full time or full-time, what is the rule here
When should com­pound words be writ­ten as one word, with hy­phens, or with spaces?
Associates in Integral Domain Let $x$ and $y$ be nonzero elements of an integral domain $D$. Then $x$ and $y$ are associates if and only if $x = yd$ for some unit $d \in D$.    I am done proving the $\Leftarrow$ part. For $\Rightarrow$ what I did was: If $x$ and $y$ are associates then $x \mid y$ and $y \mid x$, so $x \mid y$ implies that $xs = y$ for some $s \in D$ and $y \mid x$ implies that $yt = x$ for some $t \in D$. That is, $yts=y$ which implies $ts=1$. Therefore $s$ is a unit and $t$ is a unit.    Am I on the right track? Can I say that the proof is complete? Allow moderators to see delete/undelete activity on users' profiles We get auto flags for 'possible vandalism' related to deletes, and these can be helpful at times in finding 'rage quit' users, or other potential problems.  But often, I would like to know if there is a prior pattern with the user doing this. While we can see posts of theirs which have been flagged, and perhaps find previous auto flags this way, it would be nice to see an overall view of their self-deletions and undeletions; mostly just to identify patterns.  Such a feature would be nice if it was activity centered, rather than post-centered. That is; each delete/undelete action should be shown. So we could easily see, for example, if someone went back-and-forth on a single post.  The "activity" tab in the profile would be a logical place to show these events.  I think this would be best to be limited to instant self-deletions, not deletion votes. How can one prove that $\pi^4 + \pi^5 < e^6$? Word for giving animal characteristics (esp. physical ones) to humans I am writing a paper about Art Spiegelman's Maus, specifically the metaphor that Spiegelman creates by depicting his obviously quite human characters with the heads of various animals, or a couple times animal masks. The metaphor is used at times to bestialize/animalize the acts of the Nazis and, in some cases, to show the arbitrary nature of the classes/groups/divisions they and others applied to human beings.  I considered "chremamorphism," but this describes the attribution of the characteristics of an object to, or the objectification of, a human. I also considered "animalize" and "bestialize," but those describe some of the effects that can be produced by Spiegelman's metaphor, not the metaphor itself - in many scenes in the book, the characters are extremely human, and I think that the negative or degrading connotations of these words makes them inappropriate for this use. Nor do "anthropomorphism" or "personification" fit, because Spiegelman is not applying human characteristics to animals but the other way around. None of the words that I can think of quite fit.  What is a word that accurately describes Art Spiegelman's depiction of obviously human characters as having animal body parts or wearing animal masks in the comic book Maus? Why should you not use Number as a constructor? How could Fred and George have figured the exact password to the Marauder's map? Square roots -- positive and negative It is perhaps a bit embarrassing that while doing higher-level math, I have forgot some more fundamental concepts. I would like to ask whether the square root of a number includes both the positive and the negative square roots.  I know that for an equation $x^2 = 9$, the solution is $x = \pm 3$. But if simply given $\sqrt{9}$, does one assume that to mean only the positive root? And when simply talking about the square root of a number in general, would one be referring to both roots or just the positive one, when neither is specified? Find each line matching a pattern but print only the line above it I need to find a string and need to print the line above it.   case1: The same line won't have the more than one matching pattern   ie)  consider a file containing  $cat &gt; para returns between the paragaraphs italic or bold     quotes by placing italic   Here i need to find for italic, and i need to get the output as below   returns between the paragaraphs quotes by placing   How can i get the output like this? Unsung hero dilemma This is partly related to  question.  I ran some queries on odata for my work on Stack Overflow, and I have found that my statistics are the following ones:  Accepted answers: 148 Zero score accepted answers: 36 Percentage of total: 24,3%  I probably fit the idea of the Unsong hero badge, as I've mostly been active in  questions, from when it only had around 200 Questions until now.  To get the badge I could either try to get one of my accepted answers downvoted once, that would give me a 25% accept rate; I could also delete 4 of my accepted answers with 1 or more score. That would also give me the badge, but this just seems wrong: You are actually encouraging me to either try to get a down-vote on a good answer, or delete good answers.  So, should I delete good answers to receive a gold badge?  Update: It's not that I care much if I get a badge or not, it's only a badge after all and not why I spend time on Stackoverflow anyways. But it's not ideal [read: problem] that I'm encouraged to delete accepted answers or try to get downvotes to achieve a badge. I am working on a racing game in Unity3d and I have to show the rank as the winners touch the winning point.  As the winners reach at the winning point the image of the winner number should pop up for 1-2 seconds that is it.  How do I do it? Can anyone sort out this problem? Any help would be appreciated.  Thanks in advance :) Was Voldemort a Better Wizard Than Dumbledore? Pursuant to , I have a somewhat related question. The majority of Harry Potter readers automatically assume that Dumbledore must be a better wizard than Voldemort, because Dumbledore is &quot;good&quot; and Voldemort is &quot;evil.&quot; However, would Tom Riddle's prematurely developed skills demonstrate that Voldemort was inherently a better wizard than Dumbledore? In chapter 17, The Heir of Slytherin, Harry challenges Tom Riddle when he claims to be the greatest sorcerer in the world, retorting that Albus Dumbledore is the greatest sorcerer in the world. Harry reminds Tom Riddle that Voldemort is frightened of Dumbledore. Conversely, in Half-Blood Prince, Dumbledore himself states that Voldemort knows perhaps more magic than any other wizard alive. Yet, as Harry is J.K. Rowling's most direct voice, do we conclude that Dumbledore was, in fact, the superior wizard? Who was the better¹ wizard: Voldemort or Dumbledore? ¹Better meaning on a technically skilled level. The cardinality of the set of all finite subsets of an infinite set Let $X$ be an infinite set of cardinality $|X|$, and let $S$ be the set of all finite subests of $X$. How can we show that Card($S$)$=|X|$? Can anyone help, please? What happens to the energy when waves perfectly cancel each other? Can you filter out certain SE sites from the hot questions list? Is it possible to filter out Stack Exchange sites from the hot questions list? Automating DB Restore from network share Lyircs of Free by Natalia Kills:     I'm free      I just spent all my money       but I rocked that like it don't cost a thing   Shouldn't it be "I've just spent all my money"? As far as I remember, our English told us to use Present Prefect in such case because of the just. Everyone knows that Wolverine's adamantium claws are super-sharp — sharper than even a razor — and virtually indestructible. What puzzled me the first time I saw Wolverine is: how do the claws stay in his body?  As it is shown, Wolverine's flesh and skin are human in strength, but the healing factor makes it superhumanly durable and strong. Still, when Wolverine slashes something, or someone, extremely hard, dense, or thick (as he has to use great amount of force), the claws don't tear through his hand and leave his hand through the opposite side of the palm (because of the action having equal and opposite reaction). Ubuntu 18.04 bond with netplan duplicate MAC address after cloning I was reasonably certain I've seen this before, but I was wondering how to solve the Diophantine equation  $$a^2+b^2=c^2+d^2$$  I tried a web search and found nothing on this one.  I'm trying to avoid another library trip to a less than local library (maybe I should have taken better notes on that chapter...).  I'm not quite sure how to handle this one.  The only thing I can figure out with this equation, if I remember correctly, is that the sum on either side may only contain prime factors of 2 or odd primes congruent to 1 mod 4.  And if I don't want a and b equal to c and d, the sum can't be prime as I believe a prime congruent to 1 mod 4 can be represented as the sum of 2 squares in exactly one way.  But that doesn't give me any insight into actually solving this problem. Is there a possibility to search when the embedded txt file was created in the word document? I'm working in Word 2010 and the extension of the document is simple: .doc  It was inserted using the Word options:  Insert -&gt; Object -&gt; Create from file -&gt; Insert as icon   Thank you, I already tried the right click and properties option, but the problem with it, that it shows only the current date for all of the 3 options (created/modified/accessed).           I also tried to get the timestamp but it is inactive when I'm on the txt object.   Sorry not to mention it before: Thank you all of you here for the help and support it is really appreciated.