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Are there any clones/alternatives for running a Stack Exchange style Q&A site? Since the  would it make sense to create a Stack Exchange site dedicated to homework help? It wouldn't have to be limited strictly to homework either, possibly including discussions of puzzles and brain teasers and possible approaches to solving them.  I have a programming background so I would be interested in helping with CS or math related homework, discussions of programming contest problems, etc. Topics don't necessarily have to be related to programming either. That's just where my interests are.  What are your thoughts? Every subspace of a vector space has a complement I want to see if my proof is true or I thought very trivially?    If $H$ is a subspace of a finite dimensional vector space $V$, show there is a subspace $K$ such that $H\cap K=0$ and $H+K=V$    So far I have tried :    $H\subseteq V$ is a subspace $\Rightarrow\,\exists\;K=(V-H)\subseteq V$ $K$ is a subspace because it's the sum of two subspace $V$ and $(-H)$ Now we should prove that $H\cap K=0$ We assume $H\cap K\neq0\Rightarrow\exists\,\vec u\neq0\,,\,\vec u\in H\cap K$ $\vec u\in H\cap K\Rightarrow \begin{cases}\vec u\in H\\\vec u\in K\,\Rightarrow\vec u\in V-H\Rightarrow\vec u\in V,\,\vec u\notin H\end{cases}$ That's a contradiction so our hypothesis was wrong and $\vec u=0$ If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$ I was working my way through some number theoretic proofs and being a newbie am stuck on this problem :     If $(x, 4) = 2$ and $(y, 4) =2$, then $(x + y, 4) = 4$,     where $(a,b)$ denotes the greatest common divisor of $a$ and $b$.   My Solution  (Incorrect)   $x-4 = 2t$ $y-4 = 2p$ $x + y - 8 = 2(t+p) \Rightarrow x + y - 4 = 2f + 4 = 2(f+2)\Rightarrow 2$ divides $(x+y , 4)$   My Question:  My solution is definitely inadequate. Can someone help me out? How to get function's name from function's pointer in Linux kernel? Bash built-ins with no manual entries Most efficient way to convert an HTMLCollection to an Array Is there a more efficient way to convert an HTMLCollection to an Array, other than iterating through the contents of said collection and manually pushing each item into an array? PostgreSQL check bloating of a table Inequality ${n \choose k} \leq \left(\frac{en}{ k}\right)^k$ This is from page 3 of  ().  Copying the relevant segment:     Stirling’s approximation tells us $\sqrt{2\pi n} (n/e)^n \leq n! \leq e^{1/12n} \sqrt{2\pi n} (n/e)^n$. In particular we can use this to say that   $$ {n \choose k} \leq \left(\frac{en}{ k}\right)^k$$   I tried the tactic of combining bounds from $n!$, $k!$ and $(n-k)!$ and it didn't work. How does this bound follow from stirling's approximation? What's the function like sum() but for multiplication? product()? Python's  function returns the sum of numbers in an iterable.  sum([3,4,5]) == 3 + 4 + 5 == 12   I'm looking for the function that returns the product instead.  somelib.somefunc([3,4,5]) == 3 * 4 * 5 == 60   I'm pretty sure such a function exists, but I can't find it. When did Tom Riddle get his new face? Recently I asked about the  pertaining to Voldemorts new face. However I was corrected by ...     Well, I think the confusion comes with mixing movie canon with book canon. In Philosopher's Stone, here's what Harry sees when Quirrell unwraps his turban:           Harry would have screamed, but he couldn’t make a sound. Where there should have been a back to Quirrell’s head, there was a face, the most terrible face Harry had ever seen. It was chalk white with glaring red eyes and slits for nostrils, like a snake.          Philosopher's Stone - page 212 - UK - chapter 17, The Man With Two Faces      So it seems at some point between leaving school, and sticking his face to the back of Quirrel's head possessing Quirrel he got a new face some how.   How did he manage that? Is it some dark magic he applies? Is it from possessing snakes in Albania? Centering in the \align* environment How to make sure that Thinkpad discharges external slice battery first? The thing is that when an external slice battery pack is connected, the laptop first discharges the internal one. This is a problem because then it is impossible to switch between multiple external battery packs without powering off the laptop. It is also not possible to just disconnect the external battery pack when you e.g. need to insert it into a docking station.  Thus, my question: how to change the discharge order under Linux?  For my use cases following order would make much more sense: when an external slice battery is connected, first discharge it completely before using power from the internal battery.  Background: For some Thinkpad models (e.g. X220) there are slice battery packs () available that you can connect to the bottom of the laptop (similar to a docking station).  They seem to be supported well on Linux - e.g. the Gnome Shell battery applet includes both batteries (internal and external) when connected - including displaying the current capacity for each. Resize partition without affecting other OSes in dual-boot I wanted to resize (increase or decrease the partition size) the existing Ubuntu partition without affecting it and the other OS(es) installed in the machine. A very compact list in Beamer I would like to make a very compact list (e.g., itemize) in Beamer.  has been asked for an article-type document class; the answer uses the enumitem package, known to be .  My question is: How do I make the same compact list in the Beamer document class? As in the above linked question, I would like the list to have   No whitespace before list No whitespace after list No whitespace between lines Less indent before the bullet points Why do Star Trek vessels always approach each other on parallel planes? Space is just open 3D space, right? In Star Trek, ships are always coming from somewhere else: different solar systems, galaxies, etc. However, when they meet, they always seem to be on parallel planes (facing each other).  In some episodes I recall seeing ships that were adrift (and they appeared facing a different trajectory). How can there possibly be some standardized reference plane in space? Do ships just choose to align with each other to be polite? Or perhaps when entering a solar system, the pilot, or navigation system aligns orthogonally with the local orbital axis? (Originally  by AJAY.)  What is the geometric, physical, or other meaning of the third derivative of a function at a point?  If you have interesting things to say about the meaning of the first and second derivatives, please do so. I'm trying to prove that the rationals are not the countable intersection of open sets, but I still can't understand why   $$\bigcap_{n \in \mathbf{N}} \left\{\left(q - \frac 1n, q + \frac 1n\right) : q \in \mathbf{Q}\right\}$$   isn't a counter-example. Any ideas? Thanks! How are constraint forces represented in Lagrangian mechanics? Saleforce Too many future calls: 11