What makes a function static?
When to use static methods
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction I've done the base step, but how do I prove it is true for $n+1$ without using a fallacy? $$4(n!)&gt;2^{n+2}\quad \text{for } n\geq 4$$ Please help. Are repository lists secure? Is there an HTTPS version? How do I disable notifications in my personal profile for activity on pages I am an admin of? I'm an admin of several pages on Facebook (for technical stuff like RSS imports, etc.), but neither do I contribute content nor do I care about their content.  Still, as an admin, I get notifications (upper left hand, the globe icon) about activity (someone liked this, someone posted that) on those pages in my personal (!) profile .  Does anyone have the same issue? Is there any way to explicitly disable notifications for certain pages?  (This behavior seems to be new, by the way; I'm only seeing those notifications for a few weeks now.) How did half of Darth Maul survive? I read somewhere that companies are not required to pay dividends to shareholders (this is correct, yes?).   If so, then if company A never pays dividends to its shareholders, then what is the point of owning company A's stock? Surely the right to one vote for company A's Board can't be that valuable.   What is it that I'm missing? How do I unit test code that includes a callout? If $a \cdot a = 1$ then $a = 1$ or $a = -1$ How do ${0##*/} and ${0%/*} work? I'm quite confused about the following regular expressions I found in a shell script:  ${0##*/} ${0%/*}   How do they work? A TV show, from the 90's or 80's, very weird Does anyone remember a show, where:   An alien girl lives with a family She comes from the moon She is looking for a new king because their king (a giant baby) is dying Her spaceship its a VW van They had a doorframe, yes a doorframe, that could open to other alternative universes or dimentions How to model this odd-shaped distribution (almost a reverse-J) Why do electron and proton have the same but opposite electric charge? How do I "decompile" Java class files? What program can I use to decompile a class file? Will I actually get Java code, or is it just JVM assembly code?  On Java performance questions on this site I often see responses from people who have "decompiled" the Java class file to see how the compiler optimizes certain things. Shortcut to view wireless networks in Windows 7 Does anyone know how to create a shortcut which opens the wireless networks dialog box in Windows 7?  I'm looking for a shortcut that takes me directly to the window which shows you the available wireless networks around you. (Last Jedi spoilers ahead, if you haven't seen the movie, please don't read on.)  So, fridge logic moment for me:      If Vice Admiral Holdo had told Poe Dameron about the plan to just hold on long enough to make a covert run to Krait, then Poe wouldn't have felt the need to send Finn and Rose on their little side-trip, and the code-breaker wouldn't have overheard anything nor sold them out, and the First Order would've had no reason to notice the cloaked ships.   I do understand that there's a lesson in there about following orders, even if said orders come from a pretty face in a pretty dress, but that's kind of an out-of-universe reason. What was Holdo's reasoning? Surely she knew enough about Poe to realize that treating him like a mushroom1 would not result in anything good.  1 "kept in the dark and fed shit" Evaluating the indefinite integral $ \int \sqrt{\tan x} ~ \mathrm{d}{x}. $ I have been having extreme difficulties with this integral. I would appreciate any and all help. $$ \int \sqrt{\tan x} ~ \mathrm{d}{x}. $$ Could someone please explain? I couldn't find anything on the internet, everything talks about how to go about it in some way, but nothing says exactly what it is.   Also, what is a fully trusted assembly and how do they differ from one another?  I have a MS certification exam and this is the only topic that I just don't understand.  EDIT: Thanks guys. Now I have a better understanding of security in .NET. I was able to pass my certification exam. I am attempting to solve this counting problem through combinatorial argument. The following is the equation I am given:   $$\sum_{i=1}^n (i-1)(n-i) = \binom{n}{3}$$  I understand that the right-hand side of this equation represents a set of $n$-elements out of which we choose 3. For example I believe we can say suppose we have a group of $n$ people and we want to choose 3 out of $n$ to be in a committee. However I'm not sure how to express the left-hand side in words. If forming a committee is an appropriate way to tackle this problem then I know the left-hand side must utilize the addition and multiplication principles, but I don't know how to put it into words. Also my intuition tells me that in solving this we should first flip $$(n-i)(i-1)$$  Thanks! How to evaluate the integral $\int \sqrt{1+\sin(x)} dx$ To find:  $$\int \sqrt{1+\sin(x)} dx$$  What I  tried:  I put $\tan(\frac{x}{2}) = t$, using which I got it to:  $$I = 2\int \dfrac{1+t}{(1+t^2)^{\frac{3}{2}}}dt$$  Now I am badly stuck. There seems no way to approach this one. Please give a hint. Also, can we initially to some manipulations on the original integral to make it easy? Thank you. Check if user is using IE 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!