$\mathcal{C}$ is an algebra
Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra
Let $f$ be defined on $\mathbb{R}$ by $f(x) = e^{-1/x^2}$ for $x$ not equal to $0$. and $f(0)= 0$. Prove that $f^{(n)}(0)=0$ for all $n = 1, 2,3$ ...  Do I need to use Taylor expansion from calculus class?  Any hint would be appreciated. How do you determine what technology a website is built on? Quite often I come across a nice looking or functional website, and wonder what technology was used to create it. What techniques are available to figure out what a particular website was built with?  Few frameworks seem to include any kind of generator meta tag like web editors do. Are there any tell-tale signs of particular languages and/or frameworks?    Summary of answers  Site URLs may betray the framework and/or programming language but cannot be relied upon (e.g. file extensions such as .asp). HTTP response headers, cookies, stylesheets and source comments may also give clues.  Some nice tools for querying site details (no doubt there are many more):          Firefox addons:    - CMS, frameworks/libraries, e-commerce, message boards etc.  - IP, country and webserver details  - Javascript libraries in use   Chrome Extensions:        Bookmarklets:    - shows Javascript framework in use nginx support for .htaccess / rewrite rules? Differences from Apache? Recover data from hard drive with partitions (but not most data) overwritten I have a 500GB hard drive I've been keeping around to recover data from that I removed from a failing NAS drive that got sort of... erratic at the end. I finally got rid of the NAS when during a firmware update it removed the partition table.  Fast forward to a week ago, when I was building a new PC, and a mixup resulted in me placing the hard drive in question in the new PC and installing Windows XP on the first 100GB. I'm presuming any data on that first 100GB is now gone, but for the rest of it, is there any way I can recover it at home, as professional data recovery is currently too expensive?  I have a blank 1TB HDD if I can store any images of that hard drive on. The problem was definitely with the NAS and not the hard drive, as the hard drive had a successful install of Windows when mistakenly place in the new PC, and there were capacitors in the NAS's circuitry clearly broken.  The data I want to recover (in order of priority) is:   High: Some jpgs of family photos. Medium: Some RAW files. (There are also jpg versions of all of these) Low: Some mp3s, avis and ISOs, I can re-rip most of these if need be, but it'd be handy not to have to.    (I don't need a backup lecture, and if you can hold it in from nagging Jeff Atwood for it, you can hold it in from nagging me for it)  In short:   The partition tables are gone and overwritten. The data is not overwritten, except for an amount equal to the size of a Windows XP SP3 installation. How do I use formatting in comments? I see some people write comments that are for example - in italics.  I do not see any way of doing that while writing my comments. Why is it so? "Always on top" option missing for Firefox/Chrome in 18.04 table side by side with minipage I can't manage to get two tables side by side in a minipage environment. Any kind suggestion would be highly appreciated!   \documentclass{article} \usepackage{array}  \begin{document} \begin{table}[htbp] \centering \begin{minipage}{.2\textwidth}     \begin{tabular}{| m{3cm} | m{4.3cm} | c |}   \hline  number of entity filter (size 1) &amp; number of context filters (size 2, size 3,  size 4) &amp; Accuracy\\ [2ex]   \hline  32  &amp;  32  ,  32  ,  32  &amp;  0.835 \\[0.5ex] \hline 32  &amp;  64  ,  64  ,  64  &amp;  0.821 \\[0.5ex] \hline 32  &amp;  128  ,  128  ,  128  &amp;  0.819 \\[0.5ex] \hline 32  &amp;  256  ,  256  ,  256  &amp;  0.749 \\[0.5ex] \hline 32  &amp;  512  ,  512  ,  512  &amp;  0.683 \\[0.5ex] \hline 32  &amp;  1024  ,  1024  ,  1024  &amp;  0.528 \\[0.5ex] \hline 32  &amp;  2048  ,  2048  ,  2048  &amp;  0.235 \\[0.5ex] \hline 64  &amp;  32  ,  32  ,  32  &amp;  0.850 \\[0.5ex] \hline 64  &amp;  64  ,  64  ,  64  &amp;  0.816 \\[0.5ex] \hline 64  &amp;  128  ,  128  ,  128  &amp;  0.786 \\[0.5ex] \hline 64  &amp;  256  ,  256  ,  256  &amp;  0.795 \\[0.5ex] \hline 64  &amp;  512  ,  512  ,  512  &amp;  0.765 \\[0.5ex] \hline 64  &amp;  1024  ,  1024  ,  1024  &amp;  0.669 \\[0.5ex] \hline 64  &amp;  2048  ,  2048  ,  2048  &amp;  0.331 \\[0.5ex] \hline 128  &amp;  32  ,  32  ,  32  &amp;  0.920 \\[0.5ex] \hline 128  &amp;  64  ,  64  ,  64  &amp;  0.890 \\[0.5ex] \hline 128  &amp;  128  ,  128  ,  128  &amp;  0.886 \\[0.5ex] \hline 128  &amp;  256  ,  256  ,  256  &amp;  0.846 \\[0.5ex] \hline 128  &amp;  512  ,  512  ,  512  &amp;  0.789 \\[0.5ex] \hline 128  &amp;  1024  ,  1024  ,  1024  &amp;  0.755 \\[0.5ex] \hline 128  &amp;  2048  ,  2048  ,  2048  &amp;  0.488 \\[0.5ex] \hline 256  &amp;  32  ,  32  ,  32  &amp;  0.920 \\[0.5ex] \hline 256  &amp;  64  ,  64  ,  64  &amp;  0.922 \\[0.5ex] \hline 256  &amp;  128  ,  128  ,  128  &amp;  0.912 \\[0.5ex] \hline 256  &amp;  256  ,  256  ,  256  &amp;  0.877 \\[0.5ex] \hline 256  &amp;  512  ,  512  ,  512  &amp;  0.872 \\[0.5ex] \hline 256  &amp;  1024  ,  1024  ,  1024  &amp;  0.771 \\[0.5ex] \hline 256  &amp;  2048  ,  2048  ,  2048  &amp;  0.683 \\[0.5ex]  \hline  \end{tabular} \end{minipage}% \hfill \begin{minipage}{.2\textwidth}     \begin{tabular}{| m{3cm} | m{4.3cm} | c |}   \hline  number of entity filter (size 1) &amp; number of context filters (size 2, size 3,  size4) &amp; Accuracy\\ [2ex]   \hline 512  &amp;  32  ,  32  ,  32  &amp;  0.910 \\[0.5ex] \hline 512  &amp;  64  ,  64  ,  64  &amp;  0.922 \\[0.5ex] \hline 512  &amp;  128  ,  128  ,  128  &amp;  0.909 \\[0.5ex] \hline 512  &amp;  256  ,  256  ,  256  &amp;  0.910 \\[0.5ex] \hline 512  &amp;  512  ,  512  ,  512  &amp;  0.883 \\[0.5ex] \hline 512  &amp;  1024  ,  1024  ,  1024  &amp;  0.730 \\[0.5ex] \hline 512  &amp;  2048  ,  2048  ,  2048  &amp;  0.682 \\[0.5ex] \hline 1024  &amp;  32  ,  32  ,  32  &amp;  0.925 \\[0.5ex] \hline 1024  &amp;  64  ,  64  ,  64  &amp;  0.931 \\[0.5ex] \hline 1024  &amp;  128  ,  128  ,  128  &amp;  0.920 \\[0.5ex] \hline 1024  &amp;  256  ,  256  ,  256  &amp;  0.917 \\[0.5ex] \hline 1024  &amp;  512  ,  512  ,  512  &amp;  0.899 \\[0.5ex] \hline 1024  &amp;  1024  ,  1024  ,  1024  &amp;  0.858 \\[0.5ex] \hline 1024  &amp;  2048  ,  2048  ,  2048  &amp;  0.776 \\[0.5ex] \hline 2048  &amp;  32  ,  32  ,  32  &amp;  0.933 \\[0.5ex] \hline 2048  &amp;  64  ,  64  ,  64  &amp;  0.934 \\[0.5ex] \hline 2048  &amp;  128  ,  128  ,  128  &amp;  0.925 \\[0.5ex] \hline 2048  &amp;  256  ,  256  ,  256  &amp;  0.928 \\[0.5ex] \hline 2048  &amp;  512  ,  512  ,  512  &amp;  0.907 \\[0.5ex] \hline 2048  &amp;  1024  ,  1024  ,  1024  &amp;  0.878 \\[0.5ex] \hline 2048  &amp;  2048  ,  2048  ,  2048  &amp;  0.798 \\[0.5ex]  \hline  \hline \end{tabular} \end{minipage} \caption{filter window size} \label{tab:config_filternum} \end{table}   \end{document}   What I have so far  EDIT: I followed the second solution from , and it somehow didn't work. I am not sure why. I made a script that should notify me when there's a new chapter of manga that I'm reading. I used the command notify-send to do this. The program works when I am trying to run it in terminal. The notification is showing. However, when I placed this in my crontab, the notification doesn't show. I'm pretty sure that the program is running since I made it to create a file for me. The file was created, but the notification didn't show.  Here's my script  #!/bin/bash    #One Piece Manga reminder     #I created a file named .newop that contains the latest chapter.     let new=$(cat ~/.newop)     wget --read-timeout=30 -t20 -O .opreminder.txt http://www.mangareader.net/103/one-piece.html  if (( $(cat .opreminder.txt | grep "One Piece $new" | wc -l) &gt;=1 ))     then         (( new+=1 ))         echo $new         echo $new &gt; ~/.newop         notify-send "A new chapter of One Piece was released."     else         notify-send "No new chapter for One Piece."         notify-send "The latest chapter is still $new."     fi         exit   And here's what I wrote in my crontab  0,15,30,45 12-23 * * 3   /home/jchester/bin/opreminder.sh Motivation behind standard deviation? Adjusting font size with TikZ picture Taking from the PGF manual,  \begin{tikzpicture}   \draw [help lines] (0,0) grid (3,3);   \coordinate (a) at (rnd,rnd);   \coordinate (b) at (3-rnd,3-rnd);   \draw (a) -- (b);   \node (c) at (1,2) {x};   \draw let \p1 = ($ (a)!(c)!(b) - (c) $),             \n1 = {veclen(\x1,\y1)}         in circle [at=(c), radius=\n1]; \end{tikzpicture}   I'd like to increase the size of x. The problem is that I have multiple circles in the same diagram. Some of them require a larger sized font, while others are okay at default. How do I do this? How did "When" become the customary answer to "say when"? When a waiter at a restaurant comes by with pepper or Parmesan cheese, he says, "say when" and starts putting it on your food.  Many people will say "OK" or "that's enough," but it seems that the customary answer is "when".  How did this become the customary answer?  Did everyone decide to make the exact same joke, until it became commonplace.  I thought it was funny when I was a kid, but even now as an adult, I still say it.  For evidence that this is indeed commonplace, see .  The answer "when" is used and is external to the joke of the strip. But even so, I'm curious as to just how commonplace this really is.  I see it a lot in the US.  Is it used elsewhere in the world?  (by the way, I'm new to asking questions on this site, and I have no idea what tags to put on this question) What is the significance of a mostly blank user card? Can I submit/ArXiv without my advisor? I am being blocked from publishing my work I joined a research group of a faculty member in 201x, and worked with her for three years. During that time, I collaborated with a large hospital to perform research in the domain of medical informatics. I spoke about my research at two conferences; one was a talk, and the other was a poster presentation. My advisor asked me to write up the research in a paper around the second year, which I did. Around the third year, I decided to switch research groups, because of the relationship between me and my advisor going sour, and not having funding from her (I used to work part-time to fund my PhD research).  Once this happened, she withdrew her support from me publishing my paper and ordered that I give up my work to a fellow grad student. I told her, that my manuscript is in its Nth revision, and that I would like to take it to completion as first author. She was dismissive and didn’t offer any comments on my work. I told her, that, should I pass on my work, I would like to discuss authorship issues in advance, which she wasn’t ready to discuss. She ganged up my new advisor against me, and together they forced me to give up my code, results, paper drafts. I had to then leave the university without a degree.  Fast forward couple of years, I receive an email from a student in her lab (the student whom I had to hand over my work to), saying that they are publishing a paper, and have decided I am the fourth author. I read the paper and found out that it uses my experimental setup and design, data collection, and one of the ideas I had presented (the idea wasn’t the main crux of my paper, but I believe it was novel).  I want to   Publish my original draft in ArXiv/BioArXiv, as first author. Request my advisor to cite my work in their publication.    Given how she behaved with me, I know that despite what I am asking for sounds fair, she is likely to object.  I am asking the community: Can I go ahead and ArXiv it without her permission? I could add her as an author, but not take her permission. Also, if you have any other ideas on how to deal with this situation please let me know.  (For the record, this was at a top-10 school in the US in an engineering department). Can a website know about my browsing history? When I visit a website it sometimes puts cookies on my browser. Usually cookies keep track of browsing info from that particular site. If I don't delete those cookies and browse other websites, will the cookies be able to know which site I am browsing? Also, can any website read browsing history which is saved by browsers? Can any website know about my browsing history by help of cookies, browsing histories saved by browsers, or by any scripting language e.g. javascript? Using the properties of real numbers, verify commutativity on complex numbers. I have just started self-studying Linear Algebra after a 3 year hiatus from mathematics (in an extended neuroscience foray), and I want to ensure that I am sufficiently verifying commutativity of complex numbers by using the properties of real numbers.  My attempts...  (1) Commutativity of Addition:   Verify that $w + z = z + w$ for all $w, z \in \mathbb{C}$.  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{16mm} = (a + c) + (bi + di) \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{19mm} = (c + a) + (di + bi) \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{13mm} = c + (a + di) + bi \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = c + (di + a) + bi \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{17mm} = (c + di) + (a + bi) \hspace{11mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{13mm} = z + w \hspace{34mm}\text{by definition of }\mathbb{C}$$  $$\blacksquare$$  This seems a bit verbose to me - is it acceptable to combine steps? For example, rather than:  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ can I instead write: $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{48mm} = a + (c + bi) + di \hspace{10mm}\text{by associativity and commutativity in }\mathbb{R}$$?  (2) Commutativity of Multiplication:  Verify that $wz = zw$ for all $w, z \in \mathbb{C}$.  $$\hspace{-14mm}wz = (a + bi)(c + di) \hspace{24mm}\text{by definition of }\mathbb{C}$$ $$\hspace{4mm} = a \cdot c + a \cdot di + bi \cdot c + bi \cdot di \hspace{10mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{9mm} = a \cdot c + bi \cdot c + a \cdot di + bi \cdot di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{35mm} = c \cdot a + c \cdot bi + di \cdot a + di \cdot bi \hspace{10mm}\text{by multiplicative commutativity in }\mathbb{R}$$ $$\hspace{1mm} = c(a + bi) + di(a + bi) \hspace{20mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{5mm} = (c + di)(a + bi)\hspace{34mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{4mm} = zw \hspace{55mm}\text{by distribution in }\mathbb{R}$$ $$\blacksquare$$  This also seems a bit wonky to me. Any and all suggestions on clearing up my verification, reasoning, etc. would be greatly appreciated! Adding execute permission in opt folder I am trying to install oracle database in Ubuntu 16.04 LTS. I had unzipped the oracle database file in opt folder,but now when I am trying to give execute right to the sqldeveloper file using chmod +x sqldeveloper.sh, it's throwing this error:  chmod: changing permissions of 'sqldeveloper.sh': Operation not permitted In my project requirement to access table data from Mapd Database on GeoServer  Mapd(GPU Based database) Database documentation link:   But in GeoServer provided some extension to connect and access particular database  GeoServer Extension link:    How can I connect MapD databse with geoserver is there any plugin. Javascript add js libraries by code Donating winning lottery ticket to 501(c)3 Private Foundation: cost-basis deduction + full tax free redemption for foundation? What happens with the appearance of the folder icons in dark mode of macOS Mojave Finder? In High Sierra I used some custom icons for my folders in the Finder; but with the new update to Mojave and the dark mode, the predefined icons also become darker. However the custom icons don't.  Inspecting an element you find a dark preview, but when you extract the icon this is the clear, the same as there was in High Sierra. E.g.:   Previously visualization of the developer predefined icon. It's dark:  But if you extract that icon, it's clear:    There are no dark icons in the system library, at least not in the same directory as always:  /System/Library/CoreServices/CoreTypes.bundle/Contents/Resources   Are they being actively obscured by the operative system without there being icons with that real appearance? In this case, any idea to apply this method to the custom icons without modifying it into a new coloration?