What is the difference between an electric field and gravitational field?
Noticing that Newtonian gravity and electrostatics are equivalent, is there also a relationship between the general relativity and electrodynamics?
Uniformly convergent implies equicontinuous I'm trying to prove that if I have a sequence of continuously differentiable functions $f_n$ that converge uniformly on $[a,b]$, then $\{f_n\}$ is equicontinuous for all $x_0 \in [a, b]$. My idea is to use uniform convergence to deal with the &quot;tail&quot; and then use continuity to deal with the finitely many $f_n$'s left. But I'm having trouble writing it down. IANAL et al. is usually the start of answers to [legal] questions on any SE site (e.g. ). You usually end up with personal opinions which sound sensible and the accepted answer is often the one closest to the OP's hopes. But it's probably often not correct. I know the situation can be rather complicated and even differ by location, but it would be really helpful if the SE team were providing official lawyers (indicated maybe by using a § in the username, forbidden for everyone else, just like the mod ♦) to provide some orientation that one could actually rely on beyond much doubt... Are cardinal numbers well defined? Or could we have something like $\aleph_{1/2}$? From what I understood, cardinal numbers are defined as:  $\aleph_0$ = the cardinality of $\mathbb{N}$ $\aleph_{n+1}$ = is the least cardinal number greater than $\aleph_n$  The continuum hypothesis states that the cardinality of $\mathbb{R}$ is  $\aleph_1$. I more or less understand this cannot be proven (does not follow from ZFC).  However, can it be proven dat there in fact is a 'least cardinal number' greater than $\aleph_0$?  Is it possible that there are sets with cardinality $\aleph_{1/2}$, $\aleph_{1/3}$, et cetera, so to speak?  Or expressed differently: is it possible that for every set A with cardinality CA > $\aleph_0$, there exists another set B with cardinality CB where CA > CB > $\aleph_0$? What's the difference between a Long Term Support Release and a Normal Release? Add leading zeroes to number in Java? Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric. Question: Let $(X, d)$ be a metric space. Let $A$ and $B$ be disjoint subsets of $X$ that are closed in the topology induced by $d$. Prove that there exist disjoint open sets $U$ and $V$ such that $A\subset U$ and $B\subset V$.   Is this proof correct? : By assumption, $A\cap B=\emptyset$, so there is no pair like $(x_A,x_B)$ (i.e., $x_A\in A$ and $x_B\in B$), such that $x_A=x_B$. Because every metric space is Hausdorff, so for every pair $(x_A,x_B)$ there are two disjoint open sets $U_A\ni x_A$ and $V_B\ni x_B$; and thus union of all $U_A$s (which is an open set containing A) are disjoint from union of all $V_B$s (which is an open set containing A).   Thanks a lot for any help.    PS In special case of standard metric topology on $\mathbb{R}$, if $[a,b]$ and $[c,d]$ are disjoint (say $c&gt;b$), intuitively it is apparent that there is a 'space' between $c$ and $b$ so we can have two disjoint open sets, each of them containing $[a,b]$ or $[c,d]$. Deriving the inverse of a 2x2 matrix I am looking for a derivation for the inverse of a 2x2 matrix. I am also wondering why the determinant is involved in the expression. I am familiar with high school maths and linear algebra. If there is an intuitive reason for expression i would also be interested in that. Need help identifying short story about retired military colonel who fought war at end of time I read this story in an anthology in the eighties or early nineties.  It was about an old man who lived outside a western-like town, though that might have just been how I imagined it.  He goes to town and some ex-military thugs are there causing problems.  Flaunting some odd interdimensional military tech of some sort.  He doesn't want to intervene as doing so would be bad but in the end he must.     By intervening, his military identity is revealed and that causes him (some paradox or causality law) to have to go back and fight the war again.   The war is at the end of time or the universe.  The man is maybe a colonel of the sky something... Not much to go on; I have been searching my collection and wracking my brain for years trying to recall the story. How to use variables inside single quotes How to fix error: The markup in the document following the root element must be well-formed I have recently installed Ubuntu 14.04 LTS on my laptop Sony Vaio VPCEA16FG. I have been getting system freezes (everything including display, mouse, keyboard stops working and I have to do a restart with the power switch) and there are random popups of "System program problem Detected"  On startup my screen is all splashed with black and white pixels and a System program problem detected message.  My video card info:    01:00.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI] Madison [Mobility Radeon HD 5650/5750 / 6530M/6550M Show/Hide function folding margin on Notepad++ Is it possible to get rid of the function folding margin on Notepad++? It seems like the sort of thing that should be in the prefs but I'm not seeing it anywhere. Word for seeing both sides of an argument How can I know if a branch has been already merged into master? I have a git repository with multiple branches.   How can I know which branches are already merged into the master branch? If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$ If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$   My attempt is below. Did I do wrong? Since I don't really understand it. I thought $f'(x) = f'(c)$ so $f'(x)-f'(c)=0$. Am I on the right track? Many thanks!  \begin{align} f(x)-f(c)&amp;=\frac{f(x)-f(c)}{x-c}\cdot(x-c) \\ \lim_{x\to c}[f(x)-f(c)]&amp;=\lim_{x\to c}\left[\frac{f(x)-f(c)}{x-c}\cdot(x-c)\right] \\ \lim_{x\to c}[f(x)-f(c)]&amp;=0 \\ \lim_{x\to c} f(x)&amp;=f(c) \end{align} How to disable the touchpad? I want my touchpad to be disabled when I use my mouse. How can I do that? touchpad-indicator has stopped working on 11.10. It used to work on 11.04. Gnome3 is not a solution as I don't like it and find it buggy. Suppose you want to ask someone to do something, say to tell you the way to a station. Which is more polite, "Would you tell me the way to the station?" or "Could you tell me the way to the station?"? Consider:  List&lt;String&gt; someList = new ArrayList&lt;String&gt;(); // add "monkey", "donkey", "skeleton key" to someList     for (String item : someList) {     System.out.println(item); }   What would the equivalent for loop look like without using the for each syntax? Why does a neon lamp indicator on a power strip switch flicker in the dark? Neon lamp indicators embedded in power strip switches indicate whether the switch is ON or OFF. When the neon lamp is ON in a dark environment (lights of the room are off), the lamp begins flickering and it sometimes goes off for a few seconds. When I switch the lights of the room on, it stops flickering and remains bright. Even when I unlock my phone in the dark near the lamp, it stops flickering! Is the light-making-mechanism in neon lamps affected by the light intensity of the surrounding environment?  UPDATE: I captured my observations with my iPhone and uploaded it to YouTube. Here is the link of the video:  All the lights of my room were turned off. There were no plugs connected to the power strip. The only source of light was the screen of my MacBook Pro, which was not plugged in.  I increased and decreased the brightness of the computer screen during the video.  I then produced two additional light environments using my phone. Deleting array elements in JavaScript - delete vs splice What is the difference between using  on the array element as opposed to using ?   For example:  myArray = ['a', 'b', 'c', 'd'];  delete myArray[1]; //  or myArray.splice (1, 1);   Why even have the splice method if I can delete array elements like I can with objects?