Front end displaying all lines as dashed lines
Why PlotStyle->Dashed make everything dashed?
Mechanics of Horizontal Stretching and Shrinking I know $y=2f(x)$ doubles the $y$ value in vertical shifting, and I know that $y=(1/2)f(x)$ halves the $y$ value. But, why does $y=f(2x)$ halve the $x$ value, and why does $y=f((1/2)x)$ double the $x$ value in horizontal shifting? I looked at the graphs, and I see the difference, but I want to know the math behind why it halves instead of doubling the $x$ value for $y=f(2x)$. Maybe this is a stupid question, but could someone help me out?  Thank you. Determining a matrix from its characteristic polynomial How to show the inequality for $\int_{0}^{\pi/4}\tan^n(x) dx$ I can't seem to figure out the inequality option, I substituted n=2 for the answer bit is there any elegant way of getting it? Tags on badge question list I'm trying to get the Weed-Eater hat on Stack Overflow. To do so, I'm looking at the list of questions . The problem is, no tags show up there, and so it's rather difficult to see which ones I have a shot at. Any chance of showing the tags on this page?  I realize that getting this before Winter Bash is over would be difficult, but it would be good to keep such things in mind for the future. Center-align the verbatim environment How do keyboard input and text output work? Any way to send a personal message to another user? There has been quite a few times that I wished I could send a message to another user on SO - not ask a question for everyone to see, but just a short message informing them of something or requesting them to do something.  Are there any plans to allow this to happen in the future?  Related: About number truncation of ticks display in ListPlot Formula to this pattern? $1$, $11$, $21$, $1211$, $111221$, $\ldots$ I have this pattern:  1 11 21 1211 111221   I'm guessing it's a fibo pattern, been at it for hours now. Anyone know? If $A$ is an $n \times n$ matrix and $ A^2 = 0$, then $\text{rank}(A)\le n/2$. Was revising for a Linear Algebra when I came across this question.     "Given a Matrix $A$ over $\mathbb{R}^{n \times n}$, and $A^2 = 0$,   show that rank($A$) $\leq n/2$"   My attempt:  I was thinking of the theorem from Cayley-Hamilton but the matrix is a $n \times n$ matrix hence that's probably invalid.  Is there perhaps a significance of $A^2 = 0$? apart from a special case of the nilpotent matrix? What if client doesn't like any logo design concept? I'm in a process of creating Graphic Design contract. I've decided to provide each client with 3 logo concepts and 3 rounds of revision. Ideally, I would create 3 concepts and client will chose one, but it happend to me before that client didn't like and concept and I end up with doing 10+ more (yes, I've worked without contract).  How can I prevent this situation? Should I charge hourly for each new concept separately? How can I express my thoughts clearly in a contract (without sounding like 'if you don't like any, you'd have to pay more)? I don't want to scare client and put thoughts into their minds saying that there is a possibility that they won't like me ideas. I have a log file being written by another process which I want to watch for changes. Each time a change occurs I'd like to read the new data in to do some processing on it.  What's the best way to do this? I was hoping there'd be some sort of hook from the PyWin32 library. I've found the win32file.FindNextChangeNotification function but have no idea how to ask it to watch a specific file.  If anyone's done anything like this I'd be really grateful to hear how...  [Edit] I should have mentioned that I was after a solution that doesn't require polling.  [Edit] Curses! It seems this doesn't work over a mapped network drive. I'm guessing windows doesn't 'hear' any updates to the file the way it does on a local disk. Jumping in an elevator? Copy-paste from question to snippet When I'm editing a stack snippet, I often want to copy code from the original question into the snippet. But while the snippet editor is on display, there's no way to access the question, other than opening another tab/window. What I often do instead is copy all the code in the question to the clipboard, open the snippet editor, then paste it all in and revise it to what I want. But when the original code is poorly designed, that ends up being more work than just copying the bits and pieces that I want.  There could be a "View Question" button that pops up the question over the snippet editor and allows copying. Or maybe the Snippet Editor could be draggable and resizable, so you can reveal the question and copy from it; but this would require that it not be purely modal. What is the default password of the sudo? I visit some forums, it tells that the default password is password, but it doesn't work, how can I determine the password? Redirect parent window from an iframe action How to make a ISO file out of a folder containing Windows setup files I copied the Windows 8 CD to my HDD. I want to convert that folder to an ISO and use that to create a bootable USB.  Please tell me how I can make an ISO image out of that folder containing files.  This is my folder which I want to convert to a ISO file: Suddenly, to everybody's surprise, the silent Mr.Smith swung around and addressed Barbara.   The dinner was served by a silent Mrs. Keats.   I saw an infuriated Jennifer, who started shouting at me the moment I opened the door.   It seemed Walter didn't pay any attention to a tearful Kitty.   She hasn't got lovely eyelashes like marvellous Monica.   I bet your Mum kept you well clear of horrible Jesse.      The rule I learned at university said that the is used when the adjective a permanent quality of the person in question. E.g. 'I met the wicked Matilda the other day' would suggest that Matilda is inherently wicked.  The indefinite article a/an, on the other hand, would denote the mood or an unusual quality of the person described.  However, recently I've come across a lot of examples where no article is used with names modified by adjectives (see examples 5 and 6 above).   Can anyone explain why there are no articles in sentences 5 and 6? Let $\{E_i\}_{i=1}^n$ be finitely many disjoint sets of real numbers (not necessarily Lebesgue measurable) and $E$ be the union of all these sets. Is it always true that  $$ m^\star (E)=\sum_{i=1}^N m^\star(E_n) $$ where $m^\star$ denotes the Lebesgue outer measure? If not, please give a counterexample. The Vitali set is a counterexample in the countable case, but I am not sure whether it is false in finite case. This is problem 3.18 from Patrick Morandi's Field and Galois Theory.     Give an example of fields $k \subseteq K \subseteq L$ and $l \subseteq L$ for which $l/k$ and $L/K$ are algebraic, $k$ is algebraically closed in $K$, and $lK = L$, but $l$ is not algebraically closed in $L$.   This question has been asked twice, namely  and , though neither had any answers, and only some inconclusive comments. Normally I wouldn't ask the question again, but after struggling with it for weeks at this point, I emailed Morandi, and he gave me some hints.  He told me that he remembers finding an example, but that he isn't sure. He told me that it would need to be over characteristic $p$ and that the extensions (at least some of them I suppose) could not be separable. Moreover, he told me that $K = k(x)(a)$, where $a$ is a root of an irreducible polynomial $f(x,y) \in k(x,y)$ (I'm not 100% what the root of a two variable polynomial is). Finally, he said that $l$ is an algebraic extension of $k$, where $f$ becomes reducible over $l$. Still however, I can't come up with anything. I was hoping that with these extra hints, someone would be able to figure it out.  He did point out that there is a chance that there is an error in the question, but I haven't managed to prove that such an example cannot exist.