Is Kylo Ren's fizzling lightsaber blade intended by design?
Why does Kylo Ren's lightsaber look different from normal lightsabers?
How does the telepathy supernatural ability work? Why aren't logarithms defined for negative $x$? Given a logarithm is true, if and only if, $y = \log_b{x}$ and $b^y = x$ (and $x$ and $b$ are positive, and $b$ is not equal to $1$), are true, why aren't logarithms defined for negative numbers?  Why can't $b$ be negative? Take $(-2)^3 = -8$ for example. Turning that into a logarithm, we get $3 = \log_{(-2)}{(-8)}$ which is an invalid equation as $b$ and $x$ are not positive! Why is this? TimeSpan to String causing an error I'm taking Calculus II next semester so I don't have all the tools from it to back me up but something came up in a discussion this evening that asked me to prove that the following sequence converges. As I'm new to formal math I'm hoping someone can verify my proof, especially step $6$. I must prove that $$\lim_{n\to\infty}P_n=b$$ where $$P_{n+1} = P_n + \frac{b-P_n}{2}$$ $$P_0 = a$$ and $a,b \in \mathbb{R}$ such that $a&gt;b$ My proof goes as follows:   We must prove that $$\lim_{n\to\infty}P_n=b$$  That is, $\forall\epsilon&gt;0$ there exists a $\delta$ such that there exists an $n$ satisfying $$n&gt;\delta \iff b-P_n&lt;\epsilon$$  First, let us prove that $P_n$ is bounded by $b$ by contradiction. Let us choose an $i$ such that $P_i &lt; b$ and $P_{i+1}&gt;b$. Then we have $P_{i+1} = P_i + \Delta P$ where $\Delta P &gt; b-P_i$. but this is impossible because by the definition of the recurrence $\Delta P = \frac{b-P_i}{2} &lt; b-P_i$. Therefore, $P_i$ is bounded from above by $b$.  Additionally, it is trivial to show that $P_{i+1} &gt; P_i$.  With this in mind, choose an arbitrary $\epsilon$. We need to show that there exists an $n$ such that $P_n &gt; b-\epsilon$. Assume the contrary, that $P_n$ is bounded by $\epsilon$.  Using a similar argument to what which was used before, assume $P_n$ is bounded by $\epsilon$ and then there exists a $P_i$ such that $P_{i+1}\not &gt; P_i$. But this results in a contradiction with (4)  Therefore, $P_n$ is not bounded by $\epsilon$ and we have proved what we want to prove. How do I make my document use the Times font, both for the text and the math? I know that I can put \usepackage{times} in the preamble in order to use the Times font instead of Computer Modern for my document.  But this only affects the text; the math is still typeset using Computer Modern.  How can I make Latex use Times also for the math? Find all integer solutions to $x^2+4=y^3$. Getting "'file' is different from the same file on the system" when I attempt to update through synaptic Encountered an error while updating through Synaptic Manager. Subsequent updates gave the error at the bottom of the output. I'm a noob so any help is appreciated.  al@al:~$ sudo apt-get -f upgrade Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following NEW packages will be installed:   libjack-jackd2-0:i386 The following packages have been kept back:   linux-headers-generic skype 0 upgraded, 1 newly installed, 0 to remove and 2 not upgraded. Need to get 0 B/202 kB of archives. After this operation, 493 kB of additional disk space will be used. Do you want to continue [Y/n]? y (Reading database ... 310056 files and directories currently installed.) Unpacking libjack-jackd2-0:i386 (from .../libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb) ... dpkg: error processing /var/cache/apt/archives/libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb (--unpack):  './usr/share/doc/libjack-jackd2-0/buildinfo.gz' is different from the same file on the system dpkg-deb: error: subprocess paste was killed by signal (Broken pipe) Errors were encountered while processing:  /var/cache/apt/archives/libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb E: Sub-process /usr/bin/dpkg returned an error code (1) I thought it was The Tommyknockers by Stephen King, but after a check with Wikipedia, it appears that's not the case.  What I remember about the story (a TV movie I think, but definitely based on a book) was that the world is created anew every night, and that the old, used up, Earth was eaten nightly by some scary creatures.  The major plot point involved some protagonists not getting onto the new world at midnight, and having to escape from the monsters that were eating up yesterday's planet.  Does this ring a bell for anyone? I'm finding it very hard to Google for. What is the current state of apple device (iPhone, iPod, etc.) support? What ubuntu applications provide support? (guides, how to's, status) Also, specifically, details on support for syncing music to iPhone's and iPod's with the latest OS version:   Can you sync music to apple devices using >iOS4? (iPhone &amp; iPod) What applications allow you to do this and how? (guides, how to's, status)    What has already been established is:   Apple does not support Linux and has no plans to.  provides some support, however it currently does not support music/video synchronization with devices &gt;iOS4. Go to  and scroll to the section titled "" to see if your device version is supported. What's the best way to season a cast iron skillet? I just purchased a new cast iron skillet. What's the best way to season it?   And if I need to re-season an old pan, is the process any different? What is a good data plan for Internet surfing in northern Italy? I've checked the webpages of some their providers, but franly, just like in the case of those in my own language, I literally cannot find my way around them. So if you wouldn't mind sharing a word of two or advice.  I'm looking for a good solution for mobile internet surfing in northern Italy, that can be connected to a laptop (you know, that usb stick with a SIM card inside kind of thing). 15 Gb or so at some decent speed. Can you perhaps give a recommendation or two of what to get?    Edit: Just to define what I'm looking for exactly. A data plan of 15 Gb with an internet key (usb stick into which a SMS card goes) that you plug into a laptop. Preferably non-contractual, so I can cancel when I leave. I am not interested in surfing on my mobile phone since due to size I still prefer the smaller Nokia-like models for calls (smaller to carry) - no internet on them. How can I change GNOME Shell theme? Does it just vanish into space leaving nothing behind or does it expel some material?    Also, talking more about black holes, as far as I understand the term "temperature", it is defined by the amount of kinetic energy of the particles of a body and from what I have read, there are no particles inside a black hole, I know that you can find the temperature of a black hole by analyzing its Hawking radiation but I cant really understand how the term "temperature" can be applied to a black hole. Does it mean that whatever is that it is inside a black hole has kinetic energy? Have physicist already experienced the death of any regular black hole (by regular I mean space-sized black holes not micro ones created in labs)? Also, where is the Hawking radiation form? Because if it is released by the black hole I bet it must have formed outside the event horizon, but how exactly? What is the tolerable magnetic field (in Tesla) for a hard disk? I was wondering what would be the safest magnetic field for a hard drive so that the data inside it is safe and not wiped off?  For example I have a 2.1 home theatre system and when I take my android phone near it to check the magnetic field range it gives me a reading of 1000 micro Tesla. Would that be considered safe for a nearby hard disk? My actual WhatsApp back total size is 474Mb but when I go to I cloud back up it is showing 10GB, how is it possible? I mean I have deleted all media files from my WhatsApp and in WhatsApp application the total space is 474MB and also in iCloud storage it is 474MB, but when I entered further in to Backups and then choose my phone, it shows total backup size is 14GB and WhatsApp itself is taking 10GB. Can someone help with this? How can one change an entire document to use bold font? What level are spells cast at if a warlock multiclasses as another caster? I was reading a textbook. I found that it was mentioned the speed of sound increases with increase in temperature. But sound is a mechanical wave, and it travels faster when molecules are closer.   But an increase in temperature will draw molecules away from each other, and then accordingly the speed of sound should be slower. How is it possible that the speed of sound increases if temperature increases? What is the relation of speed of sound and temperature? The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$ I have a folder on my desktop which is named ".." (which itself contains subfolders with an empty name). The folder can't be deleted the usual ways, even not when using the CLI. Does anyone know how I can remove this folder on Windows Vista 64-bit?  Renaming does not work, either (obviously).  This is what "dir /x" echoes:  09.10.2009  15:04    &lt;DIR&gt;                       . 09.10.2009  15:04    &lt;DIR&gt;                       .. 08.03.2007  11:18    &lt;DIR&gt;                       cgi-bin                0 Datei(en),              0 Bytes                3 Verzeichnis(se), 45.866.037.248 Bytes frei