Was Count Dooku a Sith? A friend of mine said that Count Dooku only was a good friend of the Sith. I think that Count Dooku is a Sith.   So was Count Dooku a Sith?   Is there any evidence of him being a Sith?
Why was Count Dooku not given the title "Darth"? I don't know the exact significance of the word "Darth" in the Sith world, but I think it was a word of honor for powerful Sith. That's why Anakin was given this word in his new name.  All powerful Sith in canon had this word in their names: Darth Plagueis, Darth Bane, Darth Sidious, Darth Vader, Darth Maul, etc. As such name similarity can't be names given by their parents, I can assume they were given such words in names as a honor.   Now, look at Count Dooku... he was a powerful Sith too. So, why wasn't he given this title?    Darth word to address Dooku hasn't been used in the movies, as far as I know. If you are claiming that Darth and Lord words are same, give citations because my vocabulary rejects it.
I'm reading Algebraic Number Theory by Jurgen Neukirch. I have some problems with some of the exercises in Section 9 of Chapter 1.  They are:  1) If $L / K$ is a Galois extension of algebraic number fields with non-cyclic Galois group, then there are at most finitely many non-split prime ideals of $K$.  2) Let $L / K$ be a finite (not necessarily Galois) extension of algebraic number fields and $N / K$ the normal closure of $L / K$. Show that a prime ideal $p$ of $K$ is totally split in $L$ if and only if it is totally split in $N$.  I have worked on them for a long time but couldn't get any idea of it.   Can you please help? Thank you! iOS navigation bar item image size In Python, what's the difference between 'except Exception as e' and 'except Exception, e' Do circular wheels maximize mechanical efficiency? I recently wondered whether there is a simple proof that circular wheels maximise mechanical efficiency. By this I mean:     Show that for a wheel with a given width and cross-sectional area, the   circular wheel reaches the bottom of an incline faster than a wheel   with any other shape.   This sounds like a rather elementary problem in classical mechanics but I haven't found a proof of this fact in any of the classical mechanics texts that I have read.   Note 1: I assume that the distribution of mass is uniform across the wheel so comparable wheels will have equal mass.   Note 2: Dry friction is assumed to be present. How can I force a program to open in a specific desktop? I've created an environment where I use 3 different desktop configurations, but every time I reboot, I have to manually open each program in that target desktop to make it look like it did before.   So, I'd like to write a .bat file that can get all my programs running in their appropriate desktops. I'm wondering if something like this is possible:  "C:\Program Files (x86)\Mozilla Firefox\firefox.exe" -desktop:2 "C:\Program Files\My\Other\Software.exe" -desktop:3 ...etc.   Obviously, this example is not real, but I hope there's something similar. I don't care if it's hacky :) How can I use awk to (sometimes) remove the first character of a column? Show that $n-m$ is a multiple of 9 when $n$ and $m$ have same digits I have just proved the divisibility rule for 3 and 9.  Let $n\in\mathbb{N}$. Let $m$ be a number that appears when you shuffle the digits in $n$. Show that $n-m$ is a multiple of 9.  Can anyone offer some help? It is a theorem in elementary number theory that if $p$ is a prime and congruent to 1 mod 4, then it is the sum of two squares. Apparently there is a trick involving arithmetic in the gaussian integers that lets you prove this quickly. Can anyone explain it? Let $A$ be the following subset of $\mathbb{R}^{2}$:$$A=\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x&gt;0\}$$ Then  $1.$ $A$ is connected.  $2.$ $A$ is compact.  $3.$ $A$ is path connected.  $4.$ $A$ is bounded.  It is clear that $A$ is unbounded as the graph of $x\sin(\frac{1}{x})$, so option $2$nd and $4$th are not correct. Again $A$ is connected by using the fact that closure of connected set is connected. But i am confused about path connectedness of $A$. Please help me about path connectedness of $A.$ Thanking you. Phrase for a situation where a problem disappears when you are about to fix it, but reappears later For example, the car mechanic can't replicate the problem you are having every day, but when you drive it off the service dept, there it is again. Or, when seeing the dentist, the tooth ache goes away, and comes back when you leave. Do we use abstract algebra in real life? Do we use abstract algebra in real life?   Is there any application of abstract algebra in real life? I am new to Salesforce and hence a lot of silly questions. What is the rational behind defining future methods as Static? I mean has these methods been not static what harm would have they caused? What is the difference between I play and I do play?  For example:  If someone were to ask to me, do you play soccer? How to calculate the $H_2$ and $H_\infty$ norms of TransferFunctionModels or StateSpaceModels? Canonical copies of sets Sometimes one needs two disjoint copies of a given set $X$. This can be canonically done by taking $\{0\} × X$ and $\{1\} × X$. Sometimes we want to identify one of the copies with the original set $X$. So I wonder, is it possible to take a disjoint copy of $X$ straight ahead? And can this be done canonically? More precisely, are the following claims true? $ \def\dom{\operatorname{dom}} \def\rng{\operatorname{rng}} \def\On{\mathbf{On}} $   For every $X$ there is a one-to-one function $f$ such that $\dom(f) = X$ and $\rng(X) ∩ X = ∅$. There is an explicit formula $φ(X, f)$ such that for every $X$ there is exactly one $f$ satisfying $φ(X, f)$ and this $f$ satisfies 1. for $X$.   Since such construction of a disjoint copy is intuitively trivial, I'm interested in proofs of 1. and 2. without using regularity, choice, or infinity.   Some ideas:   We may simply put $f(x) := (x, X)$, but we need regularity to show that $(x, X) ∉ X$. We may consider $α = \sup(X ∩ \On)$ and pair members of $X$ with some ordinals above $α$, but we need AC to well-order $X$, and we need global choice to obtain 2. Let $&lt;$ be the transitive hull of $∈$. If the relation $&lt;$ is narrow, i.e. $\{y: y &lt; x\}$ is a set for every $x$, then we may choose $z ∉ ⋃\{(\leftarrow, x)_&lt;: x ∈ X\}$ and put $f(x) := (x, z)$ since $(x, z) = y ∈ X$ would imply $z &lt; y$. Note that we don't need the axiom of infinity to define $&lt;$, but I don't know how to prove its narrowness without infinity. Evaluating $\int \frac{1}{{x^4+1}} dx$ I am trying to evaluate the integral  $$\int \frac{1}{1+x^4} \mathrm dx.$$  The integrand $\frac{1}{1+x^4}$ is a rational function (quotient of two polynomials), so I could solve the integral if I can find the partial fraction of $\frac{1}{1+x^4}$. But I failed to factorize $1+x^4$.   Any other methods are also wellcome. Iridescence In Cycles? Sharepoint 2010 - Deploy webpart as Feature scope = web I want to create and deploy a web part as web-scoped feature.  In Visual Studio 2010, when I make the feature scope=web, I cannot add the webpart to that feature as I am able to do when scope=site. I'm using post thumbnails to link to a page.  Is it possible to add a class name to the post thumbnail image.  &lt;li&gt;&lt;a href="&lt;?php the_permalink(); ?&gt;" &gt;&lt;?php the_post_thumbnail(); ?&gt;&lt;/a&gt;&lt;/li&gt; I'm a mathematician interested in abstract QFT.  I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal operator.  I understand from the Wikipedia article that requiring that energy stay positive forces $T$ to be represented by an anti-unitary operator.  But I don't see how this forces $T^2=-1$.  (Or maybe it doesn't force it, it merely allows it?)  Here's another version of my question.  There are two distinct double covers of the Lie group $O(n)$ which restrict to the familiar $Spin(n)\to SO(n)$ cover on $SO(n)$; they are called $Pin_+(n)$ and $Pin_-(n)$.  If $R\in O(n)$ is a reflection and $\tilde{R}\in Pin_\pm(n)$ covers $R$, then $\tilde{R}^2 = \pm 1$.  So saying that $T^2=-1$ means we are in $Pin_-$ rather than $Pin_+$.  (I'm assuming Euclidean signature here.)  My question (version 2): Under what circumstances are we forced to use $Pin_-$ rather than $Pin_+$ here?  (I posted a  on physics.stackexchange.com last week, but there were no replies.)    EDIT: Thanks to the half-integer spin hint in the comments below, I was able to do a more effective web search.  If I understand correctly, Kramer's theorem says that for even-dimensional (half integer spin) representations of the Spin group, $T$ must satisfy $T^2=-1$, while for the odd-dimensional representations (integer spin), we have $T^2=1$.  I guess at this point it becomes a straightforward question in representation theory: Given an irreducible representation of $Spin(n)$, we can ask whether it is possible to extend it to $Pin_-(n)$ (or $Pin_+(n)$) so that the lifted reflections $\tilde R$ (e.g. $T$) act as an anti-unitary operator.