If I am working on a post, and try to close the browser window, then a prompt is displayed asking if I want to leave the page.  However, the same thing does not happen if I am working on a comment.  I am proposing extending the "navigate away" prompt to include the situation where there is a comment on the page that has not yet been saved (either a new comment, or one that is being edited, which has a non-zero length).
If I add a comment but navigate (by mistake) to another page, I lose my unfinished comment (ok, depends on browser etc). On the other hand, when formulating a question, and I click on a link by mistake, I'm asked if I really want to leave.  It would be nice to have this warning for comments as well.
.gitignore for Visual Studio Projects and Solutions Prove Borel Measurable Set A with the following property has measure 0. This question is exercise 4.10 of Richard F. Bass's Real Analysis for Graduate Students, 2nd edition.  Let $\epsilon \in (0,1)$, let $m$ be Lebesgue measure, and suppose $A$ is Borel Measurable subset of $\mathbb R$. Prove that if $$ m(A\cap I)\leq (1-\epsilon)m(I)$$  for every interval $I$, then $m(A)=0$.  Collection of my thoughts  1. Try to prove by contradiction, suppose $m(A)=a&gt;0$ Borel Measurable Set satisfies the condition given. A property of any Borel Measurable Set on $\mathbb R$ is $A$ contains a closed set $F$ and is contained in open set $O$, and the measure of $F$ and $O$ can be arbitrarily close to $a$. 2. Obviously $A$ contains no interval, but it does not lead to contradiction, because we can find an example of $m(A)&gt;0$ that contains no interval(fat Cantor Set(remove middle 1/4 each time) has measure $1/2$ and contains no interval).  2'. For fat Cantor Set $C$ and given $\epsilon&gt;0$ how could we construct an interval I satisfies $m(C \cap I)&gt;(1-\epsilon)m(I) ?$   Maybe try to write Borel measurable set as countable union/intersection of intervals.   I'm stucked here and will appreciate any help, some examples/special case will be great too. How does IPv4 Subnetting Work? reports:  Two mathematicians have uncovered a simple, previously unnoticed property of prime numbers [...]. Prime numbers, it seems, have decided preferences about the final digits of the primes that immediately follow them. Among the first billion prime numbers, for instance, a prime ending in 9 is almost 65 percent more likely to be followed by a prime ending in 1 than another prime ending in 9.  Do these insights make breaking keys based on primes more mathematically plausible in a shorter amount of time? How can I specify JUnit test dependencies? I know about beamer's  feature \setbeamercovered{invisible} and \setbeamercovered{transparent} to hide or grey out upcoming item's . But is there some way to have past items greyed (transparent) and future items hidden (invisible), so that only the current item is black/highlighted? And the best would be if on or 1 slide after the last all the item's could be visible highlighted. Something like this:   [grey] past 1 [grey] past 2 current [hidden] future 1 [hidden] future 2 [hidden] future 3   Is there any easy way of doing this? Astrophotography picture with too much noise. How do I correct this in postprocessing? This is the Milky Way above Kakadu National Park, Australia, and my first try at astrophotography.    Thirty second exposure, f/4.0 at 17mm with ISO 12800 (!!) which in hindsight probably was way too high and resulted in a lot of noise. I also used Picasa to increase contrast, but I probably went a bit overboard there as well.  , I am looking for input on how to better postprocess this picture to reduce noise. How do you join or create a server in multiplayer? I just got Minecraft Pocket Edition on my iPhone, but I'm having trouble figuring out how to start multiplayer. When I go to menu, there is only one button that says Play. How do I join or create servers? I have customers who want to buy large amount of flash memories but he wants to copyright all files inside it.   The flash will contain files that will be delivered for his customers but they're not allowed to copy or delete any of the files the only allowed permission is to ready the files.   I searched and found many solutions but all have on function it WriteProtect the USB though I can't add files to Drive at all but I can delete or copy any file in the drive.   Is there any way to protect the flash memory so I can't copy data out of it? Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$. Exercise     Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.     I've posted my solution below. In case someone has a more clever solution, feel free to post it!  (TBH, I was surprised that there was no question on Math.SE regarding this equation!) Can we switch terminals at Heathrow (LHR) for shopping only? We will be flying into and out of Terminal 5 at Heathrow. Now, my wife has taken fancy to a certain duty-free store located at Terminal 3. Assuming we factor in enough time before boarding our outbound flight from Terminal 5, are we allowed to enter Heathrow from Terminal 3, shop and then shuttle over to Terminal 5? I am looking to implement a biplot for principal component analysis (PCA) in JavaScript. My question is, how do I determine the coordinates of the arrows from the $U,V,D$ output of the singular vector decomposition (SVD) of the data matrix?  Here is an example biplot produced by R:  biplot(prcomp(iris[,1:4]))     I tried looking it up in the  but it's not very useful. Or correct. Not sure which. Can any one explain me what is the use of derivatives in real life. When and where we use derivative, i know it can be used to find rate of change but why?. My logic was in  real life most of the things we do are not linear functions and derivatives helps to make a real life functions into linear.  eg converting parabola into a linear function $x^{2}\rightarrow 2x$  but then i find this; derivation of $\sin{x}\rightarrow \cos{x}$  why we cant use $\sin{x}$ itself to solve the equation. whats the purpose of using its derivative $\cos{x}$. Please forgive me if i have asked a stupid questions, i want to improve my fundamentals in calculus. Assume the dice are numbered from $1$ to $k$. My hunch is that this will form a normal distribution with a median at $n\cdot\frac{k}{2}$. However, I have no idea as to    turn this fact into an answer (I have a minimal knowledge of stats, but I know that I am missing the standard distribution) and this is probably the wrong approach   How can I approach and solve this problem? (Aside, this is not for a class, stats or other, so any and all approaches welcome).  *Edit: * I want to find the number of ways that the sum of the numbers that are rolled has a particular value, if $n$ dice are rolled, and each has $k$ sides, numbered $1$ to $k$. Lightning:input type="date": how to change the date fomat - Summer'18 How to fix task manager memory column if it shows lies I have a problem in showing memory in task manager with memory and paging columns. Why it shows so small size usage? And maybe anyone knows how to fix it?  Here is a screenshot(working set, memory, page pool) sorted by most consuming: Not enough space on /tmp I'm not able to run update manager as I get an error saying that there is not enough free space in the /tmp directory. I've practically cleaned out the tmp directory but the error persists.  here's df-h  /dev/loop0       13G   11G  952M  92% / udev            2.0G  4.0K  2.0G   1% /dev tmpfs           785M  920K  784M   1% /run none            5.0M     0  5.0M   0% /run/lock none            2.0G  584K  2.0G   1% /run/shm /dev/sda6        20G   14G  6.4G  68% /host  overflow        1.0M   16K 1008K   2% /tmp What techniques are available for collapsing (or pooling) many categories to a few, for the purpose of using them as an input (predictor) in a statistical model?    Consider a variable like  (discipline chosen by an undergraduate student). It is unordered and categorical, but it can potentially have dozens of distinct levels. Let's say I want to use major as a predictor in a regression model.  Using these levels as-is for modeling leads to all sorts of issues because there are just so many. A lot of statistical precision would be thrown away to use them, and the results are hard to interpret. We're rarely interested in specific majors -- we're much more likely to be interested in broad categories (subgroups) of majors. But it isn't always clear how to divide up the levels into such higher-level categories, or even how many higher-level categories to use.  For typical data I would be happy to use factor analysis, matrix factorization, or a discrete latent modeling technique. But majors are mutually exclusive categories, so I'm hesitant to exploit their covariance for anything.  Furthermore I don't care about the major categories on their own. I care about producing higher-level categories that are coherent with respect to my regression outcome. In the binary outcome case, that suggests to me something like linear discriminant analysis (LDA) to generate higher-level categories that maximize discriminative performance. But LDA is a limited technique and that feels like dirty data dredging to me. Moreover any continuous solution will be hard to interpret.  Meanwhile something based on covariances, like multiple correspondence analysis (MCA), seems suspect to me in this case because of the inherent dependence among mutually exclusive dummy variables -- they're better suited for studying multiple categorical variables, rather than multiple categories of the same variable.  edit: to be clear, this is about collapsing categories (not selecting them), and the categories are predictors or independent variables. In hindsight, this problem seems like an appropriate time to "regularize 'em all and let God sort 'em out". Glad to see this question is interesting to so many people! A Lebesgue measure question Possible Duplicate:          Is there a measurable set $E \subset [0,1]$ such that for any $0 &lt; a &lt; b&lt;1$, the Lebesgue measure $$m(E \cap [a,b])= \frac{b-a}{2}?$$  I am stumped and have no idea. Complex numbers equation: $z^4 = -16$