force:inputfield does not render in lightning component
Unable to get force:inputField or force:outputField to render inside other markup in Lightning Component when used in Lightning Experience
Git ignore file for Xcode projects Which files should I include in .gitignore when using Git in conjunction with Xcode? Can anyone come up with an explicit example of two functions $f$ and $g$ such that: $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective?  I tried the following: $$f:\mathbb{R}\rightarrow \mathbb{R^{+}} $$ $$f(x)=x^{2}$$  and  $$g:\mathbb{R^{+}}\rightarrow \mathbb{R}$$ $$g(x)=\sqrt{x}$$  $f$ is not injective, and $g$ is not surjective, but $f\circ g$ is bijective  Any other examples? Why does performance of a regular hard drive decrease over the duration of a benchmark while SSD doesn't? I use HD Tune to measure performance of the hard drive.  The tests typically take 2-3 minutes and the transfer rate of a regular hard drive decreases dramatically as the test comes to a close.    However, the SSD drive performance stays the same over (pic below) the life of the test.  This happens on all my computers.  Why is that? What do \makeatletter and \makeatother do? Many LaTeX “hacks” begin with \makeatletter and end with \makeatother. What do these commands do? I recently traveled from the Basel area to Stuttgart for a weekend.  I had round-trip tickets including (paid) bicycle reservations.  At our first station change, we found that our EC train was canceled.  Information gave us a replacement train schedule, using slow RE trains which don't require reservations for bicycles.  As we continued our trip, every single train we boarded arrived late, eventually causing us to reach Stuttgart roughly 2 hours later than our initial itinerary.  What monetary compensation am I justified in requesting from Deutsche Bahn in this case?  In particular:   It seems clear I should get back the bicycle reservation money, since the train we reserved on was canceled. I know DB offers compensation for late travels.  I'm not sure whether we were 2 hours late or more, or just shy of 2 hours.  But does this apply if we weren't traveling by our original trains? If we had originally scheduled our journey with RE trains and other local transport, we could have bought a Baden-Württemberg ticket for much cheaper than our tickets including an EC cost.  Can I ask them to refund the difference? Am I entitled to any other type of compensation? Please see the following image, where you can find the inconsistency of SO reputation score among different flair themes (one with 7165, while all other three 7265).   I always thought that these four themes are based on the same data until now. Is this a bug? Are different flair themes really updated individually?    P.S.: The inconsistency only shows on my mobile, no problem from my desktop. help with some Hilbert style proofs in a propositional logic axiom system. I'm very new to classical propositional logic, and my lecturer is using a system with the following axioms:  A1. X→(Y→X)  A2. (X→(Y→Z))→((X→Y)→(X→Z))  A3. (¬Y→¬X)→(X→Y)  Use uniform substitution and Modes Ponens (MP) as rule of inference. Deduction Theorem also allowed.  I'd like to deduce the following:  (a) X, Y ⊢ ¬(X→(¬Y)) (conjunction, but expressed in terms of NOT and IMPLIES)  (b) X→((X→Y)→Y)  (c) (X→Y)→(((¬Y)→X)→Y)  (d) (((¬Y)→X)→Y)→(X→Y)  Remark: The last two are to show that the axiom (A3) can be replaced with a different axiom:  B3. (¬Y→¬X)→(((¬Y)→X)→Y).  Solution: Bram28 proves (b) and (c) below. I demonstrate (a) and (d).  (d) is alright; first, I claim that X, ((¬Y→X)→Y) ⊢ Y.  Axiom (A1) gives ⊢X→(¬Y→X) so that ((¬Y→X)→Y)⊢X→Y by Hypothetical Syllogism (HS), which Bram28 shows to be valid.  Now that we have ((¬Y→X)→Y)⊢X→Y just apply the deduction theorem to get what we want: ⊢((¬Y→X)→Y)→(X→Y).  (a) is slightly trickier. Axiom (A1) gives ⊢ Y→(X→Y) so that X, Y ⊢ (X→Y).  Next, by part (b), we have as a theorem that ⊢X→((X→¬Y)→¬Y).  Therefore X, Y ⊢(X→¬Y)→¬Y.  But ⊢(¬¬(X→¬Y))→(X→¬Y) by DN Elim, which Bram28 shows to be valid.  By HS, X, Y ⊢(¬¬(X→¬Y))→¬Y.  By Axiom (A3) and MP, X, Y ⊢(Y→¬(X→¬Y)).  Also, rather trivially X, Y ⊢Y.  Finally by MP we conclude X, Y ⊢¬(X→¬Y) as required. I saw this several times in different movies, but I don't understand what is this supposed to mean. The main idea is when the scene is about to change, for one second or so we still see the picture from the old scene, but the sound is already coming from from the upcoming scene. Why do they do this? What's the purpose of this technique? Why can't Mathematica integrate this? Dupehammer creates and deletes a comment, causing notifications to go out Inequality: $ab^2+bc^2+ca^2 \le 4$, when $a+b+c=3$. About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$ Let $q: \mathbb{N} \to \mathbb{Q}$ be a bijection and denote the image of $k \in \mathbb{N}$ by $q_k$.  Let $f: \mathbb{R} \to (0,1)$, $$ f(x) = \underset{q_k \leq x}{\sum_{k \in \mathbb{N}}} 2^{-k} $$  Show that:  1) $f$ is strictly increasing  2) $f$ is continuous at $x$ iff $x \in \mathbb{R} \setminus \mathbb{Q}$.  My work:  Let $x, y \in \mathbb{R}$, $x &lt; y$. Then there exists $q_n \in \mathbb{Q}$ s.t. $x &lt; q_n &lt; y$. Now $$ f(x) = \underset{q_k \leq x}{\sum_{k \in \mathbb{N}}} 2^{-k} &lt; \underset{q_k \leq x}{\sum_{k \in \mathbb{N}}} 2^{-k} + 2^{-n} \leq \underset{q_k \leq y}{\sum_{k \in \mathbb{N}}} 2^{-n} = f(y) $$ so $f$ is strictly increasing.  I think my proof of 1) is ok, but how can I prove 2)? How can I automatically center an image? I use:  \documentclss{mwrep} ... \begin{figure}   \includegraphics{a.jpg} \caption[Long caption]{Caption} \label{pic-a} \end{figure}   How can I make images to be always visible on the center of page? (To be more specific: the center of the image should be between the left and right margin - I use different left and right margins). I don't want to put anything after every \begin{figure} in my document.  Important: I don't want to waste an entire page on a single image at the very center of the page. I want only horizontal alignment. (left &lt;-> right) How do I start a process from C#? At the end of the scene in the cemetery in GoF, the spirits who emerged from Voldemort's wand tell Harry to go grab the trophy (which, of course, was a portkey that took Harry and Cedric from the maze to the cemetery), and that the trophy portkey would take Harry back to Hogwarts.  Why would the portkey do that?  Are all the portkeys 2-way?  If possible, I would prefer as much of the answer based on canon (or JKR) as feasible I encountered such a formula for pooled variance:  $$\frac{(n-1)s_x^2+(m-1)s_y^2}{n+m-2}\left(\frac{1}{n} + \frac{1}{m}\right)$$  Here we have two samples of the following sizes $n$ and $m$. $s_x, s_y$ are the sample variances.  I understand that the first term is a weighted average, but from the second term comes? How can I explain how to play D&D to new players without them falling asleep from boredom? Some of my friends just started playing Dungeons &amp; Dragons [5e] for the first time and don't know anything about how to play. I have tried explaining to them the things that are completely necessary and teach them the rest while playing but I could not get them to understand. None of them have a players handbook and they can't afford one and they really want to play. I really want a simple way to explain the basics and since I have a habit of explaining things in ways that are much too complicated. I have already told them the basic rules so all I need to know is a simple way to explain how to play. Helix in a helix I am trying to work out a "helix in a helix" mathematically.  Intuitively I think of this as a steel cable, which is made up of a number of smaller steel cables all bound together in spiral.  If I wanted to find the length of one of the individual cables, it would be bound in a spiral in the smaller cable and then those cables bound in a larger spiral cable.  I know that if I wanted to do a helix whose ends meet, I would use the parametrization $$((a+b\cos(\omega{t}))\cos{t},(a+b\cos(\omega{t})\sin{t},b\sin(\omega{t})),t=0..2\pi$$ I've been trying to map out in my head how to, instead of curling the helix, making the helix travel in the path of a helix.  I've achieved it partially with $$((a+b\cos(\omega{t}))\cos{t},(a+b\cos(\omega{t})\sin{t},t),t=0..\infty$$ But this doesn't keep the smaller helix in tact, and turns it into a sine wave helix.  I've also tried  $$((a+b\cos(\omega{t}))\cos{t},(a+b\cos(\omega{t})\sin{t},tb\sin(\omega{t})),t=0..2\pi$$ But this gives me sort of a nautilus shape where the helix curls into itself and increases in size and curls around into itself.  What am I missing?  EDIT:  Also, what if we wanted to do this again, like a 'helix in a helix in a ... in a helix'? the weak form of 'on' I am confused at whether or not there is a weak form at preposition's 'ON'. I've checked at some dictionaries at Cambridge and Oxford dictionary, they don't mention on the weak form's pronunciation. However, I, am a Japanese, checked at English-Japanese dictionaries, they mention on the weak form as /ən/.  For example, is there the difference of pronunciation between 'It goes on' and 'There is an apple on the table' in connected speech?  Does it exist?  Thanks Yuichi  *It's Edited Shape of the universe? What is the exact shape of the universe? I know of the balloon analogy, and the bread with raisins in it. These clarify some points, like how the universe can have no centre, and how it can expand equally everywhere in all directions. But they also raise some questions, like if you are on the surface of a balloon and travel in 1 direction, you will eventually return to your starting point, is it possible our universe have this feature?  If it has, or had, would this be a symmetry of sorts ($\psi(x)=\psi(x+R)$), and as such have a conserved quantity associated with it (by Noether)? Assuming "small curled up dimensions" wouldn't these dimensions have this type of symmetry, what are the associated conserved quantities? Is it known exactly what the geometrical shape of the universe is? (on a large scale) (I am not talking about only the observable universe). How does one define the "size" of a dimension, is this scale only applicable to curled up ones? Is it possible to describe to a layman the shape of the universe without resorting to inept analogies?