This is a two part question, with the two parts being mirror images to each other.  Is the ability to use the Force a requirement, for some reason, to using a lightsaber?  And if so, why?  And on the other side, on Hoth, when Luke is hanging in ice in the wampa's cave, he uses the Force to bring his lightsaber into his hand.  But, as best I can remember and find, the Jedi always use a lightsaber like a "real" sword and keep it in their hands (although I think there's one case in a movie where a lightsaber is thrown to cut down support for a walkway).  Can a lightsaber be wielded with the Force only?  For instance, when Anakin's hand was cut off, could he have controlled the movement of his lightsaber the way Vader did with the objects he Force-tossed objects at Luke in the Cloud City?  While that's two questions (that I think are closely related), another way to put it might be to ask, "How closely is the use of the Force related to wielding a lightsaber?"  Addendum: No, this is NOT a duplicate of .  Note I am the one who asked both questions.  I asked both because they cover different groups.  See the Venn diagram.  I allow room for possible members of Sith and Jedi who do not use the Force.  (Hey, in the Star Wars universe, almost anything can happen.)  If that is not possible, then just imagine the black box not intercepting either or both of the Jedi and Sith boxes.  One can be non-aligned (with Jedi or Sith) and still use the Force and it's possible, at some point, we may find some odd story about a Jedi or Sith who cannot use the Force.  (There may be some story about how such a person is not felt by Force users, so is valuable to one side or the other.)  This question overs the black box.  The other question covers the green box.  Yes, there is overlap, but there are also distinct separate groups covered by each question that are not covered in the other question.
I understand that the mechanics and design of a lightsaber aren't that complicated.  Do others besides the Jedi and Sith (or their minions) make or use lightsabers?  And if they don't, why not?
What is a simple example of a limit in the real world? I"m studying normalization and have been reading through descriptions and examples online. One Concept that isn't clear to me is if the process can be automated at any point. I understand that a system can't tell you if you schema makes any real-world sense, but it seems likely to me that if you feed a program some arguments say, the functional dependencies, it would be able to do some steps for you.  Say you have a relationship R(A,B,C,D)  and you tell your program that A,B->C and A->D and that the primary key is (A,B)  Now if my understanding serves me correctly it should be possible for a program to identify that A->D violates 2NF because D depends on A and A is a subset of the primary key. That the proper decomposition would be R1(A,B,C) and R2(A,D).   The main book i'm learning from and my instructor indicate these normalization's are done all by hand. Is this correct or can some parts be automated? Are units in English singular or plural? Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $ Inspired by , I was wondering if there is a simple logical argument to   Show that $ a,b, \sqrt{a}+ \sqrt{b} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b} \in\mathbb Q $  Note that the original link is using a computational method, where as I am looking for a simple logical argument.  I tried (unjutifiably) to argue that if some of two square roots is rational then each one is rational, this is a different than the (incorrect) argument that if sum of two algebraic numbers is rational then each one is rational ( counter example $a=1-\sqrt{2},b= 1+\sqrt{2} $) What is wrong with my date regex? Let us consider that $u\in C^2(\Omega)\cap C^0(\Omega)$ and satisfying the following equation .  $\Delta u=u^3-u , x\in\Omega$ and   $u=0 $   in  $\partial \Omega$  $\Omega \subset \mathbb R^n$ and bounded .   I need hints to find out what possible value $u$ can take ?  Thank you for ur hints in advance . This is my first post on this forum :)  I've been trying for a while to solve this problem about symmetric difference of two sets:     Given two sets $A$ and $B$, we call symmetric difference of $A$ and $B$ the following:      $$A\mathrel{\triangle}B = (A\cup B)-(A\cap B)$$      Show that if $A\mathrel{\triangle} B = \emptyset$, then $(A\subset B) \vee (B\subset A)$.   I don’t know where to start; thank you very much for the help :) Evaluate the integral $\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x dxdy}{\sqrt{4a^2x^2-(x^2+y^2)^2}}$ Change the order of integration in:  $$\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x }{\sqrt{4a^2x^2-(x^2+y^2)^2}}dxdy$$ and hence evaluate it.    I changed the order of integration and got the limits $y=0$ to $a$ and $x=a-\sqrt{a^2-y^2}$ to $a+\sqrt{a^2-y^2}$. I then tried changing to polar coordinates, but it is only making the integrand more complex. An  can be identified by its  together with isolating intervals with rational bounds for its real and imaginary parts. The degree of an algebraic number is the  of its minimal polynomial. There are known algorithms that allow to easily compute sum and product of algebraic numbers in this representation, raise them to a rational power, extract real and imaginary parts, compare them, or evaluate them numerically to an arbitrary precision.  Is there an efficient algorithm that given an algebraic number $\alpha$ in this representation can decide if $\alpha$ can be represented as a sum or product of algebraic numbers of smaller degree? I am able to solve simple differential equations like :  $$\dfrac{dy}{dx} = 3x^2 + 2x$$  We simply bring $dx$ to other site and integrate.  But how do we find solutions of differential equations like :  $$\frac{d^2x}{dt^2} + \dfrac{kx}{m} = 0$$  ?  We have been told the solution is $x(t) = A\cos ( \omega t + \phi_o)$ where $\omega\ =\sqrt{\dfrac{k}{m}}$  but how do we actually find it? Is there a function to extract the extension from a filename? Copy material to another object? I saw a video where the person copied a material from one object to another (Cycles).  How can I accomplish this? How to change Facebook username? Is there an AmpScript function that can be used in an equivalent manner to sql left, right and mid functions?   Thanks, Mark Bidirectional 1 to 1 Dictionary in C# I am looking for a generic, bidirectional 1 to 1 Dictionary class in C# (2), ie. a BiDictionaryOneToOne&lt;T, S&gt; which is guaranteed to only contain one of each value and key (up to RefEquals anyway), and which can be searched using either key or value. Anyone know of one, or should I just implement it myself? I can't believe that I'm the first person to need this...  There is a BiDictionary in the answers to , but it is not for unique elements (and also does not implement RemoveByFirst(T t) or RemoveBySecond(S s)).   Thanks! Calculate distance between two latitude-longitude points? (Haversine formula) How do I calculate the distance between two points specified by latitude and longitude?  For clarification, I'd like the distance in kilometers; the points use the WGS84 system and I'd like to understand the relative accuracies of the approaches available. Default gender, "Male" or "Female" Should our default gender when selecting male/female on the dropdown list be based on the local  (if a country have more female than male then female is the default value)? Prove that the range of the entire function $z^2+\cos(z)$ is all of $\mathbb{C}$. Prove that the range of the entire function $z^2+\cos(z)$ is all of $\mathbb{C}$.   I'm aware this question has been  already, but the explanations were a little shakey and referenced a google sample preview of a text of whose terminology I wasn't very familiar with, so I would like some more input if possible.  Here's my attempt:  Let $f(z)=z^2+\cos(z)$. Through the power series of the cosine function $$ f(z)=z^2+1-\frac{z^2}{2!}+\frac{z^4}{4!}-\cdots=1+\frac{z^2}{2!}+\frac{z^4}{4!}-\cdots, $$ so $$ g(z):=\frac{f(z)-1}{z} $$ has a removable singularity at $z=0$ and is effectively an entire odd function. Picard's little theorem asserts that the range of $g$ is all of $\mathbb{C} $: if there exists some $z_0$ such that $g(z)\neq z_0$ for all $z\in\mathbb{C}$, then $-z_0$ is also missed by oddness of $g$, which is a contradiction (since $g(0)=0$ we rule the possibility that $z_0=0$). (I'm not sure about the following step) It follows that $zg(z)$ and so $zg(z)+1=f(z)$ is surjective.  Is this method valid? Would I need further justification to show that $z\mapsto z$ and $z\mapsto g(z)$ surjective imply its product -- $z\mapsto zg(z)$ -- is also surjective (if this is even true). Any input is greatly appreciated.  Edit: After thinking about this for a moment longer, I realize this logic would also show that the range of any entire even function is all of $\mathbb{C}$, which seems like quite a strong conclusion. This makes feel like there are holes in my logic. I want to write several classes, most of them will use KOMA classes as base class.  However I stumbled upon the problem that some options (mainly concerned with layout) are not processed if given in the wrapper class:    \begin{filecontents}{test.cls}     \ProvidesClass{test}[2015/01/01]     \DeclareOption*{\PassOptionsToClass{\CurrentOption}{scrartcl}}     \ProcessOptions\relax     \LoadClass[paper=a5]{scrartcl}   \end{filecontents}  \documentclass{test}  \usepackage{blindtext}  \begin{document}   \section{Test}   \blindtext \end{document}   This results in   LaTeX Warning: Unused global option(s):     [paper=a5]  If i give the option as \documentclass[paper=a5]{test} it is used correctly, because I pass the options to scrartcl. However I want to change the defaults for the layout.   How can I achieve this? Why does a force not do any work if it's perpendicular to the motion? I have a book that says the Moon's orbit is [in this context assumed to be] circular. The Earth does no work on the moon. The gravitational force is perpendicular to the motion. Why is there no work done if support force is perpendicular to the motion?