in object mode through an addon. Fully transparent windows in Pygame? Is it possible to get a fully transparent window in Pygame (see the desktop through it)?  I've found how to create a window without a frame, but there doesn't seem to be any obvious way to make it transparent.  I'd be willing to tie into system-specific technology/frameworks as long as there are solutions for both Windows and Mac OS X, but I'm not sure which direction to be looking.  The only topic I was able to find , which isn't something I can do for this particular project (needs to be Pygame). Trigger a button click with JavaScript on the Enter key in a text box Chrome S3 Cloudfront: No 'Access-Control-Allow-Origin' header on initial XHR request Did Sidious know the secret of cheating death? In Star Wars: Revenge of the Sith, Chancellor Palpatine tells Anakin the tale of Darth Plagueis the Wise. He told Anakin that if he joined the dark side he could save the people he loved from death by extending their midichlorian count, just as Darth Plagueis had done (obviously more subtly than that).  When Anakin asked what had happened to Plagueis, Palpatine says:      Unfortunately, he taught his apprentice everything he knew. Then his apprentice...killed him in his sleep.   It is revealed (not in the movie) that it was Palpatine himself that was Plagueis' apprentice  After Anakin and Palpatine kill Mace Windu, Palpatine says,     To cheat death is a power only one has achieved, but if we work together I know we can discover the secret.   This implies that Palpatine doesn't already know the secrets but if Plagueis taught him "everything he knew" then surely he would have.  So did Sidious know the entire time or was "everything he knew" an exaggeration?  Just to be clear when I say "cheat death" I only mean extending someone's midichlorian count, not "transfer essence" or anything else like that. If a mass moves close to the speed of light, does it turn into a black hole? I'm a big fan of the podcast Astronomy Cast and a while back I was listening to a Q&amp;A episode they did. A listener sent in a question that I found fascinating and have been wondering about ever since.   From the show :      Arunus Gidgowdusk from Lithuania asks: "If you took a one kilogram mass and accelerated it close to the speed of light would it form into a black hole? Would it stay a black hole if you then decreased the speed?"   Dr. Gay, an astrophysicist and one of the hosts, explained that she'd asked a number of her colleagues and that none of them could provide a satisfactory answer. I asked her more recently on Facebook if anyone had come forward with one and she said they had not.  So I thought maybe this would be a good place to ask. Removing unnecessary vertices? Inequality involving sides of a triangle How can one show that for triangles of sides $a,b,c$ that   $$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b} &lt; 2$$  My proof is long winded, which is why I am posting the problem here.   Step 1: let $a=x+y$, $b=y+z$, $c=x+z$, and let $x+y+z=1$ to get   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}&lt;2$  Step 2: consider the function $f(x)=\frac{1-x}{1+x}$, and note that it is convex on the interval (0,1), so the minimum of   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}$  is reached when the function takes the extreme points. i.e. $x=y=0, z=1$.    But going back to the fact that this is a triangle, we note that $x=y=0 \implies a=0$ which is not possible, so the inequality is strict. I am trying to solve the following question which is Ex3 from Arthur Engel, Problem Solving strategies. Here is the question: $\sum_{k=1}^n k^3 {n \choose k}$ and asks to find the sum. I am sincerely having a hard time trying to figure out how to solve it and get $n^2 (n+3)(2)^{n-3}$. I would really appreciate if someone could show the step-by-step process. Thank you! Mac App Store: Downloads just don't start (Mojave) I want to download apps in the Mac App Store and the apps won't start to download. As you can see in the pictures below, the spinner starts spinning but nothing gets downloaded, the download simply doesn't start. I am logged in with my account. I tried logging out of the App Store and logging in again, restarting the Mac etc, nothing helped.  This is a relatively fresh installation of Mojave 10.14. Before with High Sierra 10.13 everything worked fine. It's a Late 2013 MacBook Pro 13". Installations are allowed from App Store and identified developers.   Some screenshots from Console output below. Is there a shortcut for switching between these three modes? I was running out of space for Windows 10, so I deleted my Ubuntu partition and then combined the free space and added it to the Windows 10 partition into a single partition (the boot partition was untouched). Now all I get when I turn on my computer is:  Error no such partition. &gt;grub rescue   I have tried rebooting, but it did not work. Is there any way to fix it? My idea is that if i reinstalled Ubuntu it may fix it, but I'm not sure. I don't have a Windows repair disk, and I can't make one, but I do have a 4GB USB flash drive.