Why is $(e^{2πi})^i$ different from $(e^i)^{2πi}$
What is wrong with this fake proof $e^i = 1$?
$VAR vs ${VAR} and to quote or not to quote I can write  VAR=$VAR1 VAR=${VAR1} VAR="$VAR1" VAR="${VAR1}"   the end result to me all seems about the same. Why should I write one or the other? are any of these not portable/POSIX? How to populate options of h:selectOneMenu from database? Floating sidebar clash with footer in team page Here is a screenshot from  page, with the floating sidebar: (all good so far)        After I scroll down to footer it just combines both:        Can it please be fixed? How to sanity check a date in Java How to install program to all user accounts in Windows? I have several accounts on my home PC. I want to install a program for all user accounts, not just the one I used to perform the installation. How do I go about doing this?  I installed a program from an admin account, but it doesn't show up in the other local accounts.  I was not able to find any documentation on how to do this.  I have Windows 8.1, if that matters. I have searched in %appdata%, pulling up the list of files there, but there is no file labelled .minecraft. Searching %appdata%\.minecraft returns "no results found".   I also opened Minecraft to click on the resources button and could not locate that either. Before upgrading to 14.04 when I clicked on a file in the dash, it opened the file.   This still happens on my 12.04 machine.  In 14.04 when I click on a file in dash search results, it offers me 3 options: 'Email', 'Open' and 'Show in Folder'.  How can I get back the previous behaviour - i.e. to immediately open the files on the first click? During the First Wizarding War, why didn't Dumbledore just hunt Voldemort down, as he had done with Grindelwald?  By 'hunting down', I mean finding, defeating and imprisoning him, exactly as in Gridelwald's case, and not, say killing him, something which Dumbledore would not do, as the answers to a previous question (as to him not hunting down Death Eaters) show.  Dumbledore knew that Voldemort had delved into the Dark Arts deeper than anyone else in history and hence "had powers he will never have". But he must have also known well that he could have defeated Voldemort at a direct confrontation, given that he had defeated Grindelwald earlier even against the Elder Wand, and now had that same wand at his disposal. He is seen confident about this throughout the series.  At the Battle of the Department of Mysteries, he did not go beyond outweighing Voldemort and forcing him to flee, probably because, by then, he had reasons to suspect that there was more to Voldemort's survival than his physical body, and thus, destroying that body which had Harry's blood without permanently disposing him off would not have been wise.  But why did he not do that at the First Wizarding War? Is it just that they could not track him down, or did he suspect even then that Voldemort had more sinister things about his soul? is there any canon confirmation of the latter suspicion? Prove that a function is not injective I have always believed that it was ok to replace a capacitor with a slightly higher voltage rated one. eg 16v with 25v.Going higher than this would risk the capacitance value being out at the working voltage. However I just read the following quote from this       Electrolytic capacitors are non-ferroelectric with a very low dielectric constant. Their capacitance is derived from a very high surface area and nanometer thick dielectric layers. Their capacitance is not a function of applied voltage.‐Design Solutions For DC Bias In Multilayer Ceramic Capacitors (August 2010 Electronic Engineering Times)   So does this rule not apply to aluminum electrolytics? Eg will I have no issues replacing an electrolytic 25v 100uf with a 50v 100uf assuming both are low esr, similar footprint and good quailty? How can I fix an out-of-focus blurred photo in Photoshop? How can I fix this picture?  Somebody else took this picture and well he wasn't able to do it very well, and it's blurred.    I have photoshop Epson LX-310 not working after Cumulative Update 2017-11 Windows 10 I have Windows 10 Pro x32 and an Epson LX-310 printer that was working. Yesterday, Windows 10 automatically updated with 2017-11 Cumulative Update for Windows 10.   Today, I cannot print. The printer status is on. When I click "Print a test page", it quickly says the test page has been sent but the printer does not print it.   My printer is connected to a USB port. What wrong with my Windows 10? Why does Oracle 9i treat an empty string as NULL? Arrays in Unix Bourne Shell I am trying to use arrays in Bourne shell (/bin/sh). I found that the way to initialize array elements is:  arr=(1 2 3)   But it is encountering an error:  syntax error at line 8: `arr=' unexpected   Now the post where I found this syntax says it is for bash, but I could not find any separate syntax for Bourne shell. Does the syntax stand the same for /bin/sh as well? If you want to buy a house but you also think value will drop… is there something you can do to alleviate the risk? Disclaimer: yours won't be fiscal advice. People involved will consult a professional before doing anything. This is just to gather some preliminary information.  Situation:   you want to buy a house or a flat, in UK you will get a mortgage in GBP, but you'd pay the down payment in EUR you think that there are fairly high chances that the value of houses in UK and GBP will drop the whole point of this question is actually buying the house/flat, renting is not an option by definition   What can you do to mitigate that risk? Receiving commandline input while listening for connections in Python Restrict the scope of a command to the execution of another command How to prove $D^n/S^{n-1}\cong S^n$? In my textbook it is said that the quotient space $D^n/S^{n-1}$ is homeomorphic to $S^n$. I can imagine it for $n=2$, but fail to make a mathematical proof for any dimension.  Can anyone provide a rigorous proof? Can I upload an entire folder using FTP? I need to upload a full folder using FTP.  Is there is any option for transferring a folder and all of its contents at once? I am trying to use the  package.  I have the following counters defined (hopefully this is the right way to do it!)  \newtheorem{thm}{Theorem}[section] \newtheorem{lemma}[thm]{Lemma} \newtheorem{cor}[thm]{Corollary}   This works as I would like (i.e. Theorem 1.1, Corollary 1.2, Lemma 1.3, etc.)  My problem is \cref always returns Theorem 1.2, Theorem 1.3. I   Perhaps this is not right? (In my preamble)  \crefname{thm}{theorem}{theorem's} \crefname{lemma}{lemma}{lemma's}