I ran into this situation. I had helped out a player by not placing the robber on them with my knight card. To sweeten the deal, she agreed to give me 1 wood + 1 hay in exchange for 1 wood. Is this legal?  The board mentions that trading 1 wood for 2 wood is illegal, but is 1 wood + 1 hay considered legal?
Motivation: I once had one surplus card on my hand, and knew the robbers would come soon. So I gave it to someone for free, to avoid losing more cards when they hit. I was surprised by how badly this was received. Two of the three other players (the hosts of the game) acted upset, like I had tried to cheat. I had to take the card back, get robbed the next turn and 'giving cards away for free' was banned immediately. (Oh, how I hate mid-game additions to the rules. But that's beside the point.)  So now the question: Is this really illegal in Settlers of Catan? Is it generally considered underhanded in any way? If so, why?   My reasoning was like this:        Consider players A and B.   A wants to give B a sheep.   A trades a sheep and one rock to B, in exchange for wheat.   A trades the received wheat for the (formerly his) rock.   A and B now both have the same resources they had in the beginning, only the sheep has moved from A to B.
Why does Oracle 9i treat an empty string as NULL? I know that it does consider ' ' as NULL, but that doesn't do much to tell me why this is the case.  As I understand the SQL specifications, ' ' is not the same as NULL -- one is a valid datum, and the other is indicating the absence of that same information.  Feel free to speculate, but please indicate if that's the case.  If there's anyone from Oracle who can comment on it, that'd be fantastic! How to identify a downvoting stalker Possible Duplicate:          Yeah I got a deranged stalker that keeps downvoting me.  Anyone know how going about identifying such individuals?  (I just got 4 all at the same time just after making a new post).      that was the question I originally asked. Please tell me, what is so wrong with it ? Death in SAO before Kayaba announcement I was wondering if in the novel we knew about some deaths occurring before Kayaba announcement. I remember that in the anime, Kirito plays a bit with Cline before realizing that the log off option has disappeared. Then all the people are summoned to the city and learn about the fact that if they die in the game, they also die in real life.  I don't remember any players dying before the announcement in the anime, except for those who are not waking up and their relative pulling off their NerveGear thus causing death, but maybe in the light novel, some guys died without even knowing it just while being defeated by a mob (which seems awful for me).  Do we know about some players dying before that while thinking they are still in a normal game? How to get second last page as a number without hyperref? How can I make it so that each space has its own isolated dock?  Basically what I'm looking for is:   The dock in one space should not show the icon of an app that was open in another space. If I have the same program open in two different spaces, clicking on the icon in one space should not go to the app in the other space.   Is this possible natively, or with a third party program? Compute $\Gamma(2.7)$ All I know of the Gamma function is $$\Gamma(\alpha) = \int\limits_{0}^{\infty}x^{\alpha - 1}e^{-x}\text{ d}x$$ and the recursive formula $$\Gamma(\alpha) = (\alpha-1)\Gamma(\alpha - 1)\text{.}$$ A friend asked me to try to find $\Gamma(2.7)$. I assume this involves complex analysis, which I have absolutely no background on (except for the basic Euler formula). Using Wolfram, I found that  $$\Gamma(2.7) = e^{0.434821}$$ which suggests to me perhaps writing out $e^{-x}$ as a Taylor series: $$\Gamma(\alpha) = \int\limits_{0}^{\infty}x^{\alpha - 1}\sum\limits_{i=1}^{\infty}\dfrac{(-x)^{i}}{i!}\text{ d}x$$ but alas, this doesn't look helpful.  How does one derive that $\Gamma(2.7) = e^{0.434821}$? Why is electric field of an infinite plate constant at all points? I know from Gauss law, it is $\vec{E}=\dfrac{\sigma}{2 \epsilon_0}(\hat{n})$ at all points. But it doesn't make sense because of the inverse square nature of electric field which suggests if you move further away from the plane, electric field must reduce.   Then why is electric field of an infinite plate constant at all points? I've got a PDF that is automatically generated from a certain piece of software, that I want to include in the report I'm writing. I'm using pdfpages which gets the job done elegantly, but the problem is, the PDF has a lot of white space around the actual content (which is a graphics) and I always have to do some tedious post-processing of the automatically generated document so that it fits well in my report. Changing the output of the software to eliminate the white space is not an option (or at least, would be much more trouble than it's worth).  I checked the pdfpages , but wasn't able to find an option that does that. Ideally, I'd like to be able to set margins from each direction, and the PDF is then cropped accordingly and included.  What other options do I have to control what portion of the included PDF is visible in the final document? I look today on a few fresh question, and the view count was 0. Even after I refreshed the page a few time. This is definitely a bug, since the question isn't mine.  Also I don't think the all page was cached, since that the DateTime mark was change every reload.  But maybe the SQL result is cached. Trailing characters stripped from titles bypass length minimum How can I define a math operator behaving like \lim or \sum with limits? Row space and column space of $A^T A$ and $A A^T$ Define the Lie algebra $\mathfrak{g}$ of a Lie group G to be the set of all left-invariant vector fields of $G$. I want to prove that   $$          f: \mathfrak{g} \rightarrow T_eG \\              X \mapsto X(e) $$ is a linear isomorphism.  The only thing that I have left to prove is surjectivity.Letting $v\in T_eG$, we set $X\in \mathcal{X}(G)$ such that $\forall x\in G,\,X(x)=L_{x_{*,e}}(v)$ (I still have to show that such an $X$ is indeed a vector field on $G$). We get that  $$ f(X)=X(e)=L_{e_{*,e}}(v)=v $$  where the last equality holds because  $$       L_{e_{*,e}}(v)f = v(f \circ L_e) = v(f \circ id_G) = v(f) $$ for any $f\in C^\infty(G)$. (I am thinking of the tangent vectors as derivations).  Now all we have left to do is prove that such an $X$ is left-invariant, and it is therefore an element of $\mathfrak{g}$, but I do not know how. I tried to prove that  $$            \forall f\in C^\infty(G),\, L_{{x}_*,y}(X(y))f=X(L_x(y))f $$ but with no success. Get index of each capture in a JavaScript regex PUA.Phishing.Bank Found How do you use GRASS's v.kernel? I am flummoxed on how to use GRASS's v.kernel.  I have a vector layer of around 2.5 million points. I want to make a heat map using v.kernel to show concentrations, since I have variable instances with overlapping points, sometimes huge overlaps.  I've already gotten this vector layer in GRASS, and it displays just fine.  I've tried using GRASS's v.kernel command based on what I've seen here and on other forums, and I can't get it to do anything besides output a raster that's just a pink square.  Here's the command I'm using:  v.kernel --verbose input=master_grass7 output=master_grass7a_heatmap stddeviation=.0001   I've varied the stddeviation to all sorts of values from 1000000 to .000001, and it had no effect.  I've read the  repeatedly and don't really understand what it's getting at. At least, the instructions are on esoteric concepts, nothing practical. I've also checked the , and I'm not really understanding it, either. Yes, I can read C. The problem is it depends on a lot of stuff defined elsewhere in GRASS GIS.  I've also done a lot of Google searching, and I can't find a comprehensive guide. All that I'm getting are scattered copies of the v.kernel doc/man page or people who apparently got it to work without a fuss.  I've also checked up on the concept of kernel density estimation (KDE), and even then I don't see how to use the v.kernel command. That command appears to be a specific interpretation of KDE; its switches don't appear to correspond well to generic KDE concepts.  So back to the main question here: how can someone who is not intimate with GRASS product development use the v.kernel command? Is there a plain language translation available? Show that the cardinality of $\mathbb N$ is the same as the cardinality of $\mathbb N \times \mathbb N$ Show that $| \mathbb N | = | \mathbb N \times \mathbb N |$, i.e., the cardinality  of $\mathbb N$ is the same as the cardinality of $\mathbb N \times \mathbb N$.   How do I show it using the Fundamental Theorem of Arithmetic and the Schröder–Bernstein Theorem? Can someone explain this trigonometric limit? I have $$\lim \limits_{x\to 0}  \frac {\tan(2x)}{\sin(x)}$$ and in my case the result is $\frac{2}{1}$ =2 not whether it is right.  This is my procedure.  $$\lim \limits_{x\to 0}  \frac{\frac {\sin(2x)}{\cos(2x)}}{\frac{\sin(x)}{1}}= \lim \limits_{x\to 0}  {\dfrac {\sin(2x)}{(\cos(2x))(\sin(x))}}=\dfrac{2x\frac {\sin(2x)}{2x}}{\cos(2x)\frac{x\sin(x)}{x}}$$  I separate the limit.  $$\frac{\left(\lim \limits_{x\to 0}2x\right) \cdot \left(\lim \limits_{x\to 0}\frac {\sin(2x)}{2x}\right)}{\lim \limits_{x\to 0}\left(\cos(2x)\right)\cdot\left(\lim \limits_{x\to 0}\frac{x\sin(x)}{x}\right)} = \lim \limits_{x\to 0} \dfrac{2x}{x}=\frac{2}{1} =2$$ Are collective nouns always plural, or are certain ones singular? I'd say Microsoft have a way of bending the rules and I know that McLaren have won the championship. While this sounds strange, I believe it is correct English (sorry, I'm not native).   But when it's a small company, would you still use it this way? Is a company always plural, or are small companies singular? I.e., would you say Bakery Johnson makes fine bread or Bakery Johnson make fine bread? Is it My book seller, Woody's, have moved or is it has moved? I looked around but did not find that anyone has asked this before, but what are the fonts that are standard/recommended while writing academic reports/papers?