This isn't a question about a specific anime. However, I wonder why filler episodes exist.  At first, I thought it was to allow the manga to advance a bit more when the anime was catching up. However, in Naruto (for example), the manga has finished and the anime still has fillers.  For other series like One Piece, the anime is relatively close to the manga and there are no fillers (Thanks God!)  What's the purpose of filler episodes?
The most obvious answer everyone over the Internet is giving to this question is "Because anime is produced much faster compared to manga, they need to put in fillers in order to slow down the anime series". However, that shouldn't be the only reason.  For example, consider One Piece. The show is going on for more than 500 episodes, and less than 10% are fillers. Comparing that to Naruto, the show has almost the same number of episodes (original and Shippuuden combined), but almost 50% of its episodes are fillers. Needless to say, the manga of Naruto is so far ahead that the anime won't be able to catch up even if they produce 100+ episodes without any fillers.
If a function has a finite limit at infinity, does that imply its derivative goes to zero? I've been thinking about this problem: Let $f: (a, +\infty) \to \mathbb{R}$ be a differentiable function such that $\lim\limits_{x \to +\infty} f(x) = L &lt; \infty$. Then must it be the case that $\lim\limits_{x\to +\infty}f'(x) = 0$?  It looks like it's true, but I haven't managed to work out a proof. I came up with this, but it's pretty sketchy:  $$ \begin{align} \lim_{x \to +\infty} f'(x) &amp;= \lim_{x \to +\infty} \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} \\ &amp;= \lim_{h \to 0} \lim_{x \to +\infty} \frac{f(x+h)-f(x)}{h} \\ &amp;= \lim_{h \to 0} \frac1{h} \lim_{x \to +\infty}[f(x+h)-f(x)] \\ &amp;= \lim_{h \to 0} \frac1{h}(L-L) \\ &amp;= \lim_{h \to 0} \frac{0}{h} \\ &amp;= 0 \end{align} $$  In particular, I don't think I can swap the order of the limits just like that. Is this correct, and if it isn't, how can we prove the statement? I know there is  already, but I think this is different in two aspects. First, that question assumes that $\lim\limits_{x \to +\infty}f'(x)$ exists, which I don't. Second, I also wanted to know if interchanging limits is a valid operation in this case. If my question gets migrated to another site, is it possible somehow to reverse it back to the original site? How do I set a static IP address in Windows? How can I retain HTML form field values in JSP after submitting form to Servlet? Print only the Nth line before each line that matches a pattern I'm trying to print only the &lt;N&gt;th line before a search pattern. grep -B&lt;N&gt; prints all the &lt;N&gt; lines before the search pattern. I saw the awk code  that can print only the &lt;N&gt;th line after the search pattern.  awk 'c&amp;&amp;!--c;/pattern/{c=N}' file   How to modify this to print only the &lt;N&gt;th line before each line that matches pattern ? For example, here is my input file  ... ...    0.50007496  0.42473932  0.01527831    0.99997456  0.97033575  0.44364198 Direct configuration=     1    0.16929051  0.16544726  0.16608723    0.16984300  0.16855274  0.50171112 ... ...    0.50089841  0.42608090  0.01499159    0.99982054  0.97154975  0.44403547 Direct configuration=     2    0.16931296  0.16553376  0.16600890    0.16999941  0.16847055  0.50170694   ...   I need a command that can give me back the 2nd line before the search string Direct configuration. I'm trying to run this in SUSE-Linux escaping double quotes and percent signs (%) in cron The following command works from prompt but not from crontab.   grep abc  /var/log/messages | grep "`date '+%B %d'`" | mail -s"abc log of `hostname`" shantanu.oak+`hostname`@gmail.com   I need to add it to daily cron. I've been interested in non-standard analysis recently. I was reading up on it and noticed the following interesting comment on the , right after giving an example of a nonstandard differentiation:     The use of the standard part in the definition of the derivative is a rigorous alternative to the traditional practice of neglecting the square of an infinitesimal quantity... the typical method from Newton through the 19th century would have been simply to discard the $dx^2$ term.   I've never heard anything like this before, and really find it fascinating that Newton's method was to define the relation $dx^2 = 0$. If we actually formalize the above structure by taking $\mathbb{R}$ and adjoining an element $dx^2 = 0$ to it, we get the "dual numbers," isomorphic to the quotient ring $\mathbb{R}[x]/x^2$. I'd seen some things about how this algebra plays into automated differentiation algorithms for some computer software systems, but I've never heard anything about Newton directly working in this algebra. So I have a few questions:   Does anyone have more historical information on the way that Newton performed differentiation, and its relation to the dual numbers? Does anyone know how effectively real analysis can be formalized with the dual numbers? Does the resulting system play nice enough to develop all of the important modern results? If we start with $\mathbb{C}[x]/x^2$ instead, can we likewise develop complex analysis?   Since this idea is so simple, I'm very curious how powerful it is. I'm also curious if it has any major drawbacks too, since I'm not sure why anyone would mess with the foundational baggage involved in defining the hyperreals if this simple 2-dimensional real algebra could really do the trick. Prevent questions with movie/tv shows/game spoilers from appearing in the hot questions list I've noticed that occasionally "hot questions" from SciFi and the Movies &amp; TV network contain major spoilers about the movie/show discussed.  The Matrix spoilers:      (just now there's something about Cypher betraying Morpheus in the Matrix, which is a big deal for people who haven't seen the movie).   I like browsing through those but fear that one day one of these questions will spoil a show I'm excited about and yet to finish   Breaking Bad spoilers:      (like the finale of Breaking Bad, imagine a question asking why did one character betray another at the end or something).   Can users posting such questions be asked to label those with a tag (such as 'spoilers') and then somehow have the network hide those from the "hot questions" list? Or possibly format them differently?  Similarly, this could apply to the Arcade network too.  P.S. Love how this question spikes in popularity around the time GoT starts running again. I swear it should be fairly simple technically to ban questions that have a tag that says 'spoilers' from appearing in the Hot Network Questions.  P.P.S. Oh, and with every fresh release of Star Wars (The Last Jedi being the most recent one)!  P.P.P.S. Another year, another Game of Thrones, another spike in popularity! I love R. Courant and F. John's Introduction to Calculus and Analysis because of its wide coverage, precise description and friendly written style.  Are there any classic textbooks like it on ODE/PDE?  thanks. Where is the preferred place to set the PATH envvar?  ~/.profile or /etc/environment?  What is the case when PATH is set in both places? Is the end result a concatenation of both values set in those two places? The comment with the Flagged Posts that seems to be new as of today states there are posts with flags awaiting my attention but the counter shows zero and when I go into flagged posts there is nothing waiting for me. Possible to do a MySQL foreign key to one of two possible tables? Trying to wrap my head around the ways to properly handle collision in a game designed around components.  I see many examples have some sort of PhysicsComponent that gets added to the entity's list of components but the actual implementation is confusing me.  For this to work, the PhysicsComponent would need access to the world around it. This doesn't make intuitive sense to me. Shouldn't a component be unaware of not only its container (the entity), but its container's container (the world)?  To me, it sounds like the level or scene should maintain a list of these entities and every game update, loop through the entities to determine which collide.  My question is firstly, whether or not this is good design, and secondly, how to determine which entities can collide. I suppose solid entities could implement an empty IRigidBody interface so the level could determine which entities in the list support collision. But is this breaking the component design?  Instead, should they contain an empty RigidBody component? This may actually be better because it may not always be empty and this approach is more future-proof. The only problem with this is the complexity. The scene would have to loop through not only every entity, but also every entity's components to determine if it had this RigidBody component.  Thirdly, when they do collide both entities should be informed somehow and I am unsure on how to accomplish this either.  Let's say that both entities contained a HealthComponent and when they collided both their healths would be decreased by some arbitrary value, 5. I suppose it would be the scene's responsibility to handle this when it detects a collision between two entities?  But then is the scene responsible for too much? I could see this possibly getting out of hand and becoming unwieldy when the scene is responsible for many things entities should not (?) have access to.  Edit: Question updated with more details. Prove $[A,B^n] = nB^{n-1}[A,B]$ I am trying to show that $[A,B^n] = nB^{n-1}[A,B]$ where A and B are two Hermitian operators that commute with their commutator. However, I am running into a little problem and would like a hint of how to proceed.  If A and B commute then $[A,B] = ABA^{-1}B^{-1} = e$ where e is the identity element of the group.  $$\therefore AB=BA$$  $$n=1; [A,B^1] = (1)B^0[A,B] = e$$ This statement is certainly true. however moving on to $n = 2$ I find...  $$[A,B^2] = AB^2A^{-1}B^{-2} = ABBA^{-1}B^{-1}B^{-1} = BBAA^{-1}B^{-1}B^{-1}$$  Where in the last step I have used the fact that A and B commute to rearange the terms. However, it is plain to see that this last term simply reduces to the identity as well and for the n = 2 case we have:  $$[A,B^2] = e \ne 2B[A,B] = 2Be = 2B$$  Clearly I have assumed something I shouldn't have. The fact that there is a multiplicative factor of n implies I should be adding things, but I thought if I kept it as general as possible, the answer should just fall out naturally. I don't want an answer please, only guidance. If $A$ is an $m \times n$ and $B$ is an $n \times m$ matrix with $n &lt; m$ then prove that $C = AB$ is not invertible.  I am not getting any idea. May be I am missing vary basic point. $C = AB$ where both $A$ and $B$ are square matrices  will be invertible iff both $A$ and $B$ be invertible. I know it and its proof.  May be this question has been discussed earlier, but I am not seeing the link. Thank you for your help. tar compression without directory structure I use ssh on a variety of machines, mainly linux. Accounts on these machines vary in naming scheme: if my name is First Last, then I have accounts: first, flast, last_f, lastf, and sometimes I need to log in as root. For each machine I use, I would like the openssh client to know which account to use when I don't specify on the command line.  So the question is: How do I make ssh server Do The Right Thing when a username is not specified? I was just reading Harry Potter and the Deathly Hallows, and I was wondering, when Hermione Granger changed into Bellatrix Lestrange, she should've obtained the Dark Mark, temporarily.  Now, my question is: would the Dark Mark work if pressed? "No, I didn't see him" vs "Yes, I didn't see him" Bob didn't come to office today.  I was asked "Didn't you see Bob today?"  Should I say "Yes, I didn't see him today" or "No, I didn't see him today"? How to install folding at home (Folding@home FAHControl) on Ubuntu 19.10