Monoid vs MonadPlus
Why MonadPlus and not Monad + Monoid?
When at home I use my 13" MacBook Pro hooked up to an 27" external monitor. When working on my 27" screen I prefer to have a visible dock at all times. I have enough screen real estate to afford this luxury.  When I'm on the road working on my 13" screen I prefer to automatically hide the dock as it really gets in the way when screen real estate is limited.  I now manually switch between enabling and disabling hiding (using ⌥⌘D) but I would prefer this to happen automatically. Can I enable hiding the dock on my MacBook monitor and disable hiding the dock on my external monitor? The  lists various combinatorial objects that are described by them. I posit that there might be bijections between these various combinatorial objects. For some of them (like Dyck paths, correctly matched parentheses and paths from the bottom left to top right of a $2n \times 2n$ grid) they are quite obvious.   I was then trying to find a bijection between the number of Dyck words and the number of ways of associating $n$ applications of a binary operator to $n+1$ items (third one on the list). I attempted to do this for a simple case ($n=3$ which is the example provided in the Wikipedia article). However, couldn't find one after multiple hours. Is it reasonable to expect such a bijection will exist? If so, how do we go about finding it?    EDIT: In addition to the very nice answer by @Marc, the following page also helped me see the bijection:   "Let $P$ be the Dyck path and $f(P)$ be the binary tree. If you go up in the Dyck path, create a left child. Otherwise, go up one vertex until creating a new right child is possible and create one."    Here is one of my attempts:   Number of Dyck words with length $2 \times 3$ is $\frac{6 \choose 3}{4} = 5$. They are:  hhhttt; hhthtt; hhttht; hthhtt; hththt  And the number of applications of a binary operator among $3+1=4$ factors is:  ((ab)c)d;     (a(bc))d;     (ab)(cd);     a((bc)d);     a(b(cd))  Both combinatorial objects have been arranged in a way that there is some kind of ordering between them. For the Dyck words for example, if h equals +1 and t equals -1, then the order is lexicographical from the left to the right of the cumulative score along the sequence.   Now, the first and last characters of the Dyck words are always h and t respectively. So, we can ignore them. We are left with:  hhtt; htht; htth; thht; thth  I tried to start from the left of the sequence abcd and if I see 'h', merge the character with the one to its right. This approach didn't produce a valid mapping from the third Dyck word to the third binary operator precedence order. When I was a kid we had a VHS tape of some Disney live action (not animated) sci-fi movie. It may have been a mini-series or a made-for-tv movie, but I'm not sure. I'm also not sure about the year but it would probably have been late 80s or early 90s based on when I would have seen it. I know it was Disney because they had some live action Goofy and Mickey running around the movie's set as an introduction discussing the plot with a host before the movie.  The plot is basically as follows:   A starship is loaded with mostly children and teenagers as a cross-galaxy human settling effort. Accidents (which are not really accidents and later revealed) cause adult crew members to be killed.  They travel to another planet and face all sorts of troubles. It arrives at the new planet after overcoming obstacles.   Other memorable scenes that may help:   Navigating out of earth's asteroid belt made out of space junk. One of the adults was killed via an airlock malfunction. The ship was supposed to be peaceful with no weapons. At one point they bring on board some crazy guy who puts together a rail gun. There's a memorable line like "Do you want no weapons at all or a well aimed rock?"  There's a planet or space station (I can't remember which) that has a fight scene with the evil bad guy. This scene takes place on what looks to be a carnival or fairground. The bad guys are trying to steal the ship the kids are on because it has some kind of really good futuristic space drive.   Hopefully you remember it better than I do! I've tried looking online for it before with no luck. Circular determinant problem I'm stuck in this question: How calculate this determinant ? $$\Delta=\left|\begin{array}{cccccc} 1&amp;2&amp;3&amp;\cdots&amp;\cdots&amp;n\\ n&amp;1&amp;2&amp;\cdots&amp;\cdots&amp; n-1\\ n-1&amp;n&amp;1&amp;\cdots&amp;\cdots&amp;n-2\\ \vdots &amp;\ddots &amp; \ddots&amp;\ddots&amp;&amp;\vdots\\ \vdots &amp;\ddots &amp; \ddots&amp;\ddots&amp;\ddots&amp;\vdots\\ 2&amp;3&amp;4&amp;\cdots&amp;\cdots&amp;1 \end{array}\right|$$ Thanks a lot. In the following method definitions, what does the * and ** do for param2?  def foo(param1, *param2): def bar(param1, **param2): How to import Ordnance Survery raster layer to ArcGIS Desktop? I have downloaded raster map data from ONS, the data has come in the form of two files... one is full of  .tlw files and the other is full of .tab files...   How do I import it into a raster layer to ArcCatalog? I've got a circuit in the basement carrying a handful of outlets.  This circuit has no ground wire.  I want to add a couple of outlets and want them to be grounded.  I may even want gfci outlets on them in the future.  I have no reasonable way of getting a ground wire to the panel but I do have easy access to another circuit that does have a ground wire.  Is it acceptable to borrow or share a ground wire between circuits?  If not, why not?  Both circuits are 20A with 12 AWG wire. Adding Basemaps from Google or Bing in QGIS For which $n≥2$ does there exist $\sigma\in A_n$ with $|\sigma| &gt; n$? I have a proof that I'd like to be verified. My proof that there exists $\sigma\in A_n$ with $|\sigma| &gt; n$ if and only if $n\geq 8$: For $n&lt;8$, one can manually verify for each $n$ that there is no $\sigma\in A_n$ with order greater than $n$. Suppose $n\geq 8$. Case 1: $n$ is even and $3\not\mid n$. Then the permutation $(1,2,3)(4,\dots,n)$ is even and has order $\operatorname{lcm}(3,n-3)=3n-9\geq n+16-9\geq n + 7$. Case 2: $n$ is even and $3\mid n$. Then $n\geq 12$, so $n-2\geq 8$ is even and is not divisible by 3. Applying Case 1, we see that $(1,2,3)(4,\dots,n-2)\in A_n$ has order at least $n+5$. Case 3: $n$ is odd. Then apply one of the previous two cases with $n-1$ to get an even permutation with order at least $n+4$. $\blacksquare$ Is my proof correct? It doesn't seem very elegant. Is there some slicker proof? I am using Ubuntu 12.04.  My /etc/network/interfaces file consists of:    # The loopback network interface   auto lo   iface lo inet loopback     # The primary network interface   auto eth0  iface eth0 inet static   address 192.168.1.58   gateway 192.168.1.1 network 192.168.1.0   broadcast 192.168.1.255 dns-nameservers 66.212.63.228 66.212.48.10     I ran the command: /etc/init.d/networking restart  Which responded with:   *Running /etc/init.d/networking restart is deprecated because it may not enable again some interfaces   *Reconfiguring network interfaces...   RTNETLINK answers: File exists   Failed to bring up eth0   [ OK ]     Next I ran ping google.com and received:    ping: unknown host google.com   I am not sure if my interfaces refreshed. How do I properly configure my network with my static DNS addresses? Why can I modify a read-only file? Short Question:  Why can we manipulate a read-only file in Vim using : + w + q + ! even without being an administrator?  Long Question:  I have a text file (myFile.txt) which is read-only for everyone:  navid@navid-ThinkPad-T530:~/ubuntuTest$ ls -l myFile.txt  -r--r--r-- 1 navid navid 26 Aug 22 21:21 myFile.txt   I can open it with Vim without having admin privileges:  navid@navid-ThinkPad-T530:~/ubuntuTest$ vi myFile.txt    I modify it and press: Esc + : + w + q + Enter and I see this error message:  E45: 'readonly' option is set (add ! to override)   So far, everything makes sense.  But when I press: Esc + : + w + q + ! + Enter, Vim saves the changes.  I'm using Ubuntu 16.04 and VIM 7.4. How to handle repeated references in footnotes? Mandatory child record when creating parent record It seems that they can all mean "easily provoked to anger"  irascible：Easily provoked to outbursts of anger; irritable.  fractious：Irritable; argumentative; quarrelsome.  irritable：1.Capable of being irritated. 2.Easily exasperated or excited.  atrabilious：1.Characterized by melancholy. 2.ill-natured; malevolent. There have been a few questions regarding installing this package in the past, but they now seem to be out of date. I'm using MiKTeX 2.9 and TexMaker. When I try \usepackage{mathtools} in TexMaker it will try to install the package for me but will fail. I took the advice given in this thread:   As suggested I tried installing the mh package using the MiKTeX Package Manager, unfortunately I get the "unknown archive size" error, which I have read means that the package no longer exists. Another thread (lost the link) said you can use the MiKTeX Package Manager to directly install mathtools, however I do not see mathtools listed anywhere in the MiKTeX Package Manager...   So I ask, is the package under a different name? Are there any other ways to install this package? Looking for a (short?) story about a cryo ship looking for habitable planets I read this story/novella at least 15 years ago, probably 20 or more. It is about a ship, travelling through the universe, looking for habitable planets. Why, I can't remember. People are held in Cryo Stasis and I think they are wearing nothing in the chamber but some kind of mesh. Every time the ship gets close to a planet it wakes one or two of the people (one woman, one man?) to check it out but they never find anything good. I think in the end they wake up and discover, that they have arrived back at Earth. Other details are very vague but I seem to recall there was lots of stuff about a (blue?) light, dreaming/dreams and something about the cold, or cold blue lights or similar. Does that ring a bell for anyone? I want to describe my business and want to refer to it in a sentence.  I am trying to say:      "In 2015 we established a business (that is) named X".   Intuitively, the "that is" part is redundant, and makes the sentence more cumbersome. But I cannot think of a reason why we should be able to drop the verb.  Is the version without the "that is" part grammatically correct? How can it be explained? How to show $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$? I am able to evaluate the limit $$\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$$ for a given $n$ using l'Hôspital's (Bernoulli's) rule.  The problem is I don't quite like the solution, as it depends on such a heavy weaponry. A limit this simple, should easily be evaluable using some clever idea. Here is a list of what I tried:   Substitute $y = x - 1$. This leads nowhere, I think. Find the Taylor polynomial. Makes no sense, it is a polynomial. Divide by major term. Dividing by $x$ got me nowhere. Find the value $f(x)$ at $x = 1$ directly. I cannot as the function is not defined at $x = 1$. Simplify the expression. I do not see how I could. Using l'Hôspital's (Bernoulli's) rule. Works, but I do not quite like it.   If somebody sees a simple way, please do let me know.    Added later: The approach proposed by Sami Ben Romdhane is universal as asmeurer pointed out. Examples of another limits that can be easily solved this way:   $\lim_{x \to 0} \frac{\sqrt[m]{1 + ax} - \sqrt[n]{1 + bx}}{x}$ where $m, n \in \mathbb{N}$ and $a, b \in \mathbb{R}$ are given, or $\lim_{x \to 0} \frac{\arctan(1 + x) - \arctan(1 - x)}{x}$.   It sems that all limits in the form $\lim_{x \to a} \frac{f(x)}{x - a}$ where $a \in \mathbb{R}$, $f(a) = 0$ and for which $\exists f'(a)$, can be evaluated this way, which is as fast as finding $f'$ and calculating $f'(a)$.  This adds a very useful tool into my calculus toolbox: Some limits can be evaluated easily using derivatives if one looks for $f(a) = 0$, without the l'Hôspital's rule. I have not seen this in widespread use; I propose we call this Sami's rule :). I have installed the pimd service by means of apt. This comes with an upstream systemd unit file (/lib/systemd/system/pimd.service).  I want the service to be restarted when for some reason it gets killed, hence I wish to add the line Restart = always in the unit file.   However, I don’t want to modify the upstream unit file.  Is there any workaround for this? Excluding System admin from this validation rule I have the following validation rule ;  OR(      AND(         Upper(MailingCountry) &lt;&gt; 'UK',             NOT(ISBLANK(TEXT(UK_Email_Consent__c)))     ),      AND(        Upper(MailingCountry) = 'UK',          ISBLANK(TEXT(UK_Email_Consent__c))     ) )   I know to exclude system admins I need to include the following line   $Profile.Name &lt;&gt; "System Administrator"   In the validation rule above where do I add profile &lt;> system admin   Looking forward to your help   many thanks