Is Sidious more powerful than Plagueis? The Rule of Two dictates that when the Apprentice surpasses the Master in power, becoming the greater of the two Lords of the Sith, the Master has served his purpose. The Apprentice must challenge the Master in open combat, fighting to their utmost, as the final trial: killing the Master and taking his place is the final proof that the Apprentice is indeed more powerful.  This is how Darth Bane, founder of the Rule of Two, defines power when determining how to ensure each master is more powerful than the last.  Darth Sidious, however, violated the requirements of the Rule of Two: By killing his master, Darth Plagueis, in his sleep, he did not go through the trial of a duel to the death to prove he has indeed become the more powerful of the two.  As such, there is a need to search elsewhere for clues to the answer. Is Darth Sidious more powerful than Darth Plagueis, according to Darth Bane's definition of power being battle superiority?  Canon sources preferred.
Because of the Rule of Two, is/was Sidious the strongest Sith ever? The Sith Rule of Two says: One to embody power, one to crave it. It's like a survival of the fittest.   If the apprentice must kill the master to be the master, that usually means the apprentice is stronger than the master. If this chain went on for many years, does this mean Sidious was the strongest Sith ever, just by the transitive property?
Product and Box Topologies I am having a hard time understanding why the box topology is finer the the product topology. Of course I know that with finite product, the two are the same. With product topology, the basis elements are defined so that the $U_{\alpha}=X_\alpha$ except for finitely many $\alpha$. So how can this topology be contained in the box topology which has only the product of the  $U_{\alpha}$ as basis. I think it should have been the other way round. Am I missing something here? I need help with this because I have been confused over it for a long time. Is the series $\sum_{1}^{\infty}\frac{1}{p_{j}}$ where $p_{j}$ is the $j$th prime convergent? Does the series $\sum_{n=1 }^{\infty}1/p_{j} $ of  reciprocal primes converge?  Experimentally, it seems convergent. How do I repair a corrupted Firefox places.sqlite database? I had some problems with my RAM (bluescreen several times, Windows XP) and now are my Firefox databases damaged. Firefox is working, but my history is gone and it's reporting several inconsistencies and errors when executing pragma integrity_check on places.sqlite:     database disk image is malformed   Now the question, how do I repair SQLite-Databases? If $p,q,r$ are all primes,and $p|qr-1$,$q|pr-1$ and $r|pq-1$,find all possible values of $pqr$. How to recover a removed file under Linux? By accident, I used rm on a file I didn't want to delete. Is there a way that I can get it back under Linux? `--no-install-recommends` only specified packages I want to install xfce4-goodies but I don't want Midori Browser. With --no-install-recommends I don't know how to specify only Midori. I want the rest of packages. How to do that? Thanks! Is there a way to determine what version (distribution &amp; kernel version, I suppose) of Linux is running (from the command-line), that works on any Linux system? Does assumption of normality of each mixture components implies that each margins is normal I just would like to understand some information about the joint normality and the margins. I read that the normal joint distribution almost always implies that the univariate margins are all normal.   My question is:  1- Is this apply for Gaussian mixture models? For example, in the Gaussian mixture model, each mixture component follows a Gaussian distribution. Hence, does it imply that each margin will be a Gaussian distribution as well? "I understand that mixture components are used to describe the dependency structures, and they are the joint distribution. is that correct?  2- I read this from one answer to a question in this site . "So yes, the assumption of joint normality is a sufficient condition for all marginal distributions to be normal, irrespective of the dependence structure. Hence, the theory of Copulas does not affect this result in any way."  However, I really do not understand this: irrespective of the dependence structure. As I understand if the joint distribution in normal then the dependence structure is normal.   Could someone help me with my questions, please? I have problems with my Tilgin Vood Router. As I try to start my router by turning the power on (captain obvious), it generally doesn't work the first 3-4 times. This is getting very annoying.  Five minutes after turning the power on the router's signal LEDs don't blink in the way they should do in a connected state. I can connect to my routers web configuration interface through my PC connected to it via LAN though I can't access the internet.  It usually takes the router five minutes to get to the point where it should be connected to the internet but as it doesn't work the first times.  So I turn on my router 3-5 times, let him work 5 minutes and then suddenly, after turning the power off and on again it all works.  I also have to restart my PC too in order for everything to work.   How can I solve this problem? Just leave the router turned on all time? I prefer a daily IP switch, though. May the problem have something to do with my PC? There is another one connected to the router too and it doesn't work there either. Making a Laser in Cycles - Straight Beam of Light? SQL Server - copy stored procedures from one db to another The browser's "Back" button cause problems with the review buttons Distribution of $Z_n=n \log\left(\frac{\max\left(X_{(n)},Y_{(n)}\right)}{\min\left(X_{(n)},Y_{(n)}\right)}\right)$ The random variables $X_1,X_2,...X_n,Y_1,Y_2,...Y_n $ are independent and $U(0,a)$-distributed. Determine the distribution of $$Z_n=n\cdot \log\left(\frac{\max\left(X_{(n)},Y_{(n)}\right)}{\min\left(X_{(n)},Y_{(n)}\right)}\right)$$ where $X_{(n)},Y_{(n)}$ denotes $n$th order variable.  This problem is giving me a headache. The answer is that $Z_n$ is $\text{Exp}(1)$-distributed. But i can't derive that conclusion. I'd like to show you my derivation, but its so long and contains so many integrals and fractions that it would take a while to write it here. But basically my approach was to derive the distribution of $M=\max(X_{(n)},Y_{(n)})$ and $L=\min(X_{(n)},Y_{(n)})$. I get the following cdf's: $F_M=(F_X\cdot F_Y)^n=(F_X)^{2n}$ and $F_L=1-(1-(F_X)^n)\cdot (1-(F_Y)^n)=1-(1-(F_X)^n)^2$ ,  correct? $F_X $ stands for the cdf of $X_i$  Then i define the random variable $T=\frac{M}{L}$ and compute its cdf to finally be able to derive the distribution of $Z_n=n\cdot \log(T)$. But thats where i think everything goes wrong. Any help appreciated, thanks. What's this I hear about First Edition Unix being restored? that the source code of First Edition Unix had been restored from tapes.  The response was amazement and a request for more information.  What have people done?  Who did it?  When?  And how? Should Luke's lightsaber have given away his plan? During Luke's confrontation of Kylo Ren toward the end of The Last Jedi we see that       the lightsaber Luke uses a blue lightsaber (which I thought was his original one but that really doesn't matter), not the green one of his own construction.   Given that Kylo Ren  and Rey has just     fought over and broken the blue lightsaber   Why did Kylo Ren not notice this "inconsistency" and realize that      Luke's physical body was not there? Can I travel to the UK unaccompanied on an accompanied child visa now that I am over 18? How to make 7-zip do a whole bunch of folders I got a bunch of pictures that I had to crop into 800x600 pixels. That was easily done, but now I have to upload them so the family can see them all.  Thing is, this is 500MB in pictures. I decided to simply zip the separate folders, which each contain an almost equal amount of pictures. This way I can upload a couple each day. Doing this manually is a very long and hard job. I wonder if there is a way to make 7-zip handle each folder individually?  I think I'll need a batch file to do it, but I'm not good with that. I've put everything under one folder. In the various subfolders is where the pictures are located. What I need is for the contents of that folder to be zipped. I'm not sure if I can just zip the folder along with it. I know PHP has a zip module, I've just never worked with it, so I'm not sure whether it can handle the fact that the content of the zip is a folder which contains the items, instead of just the items. There are 8 crew members, The leading member wants that only a crew of 5 people or more could open a safe he bought, To each member he gave equal amount of keys, and locked the safe with several locks.  What's the minimal number of locks he should put:   at least 5 crew members would be required to open the safe? Any team of 5 crew members could open the safe, but none of the 4 team crew members.   1,2 stands individually of course. Given a hotkey, how can I find which program owns it? How to write zero in the unary numeral system In the decimal system: $...-3, -2, -1, 0, 1, 2, 3...$ In the binary system: $...-11, -10, -1, 0, 1, 10, 11...$ In the unary system: $-111, -11, -1, \text{ ??? }, 1, 11, 111...$   I was only able to find a related question but none with an answer so far: