Recently  was closed as duplicate. However, the duplicate target isn't showing in the close banner. It shows:  This questions already exists: Closed 3 mins ago.   However,  are showing the target.
Obligatory: This is not a duplicate of , which is concerning the much older duplicate closure process.  Have a gander at . Notice anything weird?  The Community♦ user was invoked by the question asker to self-close as a duplicate (presumably of the comment below, which links to ), but the list of duplicates is entirely empty. So it would seem the question asker was able to close their own question as a duplicate of... nothing?  Screenshot, in case the post is altered later:    Any idea what happened here?
How do rays of light getting focused at a point create an image?  How are the information of object's shape and dimensions expressed as an image when light rays converge?  Is it understandable by solving wave equation for light? Use variable inside bash brace expansion I have a program that generates a variable number of pictures, ordered like that: 1.jpg, 2.jpg [...] 10.jpg..etc  I can't use *.jpg as input because the 10 will be processed before 2, 3, etc. so I want to use:  convert page_{1..$N}.jpg out.pdf   but does not work. How should the command be? Effective marketing strategies for independent game projects I would really like to hear how other independents generally approach marketing their game with limited resources. I know how critical marketing is since I've seen it first hand on several fronts. I've been part of teams that didn't put an ounce of marketing into their project and didn't come close to meeting expectations. I've also poured a lot of time into visiting forums to discuss our previous title which resulted in minor bumps over time.  I really think  is doing some amazing grass roots marketing with the way they are managing their community around their Blog. They've massed a following that is willing to pay (far in advance) them for their game before they finish it to help support them. That's awesome.  But how many people are really willing to divulge such information that early? Should that be a concern? Should I start talking about my next project before I really have anything implemented?   What has worked for you? I would be particularly interested to hear how people approach Apple's iTunes store. I believe we're looking at around 33,000 games on the store these days. Alternate property name while deserializing Does anyone know of any interesting subsets of the Cantor set? When I first started thinking about this, I thought that since the Cantor set $C$ is the intersection of disjoint unions of closed sets, those particular closed sets would be subsets of $C$. Those sets, however, happen to be intervals! The Cantor set contains no isolated points nor (open) intervals, so then what subsets does it contain besides $\varnothing$ and itself? How do we know what type of gauge field to add to a theory? I've been watching  and in one lecture, he discusses a very simple gauge theory.  We have a complex scalar field $\phi(x)$ with Lagrangian  $$\mathscr{L} = \partial_\mu \phi^* \partial^\mu \phi - V(\phi^* \phi)$$  and we want to do the gauge transformation $\phi(x) \to e^{i\theta(x)} \phi(x)$.  But the derivative term in the Lagrangian is not invariant if $\theta$ varies from place to place, so we add a new vector field $A_\mu$, and define it to transform like $$A_\mu \to A_\mu + \partial_\mu \theta$$ under the gauge transformation.  Then we change the Lagrangian to use covariant derivatives $D_\mu = \partial_\mu + iA_\mu$ instead of ordinary ones; now when the gauge transform is done all the derivatives of $\theta$ cancel out, and the result is invariant.  My question is: was there any freedom in choosing to add a vector field, with that specific gauge transformation law?  Are there any other ways we could get gauge invariance here—by using a different transformation law, or with a different type of field (say, a scalar, tensor, or spinor) with some other transformation law?  More generally, how can we tell what type of field is needed and what its gauge transformation law should be, to get some particular Lagrangian to be invariant under some particular gauge transformation? Powerset of set with empty sets I am working on a problem with the following set:  $$S =  \{\varnothing,\{\varnothing\}\}$$  My solution was: $P(S) = \{\varnothing, \{\varnothing\},\{ \varnothing , \{ \varnothing \}\}\}$, but the solution on the textbook shows: $P(S) = \{ \varnothing , \{ \varnothing \}, \{\{\varnothing\}\}, \{ \varnothing , \{ \varnothing \}\}$  Where does the $\{\{\varnothing\}\}$ come from?  Thanks Is there a word for a person who gives out too many extraneous details? Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem. I have installed Apache(LAMP) web server on my ubuntu machine and I want to do the above mentioned thing.I have tried creating symbolic links in the /var/www directory but it only shows files but not directories inside the directory linked.I want to redirect /var/www to my home folder so that I can access all the files and directories contained therein.Please help me. Why Normality assumption in linear regression Enlarged partition, filesystem still reports old size Did Emperor Palpatine know about Luke and Leia from the beginning? Did Emperor Palpatine know that Padme had given birth to twins while it was happening?  Was it his long-term goal to have Vader only discover his offspring later, at some "correct" moment? If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$? Tools to measure the nonrandomness of database I was working on historical data looking for anomalous patterns that we would not expect to occur at random. I'd like to create a scheme to analyze data and markets to test for statistical significance and consistency over time.  Question : Are there some tools we could use to evaluate the nonrandomness of a database? What do we use usually to say that something is random or not (statistically)? Figure we work with change in some value over time. What is __init__.py for? What is __init__.py for in a Python source directory? Can't Remove Cortana from Windows 10 Meaning of the word "axiom" Thus, axioms are propositions we assume to be true and we use them in an axiomatic theory as premises to infer conclusions, which are called "theorems" of this theory.  For example, we can use the  to prove theorems of arithmetic.  This is one meaning of the word "axiom". But I recognized that the word "axiom" is also used in quite different contexts.  For example, a group is defined to be an algebraic structure consisting of a set $G$, an operation $G\times G\to G: (a, b)\mapsto ab$, an element $1\in G$ and a mapping $G\to G: a\mapsto a^{-1}$ such that the following conditions, the so-called group axioms, are satisfied:   $\forall a, b, c\in G.\ (ab)c=a(bc)$, $\forall a\in G.\ 1a=a=a1$ and $\forall a\in G.\ aa^{-1}=1=a^{-1}a$.      Why are these conditions (that an algebraic structure has to satisfy to be called a group) called axioms? What have these conditions to do with the word "axiom" in the sense specified above? I am really asking about this modern use of the word "axiom" in mathematical jargon. It would be very interesting to see how the modern use of the word "axiom" historically developed from the original meaning.   Now, let me give more details why it appears to me that the word is being used in two different meanings:  As peter.petrov did, one can argue that group theory is about the conclusions one can draw from the group axioms just as arithmetic is about the conclusions one can draw from the Peano axioms. But in my opinion there is a big difference: while arithmetic is really about natural numbers, the successor operation, addition, multiplication and the "less than" relation, group theory is not just about group elements, the group operation, the identity element and the inverse function. Group theory is rather about models of the group axioms. Thus: The axioms of group theory are not the group axioms, the axioms of group theory are the axioms of set theory.  Theorems of arithmetic can be formalized as sentences over the signature (a. k. a. language) $\{0, s, +, \cdot\}$, while theorems of group theory cannot always be formalized as sentences over the signature $\{\cdot, 1, ^{-1}\}$. Let me give an example: A typical theorem of arithmetic is the case $n=4$ of Fermat's last theorem. It can be formalized as follows over the signature $\{0, s, +, \cdot\}$: $$\neg\exists x\exists y\exists z(x\not = 0\land y\not = 0\land z\not = 0\quad\land\quad x\cdot x\cdot x\cdot x + y\cdot y\cdot y\cdot y = z\cdot z\cdot z\cdot z).$$ A typical theorem of group theory is  which states that for any finite group G, the order of every subgroup H of G divides the order of G. I think that one cannot formalize this theorem as a sentence over the "group theoretic" signature $\{\cdot, 1, ^{-1}\}$; or can one? "Can’t help but" vs. "can help but" Is "can’t help but" considered to be a confused mix of the expressions "can but" and "can’t help"? If not, what is the difference between "can help but" and "can’t help but"? Send POST data using XMLHttpRequest