What is an easy to use web GIS stack to use for making fictional maps?
Web-mapping with editing capabilities?
$G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$ Let $G$ be a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$  I know G is abelian since $ab = (ab)^{-1} = b^{-1} a^{-1} = ba$ for all non-trivial $a,b \in G$ so I have several questions remaining:    How do I prove $|G| = 2^n$? I'd like to say we use induction to prove this but I'm at a loss as to where I would start. Why is $G \simeq C_2 \times C_2 \times\cdots\times C_2$?   I've read several answers to question similar to this yet unfortunately most of them involve Galois Fields and vector spaces, both concepts I'm unfamiliar with. I'd greatly appreciate an intuitive proof. The "equal angles" law of refection on a flat mirror is a macroscopic phenomenon. To put it in anthropomorphic terms, how do individual photons know the orientation of the mirror so as to bounce off in the correct direction? Winter 18  does not get values from a parent record Determine which circuits are parallel and which are in series I need to find the Equivalent Resistance across A and B. The problem is, I don't know which one's are in series and which ones are in parallel. How do I identify which ones are parallel or series? In Avengers: Endgame,       Thanos was able to stop and catch Mjolnir and Stormbreaker mid-air as both Captain America and Thor used/called them BEFORE he got the Infinity Stones.   Since this character is clearly not worthy and had no super powers at the time, how were they able to wield Thor's Mjolnir and Stormbreaker, when even the Hulk couldn't do it in The Avengers? I can always find that in some articles the production of higgs decay written as &quot;$\rm H\to {ZZ}^*\to 4l$&quot;, &quot;$\rm H\to ZZ\to 4l$&quot;, &quot;$\rm H\to Z\gamma^*\to\ldots$” What dose it mean when some particles with a superscript *? Such as “$\rm Z^*, W^*, \gamma^*, \ldots$&quot;. What’s the difference between them and &quot;$\rm Z, W, \gamma$&quot;? A 256GB SSD has Windows-10 and 16.04 installed.  BIOS not UEFI.  A charity I work with requires me to use Quickbooks Desktop on Windows.  The plan is to ghost the existing system to a 512GB or larger SSD and create a third bootable Windows 7  partition for performing charity activities.   Is this possible to have a third partition? Is there a good example you have used as a guide? Is triple booting with two Windows partitions different from 2 Linux partitions?   If you have done this before ( with GRUB) please indicate this in your response: lessons-learned are appreciated.  Thank you How long does it take for badges to be awarded? How are they generated? Do badges get calculated in real time, or do they get calculated by an external service? How long does it take for a badge to be awarded, once its requirements are met?  Does Stack Overflow use any external services to do things, like maintenance, e-mailing or badge calculation? Spider-Man is the one franchise that is on course to a third reboot in a span of 15 years.   My question is what was the reason for these numerous reboots of Spider-Man which pretty much follow the same origin story for the Marvel superhero.  Has the comic creator or studio ever spoken out about the reasoning behind the same? It's big and empty and I can't get up to the top, what should I do? I can't jump high enough, anti-gravity doesn't seem to do anything either.  My first tactic was to use the octopus summoning crown to create a pile of octopi that I could climb up, but when I teleported to the back of the room they followed me back, trapping me in the entrance. In C, is it possible to forward the invocation of a variadic function? As in,  int my_printf(char *fmt, ...) {     fprintf(stderr, "Calling printf with fmt %s", fmt);     return SOMEHOW_INVOKE_LIBC_PRINTF; }   Forwarding the invocation in the manner above obviously isn't strictly necessary in this case (since you could log invocations in other ways, or use vfprintf), but the codebase I'm working on requires the wrapper to do some actual work, and doesn't have (and can't have added) a helper function akin to vfprintf.  [Update: there seems to be some confusion based on the answers that have been supplied so far. To phrase the question another way: in general, can you wrap some arbitrary variadic function without modifying that function's definition.] Probability that two random numbers are coprime is $\frac{6}{\pi^2}$ This is a really natural question for which I know a stunning solution. So I admit I have a solution, however I would like to see if anybody will come up with something different. The question is     What is the probability that two numbers randomly chosen are coprime?   More formally, calculate the limit as $n\to\infty$ of the probability that two randomly chosen numbers, both less than $n$ are coprime. A "friends list" on Stack Overflow would be nice Which way is up? (electric outlet) Proof using Prüfer encoding The question is as below:      Show that each vertex $v$ of a tree $T$ appears $deg(v)-1$ times in the Prüfer encoding of $T$, where $deg(v)$ is the degree of $v$ in $T$.   For this, I think there are 3 scenarios a leaf should be considered for: (1) when it is a leaf as part of a tree; (2) a leaf that has been discarded; (3) the remaining edge. I feel like this will result in a short proof which is only two (or so) statements long, but at the same time, feel it is too simple.   EDIT: I've had a look at this again and narrowed it down to 2 cases:   Case 1: The vertex $v$ in question has $deg(v)\ge2$. $v$ then loses its neighbours as the algorithm is applied repeatedly until $v$ becomes a leaf itseelf. At this point, $v$ is attached to another neighbour, leaving an edge. This means the algorithm can no longer be applied and we have obtained the final Prüfer Encoding for the tree $T$.  Case 2: The vertex $v$ has $deg(v)\ge 2$. It loses its neighbours as the algorithm is applied repeatedly but is deleted itself at some point in the process.   Have I gone about this wrong?  Thank you. Density of states for arbitrary dispersion relation If I have a 3D dispersion relation   $E=E(k_x, k_y, k_z)$ I have an equation for the density of states, which is   $D(E)=\frac{1}{\nabla_k E}\int\frac{dS}{(2\pi)^3}$  1) I am confused about the integral. What am I integrating over, exactly? It must have units of the $k$ vector, so it's a k-space integral, but what is the surface that is relevant?  3) Where does that equation come from, how is it derived? Frequency encoding is a widely used technique in Kaggle competitions, and many times proves to be a very reasonable way of dealing with categorical features with high cardinality. I really don't understand why it works.   Does it work in very specific cases where frequencies are correlated with the target or is it more general? What's the rationale behind it? $\mathbb{R}$ with the lower limit topology is not second-countable I am trying to prove that $\mathbb{R}$ with the lower limit topology is not second-countable.  To do this, I'm trying to form an uncountable union $A$ of disjoint, half-open intervals of the form $[a, b)$, $a &lt; b$. Is this possible? I think this would imply the $A$ is open but no countable union of basis elements could coincide with $A$ therefore making the real numbers with the lower limit topology not second-countable.  I think there must exist something like $A$ described above but I am having trouble visualizing it and coming up with a formula to represent it.  Maybe there is some other way to show it is not second-countable. Since Naruto failed the Genin exam so many times, doesn't that mean he's older than Sasuke and Sakura? Can I get SSH to use an askpass program even if it was run from a terminal? says:  SSH_ASKPASS    If  ssh needs a passphrase, it will read the passphrase from the    current terminal if it was run from a terminal.  If ssh does not    have  a  terminal associated with it but DISPLAY and SSH_ASKPASS    are set, it will execute the program  specified  by  SSH_ASKPASS    and open an X11 window to read the passphrase.   I'd like SSH to use an askpass program even if it was run from a terminal.  On occasion, I have to connect to servers, where there's some delay in showing a password prompt (maybe due to network issues, maybe due to attempted reverse DNS lookups, …). I get annoyed and switch to something else, and forget about the attempted connection. (Insert joke about attention span of a goldfish.) When I finally get back to it, the prompt's timed out and even a correct password would just result in a closed connection.  Keys would be one solution, but not every system I use has my usual SSH keys. However, I usually use Ubuntu systems, and Ubuntu has an SSH askpass program installed by default.  If an askpass window popped up, however, I'd be immediately aware of it. That's a good enough compromise for me, if only I can get it to work.