What's the difference?  I think these two sentences seems slightly different. But I don't know the exact difference. Could anybody explain the difference to me?
Is there are rule when to use opened vs open?  I always get confused even though I've been speaking English as the dominant language for more than half my life.  E.g.         Is the door open(ed)?   Which file do you have open(ed) in your editor?
Approximation of real number to the power of irrational Say I have two numbers, $c\in\Bbb R^+\,,q\in\Bbb{R\setminus Q}$.  Is there a way to approximate the value of $c^q$?  This question bugging me because of how simple it sound in compare to how complicated it is. First I want to understand what a power of irrational number is, when talking about $\Bbb R^+$(I use this domain for sake of simplicity) we have very well defined actions for power a rational number, we can even use some theorems to get $c^{a/b}=\sqrt[b]{c^a}$, but when I am dealing with irrational number I can not do this.  I know that we have some definition for this because the solution of the equation $2^x=3$ is irrational.  So what exactly does it mean to take something to a irrational power and is there a way to approximate a numeric value for this? Solve the second order ODE $(2x^2 + 1)y'' − 4xy' + 4y = 0$ I need help solving this past exam question, the professor posted exam questions with out solutions to last year's exam, I tried reduction of order, however that seemed to complicate things. And then I tried Euler-Cauchy method however I realized that won't work due to the $(2x^2 + 1)y''$.  Given $y_1=x$ is a solution $$(2x^2 + 1)y'' − 4xy' + 4y = 0$$ Find the second solution $y_2$ for equation. Can I access private members from outside the class without using friends? Disclaimer Yes, I am fully aware that what I am asking about is totally stupid and that anyone who would wish to try such a thing in production code should be fired and/or shot.  I'm mainly looking to see if can be done. Now that that's out of the way, is there any way to access private class members in C++ from outside the class?  For example, is there any way to do this with pointer offsets? (Naive and otherwise non-production-ready techniques welcome) Update As noted in the comments, I asked this question because I wanted to write a blog post on over-encapsulation (and how it affects TDD).  I wanted to see if there was a way to say &quot;using private variables isn't a 100% reliable way to enforce encapsulation, even in C++.&quot;  At the end, I decided to focus more on how to solve the problem rather than why it's a problem, so I didn't feature some of the stuff brought up here as prominently as I had planned, but I still left a link. At any rate, if anyone's interested in how it came out, here it is:   (I suggest reading it before you decide that I'm crazy). Automorphism of rational numbers Let $\mathbb Q$ be group of rational numbers under addition.  Then I want to find out the automorphism group of $\mathbb Q$. In a book it is given that Aut($\mathbb Q$) is isomorphic to $\mathbb Q^*$, the  multiplicative group of rational numbers. I stuck in this. How did the ending happen from Neil's perspective? I am trying to figure out the scene near the finale of Tenet where Neil unlocks the door and gets shot in the face. I can't really see the flow where he opens and holds the door and the protagonist walks in and fights the bad guy. Can you tell the series of events as Neil sees them happen till he gets shot? UPDATE If I am not wrong, I see it like this: Neil was running down towards the door, both the protagonist and his mate are inside with the door locked fighting the bad guy, then, he unlocks the door and walks in and stands behind the door. The protagonist's mate comes out of the room, then the protagonist, then he closes the room, then he look back to get shot in the face. But this doesn't make sense, if he wanted to unlock the door when he was running down, they were already in fighting the bad guy!!!!! Converting a Java Keystore into PEM Format I am trying to convert from a Java keystore file into a PEM file using keytool and openssl applicactions. But I could not find a good way to do the conversion. Any ideas?   Instead of converting the keystore directly into PEM I tried to create a PKCS12 file first and then convert into relevant PEM file and Keystore. But I could not establish a connection using them. (Note that I just need a PEM file and a Keystore file to implement a secured connection. There is no restriction like "Start from a java keystore file". :) So starting from other formats is acceptable with my case)  But a direct conversion method from jks to pem is preferable. How are ETF prices calculated after the market is closed For example:  Because the NASDAQ: DAX is tracking the index INDEXDB: DAX should its trading value be completely flat when the market the markets are open in the US, but closed in Germany? I'm not seeing that artifact in any of the charts I can find. Validation Error less than training error? Table of Contents with Chapter I'm attempting to modify the Table of Contents in my document. Currently, chapter one in my document is listed as   1   Introduction   What I would like to see is  Chapter 1   Introduction   Seems like an easy enough thing to ask for, but can't seem to find a good way to do this. Any feedback would be most appreciative. How can I get my external IP address in a shell script? I need to find my external IP address from a shell script. At the moment I use this function:   myip () {      lwp-request -o text checkip.dyndns.org | awk '{ print $NF }' }   But it depends on perl-libwww, perl-html-format, perl-html-tree installed. What other ways can I get my external IP? I'm new to QGIS and have no programming skills.  Is there an easy/uncomplicated way to create multiple buffers around a line feature? Proving any number of the form $2^n$ can't be written as the sum of k consecutive numbers. I think i have proved that any number of the form $2^n$ can't be written as the sum of k consecutive positive integers, but i would be grateful if i could have some clarification as to whether this is a correct and valid proof or not.  Let $g=x+(x+1)+(x+2)+(x+3)+...+(x+(k-1))$, hence g is the sum of k consecutive positive integers.  $g=kx+\sum_{d=1}^{k-1}d$  Hence, $g=kx+\frac{k(k-1)}{2}$  Rearranging for x we find, $x=\frac{g}{k}-\frac{(k-1)}{2}$  So, for certain values of $k$, we can be sure that a positive integer value of $x$ can be found, and hence $g$ can be written as the sum of $k$ consecutive positive integers.There are two cases for $k$ to considor:  Case 1)  $k$ is odd. If $x$ exists, it must be the case $k$ | $g$, as for odd values of $k$, $\frac{(k-1)}{2}$ will alwyas be an integer, and hence $x$ will.  Case 2)  $k$ is even. $k$ does not divide $g$, but $\frac{g}{k}$ must be a multiple of $\frac{1}{2}$, and hence equals $\frac{h}{2}$, for some odd $h$.  Letting $j=2^n$, assume that we can write $j$ as the sum of $k$ consecutive positive integers.  If $k$ is odd, then if a $k$ exists, it must divide $j$, by Case 1. But, $j$ has no odd factors as it is a power of two, hence $k$ could not be odd.  If $k$ is even, by Case 2 it mut be the case $k$ does not divide $j$. Also, $\frac{j}{k}=\frac{h}{2}$, for some odd $h$.  But, this implies $2j$ has an odd factor, $h$. but, as $2j$ is a power of $2$, it can't have odd factors. So, $k$ can't be odd.  Hence, $k$ is neither odd or even, and this is a contradiction to our assumption. Hence no $x$ exists, and hence and number of the form $2^n$ can't be written as the sum of $k$ consecutive positive integers.  Any feedback on this proof would be appreciated. How can I identify duplicate image files? Over the years, I've accumulated a lot of pictures, across a bunch of different machines.  I think I've mostly kept them in a yyyy/mm/ directory structure, but especially with some of the older pictures, there seem to be a lot of duplicates.  What's the best way to identify the duplicates?  Are there good tools to do this, or am I going to have to write something on my own? Clarifications about Gstreamer I'm a bit confused about what Gstreamer does.   Does it come installed by default with Ubuntu ?  If so which version  is the default for 14.04?  Does it provide hardware accelerated video playback (decoding) ?   If so does it work with VA-API and VDPAU or is it an alternative to those?    Thanks for your help Max Block Height for a Redstone Contraption What's the max height of blocks for a redstone contraption to still work even I'm in the surface below?  Like if I build a pillar to the max height of blocks and build a redstone contraption there, is it still going to work even I'm on the surface below? Continuously copy all file changes from one folder to another on change (Windows) I'm working on a massive Java web application which is kept under centralized version control, but the source files are used to build and run the actual server, which then copies all the files I work on into a random temporary directory while it's running.  My problem is that I need to either rebuild this huge application to see any changes to my files, or keep track of all my changes and copy over the files I've changed back to their source location before committing them back to source control.  My question is: is there a command line script I can run that will monitor any changes in the source folder and automatically copy changed files across to temporary folder X?  The idea is to remove the human point of failure in having to manually mitigate the two-locations problem. If you activated a free upgrade to Windows 10 or bought and activated   Windows 10 from the Microsoft Store, you have a digital license for   your device. This means you can reinstall the same edition of Windows   10 that your device has a digital license for without entering a   product key. During reinstallation, if you’re asked to enter a product   key, you can skip this step. Windows 10 will automatically activate   online after the installation is complete.   source:   Does MS digital license 'fingerprint' hardware information  during the free upgrade / activation and store it (at Microsoft) , so that the next re-install queries MS for the fingerprint and activates Windows 10?  Thought the disk drive may change, I expect that none of the other fingerprinted hardware will change. A map is continuous if and only if for every set, the image of closure is contained in the closure of image Computer doesn't boot up, shows PXE error and/or "operating system not found", "no bootable device", "insert boot media", or other similar error My computer no longer boots Windows or the installed operating system. Instead, I may get this error:  PXE-E61: Media test failure, check cable -or- Check cable connection!  PXE-M0F: Exiting PXE ROM.   and/or one of the following messages or similar:  Operating System not found  No boot device available- No bootable devices--strike F1 to retry boot, F2 for setup utility  No bootable device -- insert boot disk and press any key  No Boot Device Found. Press any key to reboot the machine  Default Boot Device Missing or Boot Failed  Reboot and Select proper Boot device or Insert Boot Media in selected Boot device   What does this mean and what can I do?     This question comes up often and the answers are usually the same. This post is meant to provide a definitive, canonical answer for this problem. Feel free to edit the answer to add additional details. plist or sqlite