Does a space opera have to feature supernatural abilities, à la the Force? I'm creating a space opera video game and I was wondering if to be considered a Space Opera it had to feature some supernatural abilities like Star Wars has with the Force. Or can I completely forgo that entire idea altogether and keep the rest of what the Wikipedia page says about Space Operas?
Difference between Space Opera and Science Fiction? A while back a guy came into the place where I was working. He had a book (I don't remember the name). The book was, according to him, scifi. I told him, "Great! My favorite scifi is the Skylark Series by EE Doc Smith!" He sort of tsked this, saying, "Oh, that's only space opera." I really didn't know what to think of what he said. The funny thing was, I remembering looking at his book thinking, what makes his book scifi any more than mine.  I started thinking about this incident the other day and am once again curious:  What is the difference between space opera and science fiction? What identifies each genre specifically?    NOTE: I had originally asked this on meta due to the closed question:  which is very similar to my question. It was subsequently moved to the main site.
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$ Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$  My first thought is that there can not be a continuous bijection, $f$, from $[0,1]$ to $\mathbb{R}$ because a continuous function that maps $[0,1]\rightarrow \mathbb{R}$ must be bounded so there can't be a surjection. So that would then be the proof.   Though I believe I am incorrect in my thinking because a hint for the assignment says to use the intermediate value theorem. That is "Suppose $f:[a,b]\rightarrow\mathbb{R}$ is continuous. If $f(a)&lt;\delta&lt;f(b)$ or $f(b)&lt;\delta&lt;f(a)$ then $\delta=f(c)$ for some $c\in[a,b]$".   Why is my first thought wrong and how is the IVT useful? Can I send in for repair a lens that has a shattered front element?     UPDATE: The front element was not shattered, it was the UV filter. Factory diagnosis: Lens assembly had been impacted; cleaned and checked.  Helpful notes by Crowley, David Richerby (x2), Michael Clark (x2), and   mattdm (on element price vs UV filter).      Canon cleaned and checked my lens back to like new quality for $179 labor, no parts, not including shipping.      Jim Garrison answered my question, but Crazy Dino has the best info all around for a lens element shatter.   Original Question:  I recently opened my camera bag to find a shattered front element on a Canon EF 16-35mm f/2.8 L II USM lens.   There are a lot of micro glass shards on the second element.  Does anyone have experience with this sort of thing?  Some of the following are questions I have:   Can I get it repaired? What will the cost be roughly? Will the lens ever work the same and have a good image quality? Should I ship it as is, or attempt cleaning it with air? Where is the best place to cry a little?   Thanks, any good info on this would be appreciated.  I will never rest a lens on another lens, I nearly lost a 24-70mm L that shattered a UV filter also.   Good reason to have a UV always, never thought it could happen to me.  Update: Looking at it more it looks like maybe just the front ring came undone and the UV filter broke?  I can't remember what it looked like exactly before.  I threw away the glass shards (polished sand) in the Nevada desert.      UPDATE: Primary reason for thinking more than just the UV was broken,   UV filter split into two rings, depositing the locking collar into the   lens barrel. Computing irreducible components of algebraic set Changing Login Logo I simply can't figure out what the capacity of this circuit is.  I can do the math myself, I just need a hint how to create an equivalent circuit where it is obvious what is parallel and what is in series... What flash slaves can be used with a Canon Speedlite 600EX-RT? My current flash setup is a standard shoe mount but I've been thinking about getting a remote.  I've been drooling over the Speedlite 600EX-RT. It uses radio to control slaves, which is nice (longer distance, doesn't require line of sight, etc.).  One thing I don't understand: do slaves also have to be 600EX-RTs or do other flash units use radio to communicate already? Can any (cheap?) flash slaves can be used with a Canon Speedlite 600EX-RT or do I need to buy the 600EX and a ST-E3-RT transmitter in order (or multiple 600EX-RTs) to have a radio-controlled remote flash setup? Converting MultiLinestring to Linestring with PostGIS I had this "almost bonus" question on the final in Group Theory recently: prove that there is no such group $G$ which would satisfy Aut$(G)\cong \mathbb{Z}_n$, where $n$ is an odd integer. I don't have much certainty if this proof is OK, and one's opinion would be appreciated.  Here's my attempt:     Suppose that there exists such a group $G$ that satisfies the above condition. Since $\mathbb{Z}_n$ is cyclic, Aut$(G)$ is also cyclic and $G$ is abelian, which implies that Inn$(G)\cong \{e\}$. Thus Aut$(G)=$Out$(G)$. (I don't think this fact is important here though). Now, since an automorphism sends a generator to a generator, and since each automorphism is completely determined by such mapping, |Aut($G$)| must be of factorial order. But an integer factorial is always even. However, $|\mathbb{Z}_n|$ is odd, which is a contradiction. Therefore, no such $G$ exists.   I'm afraid that my proof is not very nice, but at least a genuine attempt was made. I created a thick glass bottle and duplicated the interior faces to make a new object to create the liquid inside.   I went in the edit mode, selected the faces I wanted to copy and duplicated them with ShiftD. Then I pressed P to  separate the duplicated faces.   Now I try to make a duplicate of that liquid to make it flow out of the bottle, and I simply need the duplicate of one face of it. So I go to edit mode and do as I did to make the liquid from the bottle faces... but as soon as I'm back to the object mode and I want to move the duplicated faces, every thing moves with it...   I played around and tried things, and while doing so I realized that if I dupe the liquid object in object mode using ShiftD and press 0 to place it where the original is, they move together if I duplicate it and place it somewhere else so that they are separated.   Also if I pick one of the two separated objects and make it intersect with the other one, release my left mouse button to place it there, and then try to move it again, they both move together, but not at the same speed.  I really don't understand what is going on and I'm sure it's really badly explained, so what I'll do is make a screen capture of my Outliner and record the behavior of the objects and upload those to help you understand. Please consider gathering Meta feedback before the "ship" stage Maybe I'm searching for the wrong thing, but I can't see how I can do this.  I have two servers:   Server A (has SQL Server 2012 installed) Server B (has SQL Server 2014 installed)   Server A provides an API via IIS. The code both inserts and gets data from the database depending on the API call.  Server B does exactly the same for its local database.  I would like to have it so that the two databases are consistent copies of each other. I do believe this is what HA accomplishes.   So a load balancer, for example, might direct API calls to A sometimes, and B sometimes, but the data needs to be consistent either way.  I found some documentation on HA for SQL Server 2012, but not on how to do this for a mixed environment of 2012 and 2014.  Any help or pointers to documentation would be great! Thanks. Convert integers to written numbers Is there an efficient method of converting an integer into the written numbers, for example:  string Written = IntegerToWritten(21);   would return "Twenty One".  Is there any way of doing this that doesn't involve a massive look-up table? he became firm friend or friends? Height/Radius ratio for maximum volume cylinder of given surface area So first let me state my homework problem:  Let $X$ be a set, let $\{A_k\}$ be a sequence of subsets of $X$, let $B = \bigcup_{n=1}^{+\infty} \bigcap_{k=n}^{+\infty} A_k$, and let $C = \bigcap_{n=1}^{+\infty} \bigcup_{k=n}^{+\infty} A_k$. Show that (a) $\liminf_k\; {\xi_A}_{_k} = \xi_B$, and $(b)$ $\limsup_k \;{\chi_A}_{_k} = \chi_C.$  I know that, in the context I am familiar with, that $$\liminf_{k\rightarrow +\infty}\; X_k = \bigcup_{k=1}^{+\infty} \bigcap_{n=k}^{+\infty} X_n$$ and $$\limsup_{k\rightarrow +\infty}\;X_k = \bigcap_{k=1}^{+\infty} \bigcup_{n=k}^{+\infty} X_n.$$   I also know that the characteristics (indicator) function is defined as $\chi_A(x) = \begin{cases} 1, &amp; x \in A \\ 0, &amp; x \notin A .\end{cases} $  So I wrote out $B$ in some of its `glory': $B= (A_1 \cap A_2 \cap A_3 \cap \cdots) \cup (A_2 \cap A_3 \cap \cdots) \cup (A_3 \cap A_4 \cap \cdots) \cup \cdots$, and as the first argument is the smallest, with increasing size to the right, the last term in the expression for $B$ would be $B$, which would be the largest.  So if I replace the $X_k$'s above with $\chi$'s I still don't see how I can get the correct answer - though it looks pretty clear from the definition of $B$ and that of $\liminf$ being basically the same, except in this case for the $\chi$.  Any direction would be greatly appreciated. By the way, I have checked out  but I was somewhat confused by the topology, the meets/joins, etc.  Thanks much, Nate Long ago someone demonstrated the following card trick with a standard 52-card deck:  (1) A volunteer selects 5 cards from a shuffled deck, which the performer does not see.  (2) The assistant puts exactly 4 of those in a pile and passes it to the performer.  (3) The performer can then identify the 5th card.  There are a few ways to execute this trick, one of which goes as follows.  (1) The assistant finds a suit common to 2 of the 5 cards, with values $x$ and $y$ modulo $13$.  (2) He then removes one of them, say $x$, such that $x-y \in [1..6]$ modulo $13$.  (3) He then puts the other one at the top of the pile.  (4) And he puts the 3 other cards after that in a permutation corresponding to $x-y$ modulo $13$.  Since (1) works by pigeonhole, (2) works because $\frac{13-1}{2} = 6$, and (4) works because there are 6 possible permutations of 3 cards, the trick succeeds. My question is whether the same trick can work with more than 52 cards. It is not obvious to me how to do so, nor compute the maximum number of (pairwise distinct) cards possible. Also, it seems to me that even if the trick can be made to work for $n$ cards, it may not work for $n-1$ cards! Any ideas? Bring a "human factor" into review audit composition/selection How do I check if a string is a number (float)? What is the best possible way to check if a string can be represented as a number in Python?   The function I currently have right now is:  def is_number(s):     try:         float(s)         return True     except ValueError:         return False   Which, not only is ugly and slow, seems clunky. However I haven't found a better method because calling float in the main function is even worse. The topological space $X=\omega_1\cup \{\omega_1\}$ is not first countable but $\omega_1$ is. Here $\omega_1$ denotes the set of all countable ordinals and $\{\omega_1\}$ is the first uncountable ordinal. Cardinality of $\omega_1$ is $\aleph_1.$And also $\omega_1$ is called the limit ordinal meaning it is the limit point of the set $\omega_1.$  Here I want to prove two things. $1)$ $\omega_1$ is first countable. and $2)$ $\{\omega_1\}$ is the limit point of $\omega_1$. But since no sequence converges to $\{\omega_1\}$, using this I could say that our space $X$ is not first countable.  $1)$ The proof of this I got from  with just one question: it says we need to prove that such an $S(y)$ exists,and I'm thinking $S(y)=\cap\{u\in \omega_1:u\gt y\}.$ This is correct$?$ But here is a chance that the countable base around $y$ may be finite and not countably infinite.  $2)$ If possible let us assume that $\omega_1$ is not a limit point of the set $\omega_1.$ $U$ be a nbd of $\omega_1$ that does not intersect $\omega_1.$ Then what are the elements of $U$ like? The ones coming before $\omega_1$  cannot be uncountable because $\omega_1$  is the first. Then they must be countable. This is absurd so no such $U$ exists. Thus $\{\omega_1\}$ is a limit point.  Are my proofs correct? Thank you. "errno 5 - input/output error" when trying to install Ubuntu Today I downloaded Ubuntu for my laptop. It runs great from a bootable USB, but when I tried to install it, I got the following error message: The installer encountered an error copying files to the hard disk:  [Errno 5] Input/output error  This is often due to a faulty CD/DVD disk or drive, or a faulty hard    disk. It may help to clean the CD/DVD, to burn the CD/DVD at a lower   speed, to clean the CD/DVD drive lens (cleaning kits are often    available from electronics suppliers), to check whether the hard disk   is old and in need of replacement, or to move the system to a cooler   environment.     I tried everything to install it on my laptop including redownloading the Ubuntu ISO image, but nothing worked.