What is the oldest science fiction story?
What is the earliest work considered to be Science Fiction?
I am beginning with Abstract Algebra and I'm trying to understand Lagrange's Theorem. The theorem reads      For any finite group $G$, the order of every subgroup $H$ of $G$ should divide the order of $G$.   It seems simple and I've used it to solve some exercices but I believe I'm missing the essence of it. Is there an example that can help me understand it better, or visualize it? Is there a geometric interpretation? Does it make sense to say, "The speed of light varies?"  Some may say right off the bat "Yes, it changes as a wave passes through a different medium."  However, I'd like to say no, because when I hear someone say the speed of light, I always think of the constant $c$ (unless the medium is specified to not be a vacuum, but then it isn't $c$ anymore), not the speed of a particular wave.  To me, it makes more sense to say something like, "The speed of a particular wave varies." What is the correct way to state this in the professional world? And in general, when professional physicists say "the speed of light," are they referring to the constant or the actual speed of the wave? My regex is matching too much. How do I make it stop? I have this gigantic ugly string: J0000000: Transaction A0001401 started on 8/22/2008 9:49:29 AM J0000010: Project name: E:\foo.pf J0000011: Job name: MBiek Direct Mail Test J0000020: Document 1 - Completed successfully  I'm trying to extract pieces from it using regex. In this case, I want to grab everything after Project Name up to the part where it says J0000011: (the 11 is going to be a different number every time). Here's the regex I've been playing with: Project name:\s+(.*)\s+J[0-9]{7}:  The problem is that it doesn't stop until it hits the J0000020: at the end. How do I make the regex stop at the first occurrence of J[0-9]{7}? Why does node not evaluate Math.tan(Math.PI/2) to Infinity but Chrome V8 does? Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime. Stirling's Approximation Proof I was searching for the reason why Stirling's Approximation holds true. I found the website  which apparently shows why this is the case. Does this part of the equation make sense in the proof? If so why?  $$\int_{1}^{n}\ln(x)dx\approx\sum_{k=1}^{n}\ln(k)$$ Can Hydrogen Fusion via CNO Cycle Occur in First Generation Stars CNO cycle requires the presence of carbon, nitrogen and oxygen to undergo hydrogen fusion. Does this mean that for first generation stars, no matter how big they are, can't undergo hydrogen fusion by CNO cycle because there is no carbon, nitrogen and oxygen present?   I can't seem to find any website which mentions this. All they say is if a star is large enough, it will undergo hydrogen fusion via CNO cycle, they don't specifically mention it having to be a second generation star. Find what packages are installed from a repository Beamer: How to Disable `\pause` Temporarily I've recently updated to Ubuntu 15.04 and after installing the latest nvidia drivers (346.59) which worked on ubuntu 14.10 seems to have caused some trouble on boot.  All I get is the following when booting:   A purple screen for about a second and then  [0.514409] ACPI PPC Probe failed. Starting version 219  A black screen with a message of my monitor saying : No Signal detected.   I am using a GTX 970. Currently look after 3 websites. I changed one of them to be HTTPS as it's ecommerce, however have seen a huge drop in organic traffic since this was implemented. Went from around 800 impressions to 400.   Any ideas as to why?   Very concerning as I expected it to improve if anything!  I set up 301 redirects to carry through to old pages to http://www.example.com/product1 would go to https://www.example.com/product1  I also set up a separate webmaster account for the HTTPs version as our integration wasn't working well with Google Merchant Centre, and data is flowing correctly but unsure why/if this would cause conflict.  Very confused! How to Update Multiple Array Elements in mongodb I've just begun to work learn Linear Algebra on my own through Hoffman and Kunze's book and the first problem set already has a question that I can't solve:  Prove that if two homogeneous systems of linear equations in two unknowns have the same solutions, then they are equivalent.  I can't seem to figure out how to prove this without resorting to case work where you account for the cases where one of the coefficients are zero and when both are.  Is there an elegant way to prove in general that when two systems of linear equations have the same solutions, they are equivalent? The converse is obvious enough though.  Definition of equivalence from the text :     Let us say that two systems of linear equations are equivalent if each equation in each system is a linear combination of the equations   in the other system. As the title say, I want to prove that  $C_c^{\infty}(\mathbb R^n)$ is dense in $W^{k,p}(\mathbb R^n)$  i.e.  $\displaystyle{ W^{k,p} (\mathbb R^n) = W_0^{k,p}(\mathbb R^n)  \quad (\star)}$. In a book I found that in order to prove it, we need the following claim:  Claim: Let $\displaystyle{\zeta \in C^{\infty} ([0, \infty)) }$ such that $\zeta (t)  =1 $ for $ t \leq 1 $ and $\displaystyle{ \zeta (t) =0 }$ for $ t \geq 2$. For $R&gt;0$ and  $x \in \mathbb R^n$ define $\displaystyle{ \eta_R (x) = \zeta \left( \frac{|x|}{R} \right)}$. If $ \displaystyle{ u \in W^{k,p} ( \mathbb R^n) }$ with $1 \leq p &lt; \infty $ then, $\displaystyle{ \eta_R u \to u }$ in $W^{k,p}(\mathbb R^n) $ as $ R \to \infty$.  If I prove the claim then the $(\star)$ follows using mollifiers. But unfortuently I have stuck, with the proof of the claim.  Any ideas? Why does the multi-paragraph quotation rule exist? Let G be a finitely generated abelian group and M a compact manifold,  I want to prove that $H_r(M,G)$ is finitely generated for $r\ge 0 $.  First I was thinking if  I could do induction over $r$ because for $r=0$, $H_0(M,G) \cong \bigoplus_{i=1}^nG$ where $n$ denotes the number of connected components of M.But for $r&gt;0$ I can't see a way to relate $H_r(M,G$) and $H_{r+1}(M,G)$.  Then I tried to use the fact that for every compact surface there exists a finite cover $\{A_i\}_{i=1}^m$ such that the finite intersections of $A_i$'s are contractile.Let $\{A_i\}_{i=1}^m$ such cover for $M$.Then,using induction on $m$, we have :  -For $m=0$, $M$ is contractile and $G$ finitely generated then $H_r(M,G) $is finitely generated.  -For $m=r$ it's true by induction hypothesis.  -For $m=r+1$ now putting $A_{r+1}=B$ and $\cup_{i=1}^r A_i=A$, and using Mayer Vietoris we get:  $$ ...\rightarrow H_{r+1}(A\cap B,G)\rightarrow  H_{r+1}(A,G) \oplus H_{r+1}(B,G) \rightarrow H_{r+1}(M,G)\rightarrow H_{r}(A\cap B,G) \rightarrow...$$   Here I don't know what to do, maybe I'm missing some algebraic argument It's easy to see that $H_{r+1}(A\cap B,G)$ and $H_{r+1}(A,G) \oplus H_{r+1}(B,G)$ are finitely generated.But how can I argue that $H_{r+1}(M,G)$ is finitely generated? Any idea would be aprecciated. Why do all the planets of the solar system orbit in roughly the same 2D plane? Is cross-posting wrong (to an external site)? I made a question at Stack Overflow long ago and also posted the same question in a non-Stack Exchange website (Xtreme VB Talk). The question .  According to the answer, I shouldn't have cross-posted between Stack&nbsp;Overflow and XtremeVBTalk, because     it increases the probability that wires will get crossed and everyone will waste time.   But I'm not sure why is that wrong. You see, I simply see Stack&nbsp;Overflow and XtremeVBTalk as two different communities with different users. So posting the question in both sites would just give me more answers. And if I got the answer in one of them, I would report back to the other site and let everyone know (and perhaps someone else would be benefited as well). I really doubt it is a waste of time - the more input, the better. The fact that someone was a user in both websites is simply a coincidence.  I realize that Meta&nbsp;Stack&nbsp;Exchange question  exists, but apparently it involves cross-posting within Stack Exchange sites, but this is about external websites instead.  I also realize that I was told that as "advice" (since my question was not flagged or anything), but well, I am now curious: Why would anyone consider this a bad practice? RESTful Authentication What does RESTful Authentication mean and how does it work?  I can't find a good overview on Google.  My only understanding is that you pass the session key (remeberal) in the URL, but this could be horribly wrong. The screen of my phone is physically broken, so it doesn't display anything, but the touch aspect does seem to be working, as I can unlock my phone, and get haptic feedback.  Before I go to get it replaced, I'd like to back up some personal data from the built-in memory to the SD card. I'm fairly certain that if I can get adb to recognize the device, then I can use  to see where I am touching the screen and do what I need to do. Problem is, when I plug it in, it's not recognized, while my emulator is.  I suspect that I might not have USB debugging enabled, which I think is necessary for adb to work. If this is the case, can someone give me screenshots of their Droid X (running 2.3.X) going from the home screen, through all the menus, to activating debug mode? Hopefully I can do it by dead reckoning and adb from there.  Edit: I haven't changed anything about the ROM or launcher; it's all stock.