What is the difference in a normal class who has all concrete methods and an abstract class who has all concrete methods
Abstract class with all concrete methods
How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \lfloor\frac{\lfloor x\rfloor}{n}\rfloor=\lfloor\frac{x}{n}\rfloor$. How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \left\lfloor\frac{\lfloor x\rfloor}{n}\right\rfloor=\left\lfloor\frac{x}{n}\right\rfloor$.  So we want to prove $\left\lfloor\frac{\lfloor x\rfloor}{n}\right\rfloor\ge\left\lfloor\frac{x}{n}\right\rfloor$ and $\left\lfloor\frac{\lfloor x\rfloor}{n}\right\rfloor\le\left\lfloor\frac{x}{n}\right\rfloor$  Since $\lfloor x\rfloor\le x$, we can just start from here and prove  $\left\lfloor\frac{\lfloor x\rfloor}{n}\right\rfloor\le\left\lfloor\frac{x}{n}\right\rfloor$  But for $\left\lfloor\frac{\lfloor x\rfloor}{n}\right\rfloor\ge\left\lfloor\frac{x}{n}\right\rfloor$, I have no idea how to start. df says I have 20G more disk space used than du. Why? How can you use optional parameters in C#? Note: This question was asked at a time when C# did not yet support optional parameters (i.e. before C# 4).  We're building a web API that's programmatically generated from a C# class. The class has method GetFooBar(int a, int b) and the API has a method GetFooBar taking query params like &amp;a=foo &amp;b=bar.   The classes needs to support optional parameters, which isn't supported in C# the language. What's the best approach? User systemd PulseAudio service Not much else to this question: I would like to know what I need to create a PulseAudio systemd service to be run with systemd --user.  I've tried a few different things, including various user services from Google, but I can't get it set up just right between dbus and everything else required for it.  Update: It seems to work ok with graphical sessions, but I'm still having some inconsistancy with dbus when logging in through console.  But PulseAudio is starting rather reliably, so I'm not overly concerned. alias multi commands as one alias I made an alias for youtube-dl  with some options  like that  yd="youtube-dl -cit -f 18"   so I can download it like   yd URL   I want to modify it to show only the two lines from the output using   grep -e "Downloading video #" -e ETA  I can make it in two aliases using the |   but is there a way to make it one alias Where do you go for the 'nearest railroad' in Monopoly? In the American edition of Monopoly, there is a Chance card that says:  Advance token to nearest railroad Pay owner twice the rental to which he/she is entitled. If railroad is unowned, you may buy it from the bank.   However, is this the closest railroad, or the next one? If you are standing on the Chance spot in the light blues, do you go all around the board to Reading, which is the closest to you, or do you go to Pennsylvania, which is the first one you land on? What limitations does converting question links to links with titles have? On this  there are more than 50 links to Stack Overflow questions. However, the last 6 links aren't converted to titles (http://facebook.stackoverflow.com/questions/6530420/control-the-image-that-facebook-shows-when-i-like-a-url should be converted to ).   However:  all http://facebook.stackoverflow.com/... into http://stackoverflow.com/... fixes this, both in the preview and the final result. Also, the preview won't show any title for http://facebook.stackoverflow.com/... links.  My question is, what limitations does this converting have? How are these question titles retreived? Via API? Through database?  I'm not sure about title, feel free to edit that Is $\sqrt{64}$ considered $8$? or is it $8,-8$? Can I change a user's keyboard input? Pokemon Go: Can't log in? Are everyone unable to log in right now? 2016 July 16. Where I live none can log in to the servers at the moment, and it all happened after the sudden release of the game in my country.   As I understand the game was recently released in 26 countries, so I guess they have problems and had the servers go offline in order to fix the issues. I know that electric current is the flow of electrons but electrons have a very slow drift speed (about 2mm/s). How is it that electric current reaches its destination at almost the speed of light? Would "mid-to-late" and "low-to-mid" hyphenated as compound modifiers? Would "mid-to-late" and "low-to-mid" be hyphenated as compound modifiers?  Examples:  Temperatures are expected to be in the low-to-mid 60s.  Joe, I think, is in his mid-to-late 80s.  He was in his middle-to-late 40s.  She was in her middle-to-upper 60s.  Temperatures are expected to be in the lower-to-middle 70s.  Are all correct?  Thanks!!! Smileys in LaTeX I would like to include smileys in my LaTeX document. Is there any package with lots of different smileys?  In mnsymbol and wasysym, I found some general symbols:  \documentclass{article} \usepackage{MnSymbol,wasysym} \begin{document} wasysym: \smiley{} \frownie{} \blacksmiley{}  MnSymbol: \(\smile{} \frown{}\) \end{document}     But I do not like the output. Actually, I am looking for smileys which look like "default smiles" in Google Talk, MSN, ... ;) &lt;- this one is my favourite. ;) I'm stuck in a teleporting loop. What can I do? Can't get Freeglut to work with Haskell on Windows How do I set up a supply line? Trying to make aliases that open the last modified file One thing that I frequently do is edit the most recently modified files, so instead of typing "ls -lr" and then "vim lastfile", I thought I would make some shortcuts in my ~/.bash_profile file:  alias via="vim `ls -rt | tail -1`" alias vib="vim `ls -rt | tail -2 | head -1`" alias vic="vim `ls -rt | tail -3 | head -1`" alias vid="vim `ls -rt | tail -4 | head -1`" alias vie="vim `ls -rt | tail -5 | head -1`"   The problem is that, weirdly enough, these commands don't work.  They open some file that isn't one of the last, or even a file was deleted from the current directory (I wonder if there's some kind of file cache updating issue in the directory.  This occurs on both my local machine and the cluster I work on).  However, if I type vim `ls -rt | tail -1` directly, without using the alias, it works every time. This question is inspired by    I see these constructs  for file in `find . -type f -name ...`; do smth with ${file}; done   and  for dir in $(find . -type d -name ...); do smth with ${dir}; done   being used here almost on a daily basis even if some people take the time to comment on those posts explaining why this kind of stuff should be avoided... Seeing the number of such posts (and the fact that sometimes those comments are simply ignored) I thought I might as well ask a question:  Why is looping over find's output bad practice and what's the proper way to run one or more commands for each file name/path returned by find ? How to install aircrack on Ubuntu 12.04 How is floating point stored? When does it matter? In follow up to , it appears that some numbers cannot be represented by floating point at all, and instead are approximated.  How are floating point numbers stored?  Is there a common standard for the different sizes?  What kind of gotchas do I need to watch out for if I use floating point?  Are they cross-language compatible (ie, what conversions do I need to deal with to send a floating point number from a python program to a C program over TCP/IP)?