Prove that $E^{\circ}$ is always open
Proving set of interiors is open
Is there a proof of existence of time? It seems to me that there is no such thing as time. There  is only movement in the universe and we compare our own movement to a different object to have a sense of time. It can be a clock or a atomic vibration.  Does this view of time work within the current framework of phsics?  Do physicists have an explanation/proof about time's existence? How to control spacing in a TikZ tree? Limit involving the exponential of an expression plus a small-o I'm trying to formalize the following limit:  $$\lim_{x \to \infty} \left[1+\frac{a}{x}+o\left(\frac{1}{x}\right) \right]^x= e^a$$ however I can't see how to rigorously show this identity.  Any suggestions? Enlarge a partition without losing data with Windows 7 diskmgmt? I have a 320GB hard drive currently partitioned as below:     A long time ago, a computer expert formatted my hard drive like this because I wanted to install Ubuntu. I'm now ready to do this, but I'll never need so much free space (103.09GB). I want to enlarge the D:\ volume because it already has lots of data on it.  I know that when I open diskmgmt.msc, I could possibly enlarge the D:\ volume using some free space from the unformatted 103.09GB volume, because the program offers me the option to enlarge. However I'm afraid that I might lose data doing this.  Is it possible to enlarge the partition with this Windows 7 tool or am I better using GParted via "Try Ubuntu" on my Live CD? Would either of them cause data loss in this scenario? I am trying to change the page size in the QGIS 3.0 Composer but I am not able to see the Composition tab.  I have right clicked an empty space in the toolbar but did not see anything about composition.  I am using Windows 7.  I tried looking at the QGIS docs but they are still in testing. Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$ How to prove  $$\int_{0}^{\infty} \mathrm{e}^{-x^2}\, dx = \frac{\sqrt \pi}{2}$$ recursive statistics on file types in directory? I did a website scrape for a conversion project. I'd like to do some statistics on the types of files in there -- for instance, 400 .html files, 100 .gif, etc. What's an easy way to do this? It has to be recursive.   Edit: With the script that maxschelpzig posted, I'm having some problems due to the architecture of the site I've scraped. Some of the files are of the name *.php?blah=blah&amp;foo=bar with various arguments, so it counts them all as unique. So the solution needs to consider *.php* to be all of the same type, so to speak. Can the Dispel Magic spell be Readied to counter an opponent's spell? When playing as a spellcaster, is it valid the use of the Ready action to prepare Dispel Magic to counter a spell cast by an opponent? In the same vein, when declaring said action, do I have to specify which spell slot I will use when Readying the Dispel Magic spell? If that is the case, does this tactic nullify an opponent's spell? I get the impression that this is basically turning Dispel Magic into a spell with a casting time of &quot;1 reaction&quot;. Is my reading of the rules accurate? How did Stannis's army get north of the wall? If Mance Rayder had to attack Castle Black to use the tunnel to get through the Wall and get out of the north, how did Stannis get his army across the Wall into the north without anyone knowing? If there was another way over the Wall wouldn't the wildings go that way too? Date Formatting C# Python Ctypes - loading dll throws OSError: [WinError 193] %1 is not a valid Win32 application Italian keyboard: entering tilde (~) and backtick (`) characters without changing keyboard layout Here is what the layout of an Italian keyboard looks like:  As you can see, the curly braces, which are absolutely necessary to write code in any of C, C++, JavaScript, Java, Objective-C, and others, appear in purple in this picture. This is because while the other characters can be seen visually as printed characters on most Italian keyboards, these purple characters are actually usually not printed on the keyboard's keys. These characters, found in the upper right corners of the given keys, can usually be generated with the following key combinations: (RIGHT SHIFT or LEFT SHIFT) + (RIGHT CTRL or LEFT CTRL) + (Alt or AltGR) + ([ or ]) (Actually as the MSKLC application shows, SHIFT + AltGr + [ and SHIFT + AltGr + ] are enough to generate the curly braces.) Characters such as the at (@) sign (called 'chiocciola' in Italian) and the hash (#) key (called 'cancelletto' in Italian) found in the lower right hand corner of the keyboard can be generated easily as follows (AltGr + @) or (AltGr + #). Such characters are also fundamental to programming as they can, for instance, be found in CSS, namely with media queries and with selectors referring to the id html attribute. Upon further inspection, we can see that all of the US ASCII keyboard / programmer's keyboard are covered by the keys of the Italian keyboard, except for the following, which are the tilde, which is especially useful on the Linux command line and is used to refer to a user's home directory on such system, as well as the back-tick (`), also known as the back-quote, which is also very useful on the Linux shell when we want to turn the output of a command into a command-line input. So, here comes the question: With all those empty upper-right hand corners of keys, why isn't there a better way of generating these characters, perhaps through a CTRL-ALT-SHIFT modifier key combination? All I've been able to find regarding generation of these characters are the following ALT-codes:  ALT code 96  corresponds to ` ALT code 123 corresponds to { ALT code 125 corresponds to } ALT code 126 corresponds to ~  and to generate a character via an ALT code, you make sure that the NumLock key on your keypad is toggled on, hold down the ALT key, enter the keycode, and release the ALT key. ALT code are documented at:  If someone knows of a better way of inserting these characters from an Italian keyboard without switching the keyboard layout in the Control Panel, then please let me know. Thanks. mean value theorem question I was trying to solve the following:  Given: $0 &lt; a &lt; b$ and $n&gt;1$, prove: $$na^{n-1}(b-a) &lt; b^n-a^n &lt; nb^{n-1}(b-a)$$  I managed to get this far using the mean value theorem: $$a^n(b-a)&lt;b^n -a^n&lt;b^n (b-a)$$ Any idea how to continue? How do we remove an ex-girlfriend from a car loan? Best way to deal with questions answered by the OP in the question instead of in an answer I saw this question:   I don't know what the best option is for dealing with such a question, because I've seen questions like this several times already.  So, what should we do with questions that are:   poorly asked finally answered by the OP as an update to the question itself, not as an answer. Interpolation of multibeam bathymetry using ArcGIS Desktop? I'm trying to make a 3D map with multi-beam bathymetry (65536 features, xyz), but it seems that the interpolation methods are too rigid. I need to smooth the data so it looks more natural and realistic.   Which parameters do I have to vary so I can get this? Reference style links validating as improperly formatted code I have seen many examples of how to render sprites from a spritesheet but I havent grasped why it is the most common way of dealing with sprites in 2d games.  I have started out with 2d sprite rendering in the few demo applications I've made by dealing with each animation frame for any given sprite type as its own texture - and this collection of textures is stored in a dictionary. This seems to work for me, and suits my workflow pretty well, as I tend to make my animations as gif/mng files and then extract the frames to individual pngs.  Is there a noticeable performance advantage to rendering from a single sheet rather than from individual textures? With modern hardware that is capable of drawing millions of polygons to the screen a hundred times a second, does it even matter for my 2d games which just deal with a few dozen 50x100px rectangles?  The implementation details of loading a texture into graphics memory and displaying it in XNA seems pretty abstracted. All I know is that textures are bound to the graphics device when they are loaded, then during the game loop, the textures get rendered in batches. So it's not clear to me whether my choice affects performance.  I suspect that there are some very good reasons most 2d game developers seem to be using them, I just don't understand why. How to fix "Notification access is not available" on Android Go? Parser for C# Which parsers are available for parsing C# code?  I'm looking for a C# parser that can be used in C# and give me access to line and file informations about each artefact of the analysed code.