So, my brother is watching on tv a vote a in the American Congress.  He says that the members are asked to vote with yea/nay (I have heard that from the Chamber of Commons in the UK as well).  Now we are trying to figure our whether there might be an actual difference between yea/nay and yes/no, that might have gone lost with time. In particular, a person on  gave an interesting explanation: "English used to use what’s called a “four-form” system. “Yea” and “nay” were only used to answer positive questions, while “yes” and “no” were only used to answer negative questions." However, I cannot find confirmation of what is said.  On a side note, an aspect of this answer that is intriguing me is that I have never heard of a "four-form" system. As I have studied French and German, I am know of the existence of three-form systems (in German, ja/doch and nein, and in French, oui/si and non), but four??  Can anybody confirm/refute the theory of the "four-form system"?  If you are going to confirm it, could you please provide the source of your information?  (I have looked on stackexchange for answers, but, to the best of my knowledge, questions on yay/nay never wonder about the comparison with yes/no)
I am curious as to why "nay" replaces the simple unequivocal "no" in the context of voting.  My research in Merriam-Webster tells me that "nay" means "no" (not the other way around) and the first known use of "nay" appeared in 1400s. Since the use of "no" existed before 1400 and the word remains to be used afterward, why would "nay" become the preferred choice of word when it comes to voting. Any idea?
Reprojecting LiDAR data with libLAS, error: "latitude or longitude exceeded limits"? How to render lightning in Cycles How can you render a lightning bolt using Cycles? I have a command that I want to have run again automatically each time it terminates, so I ran something like this:  while [ 1 ]; do COMMAND; done;   but if I can't stop the loop with Ctrl-c as that just kills COMMAND and not the entire loop.  How would I achieve something similar but which I can stop without having to close the terminal? How does the computer know that the PC was not properly shut down? Actually, this question struck me because of power cuts in my house. When there is a power cut, there is a sudden loss of power from the computer.   How does the computer know that the shutdown was not properly done? How to boot from iso with Grub2/Burg boot loader I'm using Ubuntu as my primary OS and alternative is Windows 7 for gaming, and another stuffs. I want to have menu to boot some live CD ISO. Is there anyway to make menu entry in Grub2/Burg to boot ISO file like the CD way?  I see there are some ways to make it possible but almost method need specified boot arguments (kernel parameters). But I have mixed kind of Live OS wan to boot up using boot loader included: Linux, Unix, DOS (for recovery purpose)...   I'm looking for more generic way to make it easy to discover and add to the menu config file. Why doesn't grep using pipe work here? Intuitive explanation for how could there be "more" irrational numbers than rational? Get top results for each group (in Oracle) I apologize if this question is posted on the wrong portion of the website, but I knew no better place to ask.  I've come to see that some effects, such as super-conduction may happen at either extremely low temperatures, or at extreme temperatures (the recent discovery of superconducting iron in the bowels of the earth, for one), and this is fascinating.  My question is: can (does?) the same principle be applied to quantum effects? Would it be applicable to, for example, say that although quantum effects happen at nano scales and below they may happen on a grand scale of say, the entire Universe (as a solitary unit)?  Can said quantum effects happen at moments of say, picoseconds after the Big Bang due to the turbulence of forces involves in such an event? Or even within the core of a dying star?  Thank you for any answers or clarification of my misinformation. "Most importantly" or "more importantly"? Which of the following two sentences is more correct?   "A picture says a thousand words, more importantly in a fraction of a second"    OR   "A picture says a thousand words, most importantly in a fraction of a second"   Nothing important, just my own quotes! Do also suggest, if I can put it in a better way to express what I want to. Book about mages who can harvest magical energy from the environment I have a vague recollection of a book I devoured while in college; it was from the late 80's or early 90's. I remember that there were two 'classes' of mages, the ones who could harvest magical energy from the environment and supply that power to the other 'class' of mages.  The main character learned that he could reverse the flow and sap the other mage of his/her power. I also seem to remember that there was a lot of technological warfare and travel to the planets moon(s)? Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$. $$\lim_{x \to 0} \frac{f(x)}{|x|}=1$$ Then prove that $f$ is not differentiable at $0$. I was given this assignment and I'm not sure about my proof.. it feels like I'm assuming too much and not explaining with enough detail. Is there anything I need to add to make it sufficient? Assume toward contradiction that $f$ is differentiable at $0$. Then by definition we know that $f$ is continuous at $0$. Therefore $\lim _{x\to 0}f\left(x\right)=f\left(0\right)$ We know that $\lim _{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}=1$ Therefore we can conclude $\lim _{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \left|x\right|=1\cdot 0=0$ But we can also rewrite this as $\lim _{x\to 0}\left(f\left(x\right)\right)\cdot \frac{\left|x\right|}{\left|x\right|}=f\left(0\right)\cdot 1=0$ Therefore $f(0) = 0$. Since $f$ is differentiable at $0$ we have $\lim _{x\to 0}\frac{\left(f\left(x\right)-f\left(0\right)\right)}{x-0}=\lim _{x\to 0}\frac{\left(f\left(x\right)-0\right)}{x}=\lim \:_{x\to \:0}\frac{\left(f\left(x\right)\right)}{x}\cdot \frac{\left|x\right|}{\left|x\right|}=\lim \:\:_{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\frac{\left|x\right|}{x}$ Since the one sided limits of $\frac{f\left(x\right)}{\left|x\right|}$ exist, and are both equal to 1, we have $\lim \:_{x\to 0^+}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\:\frac{\left|x\right|}{x}=\lim \:_{x\to \:0^+}\frac{\left(f\left(x\right)\right)}{x}\cdot \:\:\:\frac{x}{x}=1\cdot 1=1$ $\lim \:_{x\to 0^-}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\:\frac{\left|x\right|}{x}=\lim \:_{x\to \:0^-}\frac{\left(f\left(x\right)\right)}{-x}\cdot \:\:\:\frac{-x}{x}=1\cdot -1=-1$ Since the limit doesn't exist, we have a contradiction to the fact $f$ is differentiable at $0$. Therefore $f$ is not differentiable at 0. Is it possible to keep publishing under my professional (maiden) name, different from my married legal name? Compiling with either XeLaTeX or LuaLaTeX, \emph{} no longer displays text as expected, i.e. in italics. \textit{} works fine. Here is a MWE demonstrating the issue.  \documentclass{article}  \usepackage{fontspec}  \begin{document}      \emph{lorem ipsum}      \textit{lorem ipsum}  \end{document}   Here is the output I get :   I have TeXLive 2016 (MacTeX) installed. I updated it an hour ago with sudo tlmgr update --self --all.  I guess there is something wrong but what ? I'd be happy to have some help. Thank you. Probability to choose specific item in a "weighted sampling without replacement" experiment Given $n$ items with weight $w_n$ each -- what is the probability that item $i$ is chosen in a $k$-out-of-$n$ "weighted random sampling without replacement" experiment? Can a closed-form solution that depends only on $w_i / w_\cdot$ be derived ($w_\cdot = \sum_j w_j$.)?   EDIT: A solution that depends only on $w_i / w_\cdot$ is impossible. Assume $n=3$, $i=1$, $w_1 = 1$, and two cases: (1) $w_2 = 1, w_3 = 1 + \varepsilon$, (2) $w_2 = 2, w_3 = \varepsilon &gt; 0$. In case (1) the probability is almost $2/3$, in case (2) it is almost $1$, but in both cases $w_1 = 1$ and $w_\cdot = 3 + \varepsilon$.  What I have tried so far to solve the problem:  Let $P^n_k(w, i)$ be the probability that item $i$ is chosen in an $k$-out-of-$n$ experiment with weight vector $w$. In the first draw, the item is chosen with probability $w_i / w_\cdot$. Otherwise, we are looking for the probability to choose this item in a $k-1$-out-of-$n-1$ experiment, with the same weight vector except for the item that has been selected. Hence:  $$ P^n_k(w, i) = w_i / w_\cdot + \sum_{j \neq i} w_j / w_\cdot \cdot P^{n-1}_{k-1}(w - j, i) $$ $$ = w_\cdot^{-1} \left( w_i + \sum_{j \neq i} w_j \cdot P^{n-1}_{k-1}(w - j, i) \right) $$  with $w-j$ being "the vector $w$ without the $j$th element".  How to solve this recurrence relation? (If it is correct at all...) What does "...from nonmagical attacks not made with silvered weapons" mean? I'm sure your first thought is, that's perfectly clear.  Unfortunately my group who aren't normally rules lawyers disagree.  Party encounters a  (MM p.211).  It has:     Damage Immunities: bludgeoning, piercing, and slashing from nonmagical   attacks not made with silvered weapons.   My reading of that is if the weapon has to be magical and silvered to hurt it.  So a +1 silver dagger will hurt it, but a +1 regular dagger or a +0 silver dagger won't.  The group's interpretation was that all three of those weapons would hurt and only a +0 regular dagger would be ineffective.    I would also note my interpretation would mean something like blade barrier would also not harm it since you could argue they're magical blades but nothing indicates that they're silvered.    This also appears to be the same wording for some undead so I'm not looking for a lycanthrope specific interpretation but something general for every time that wording is used.    Thanks in advance. The limit of reciprocal is the reciprocal of the limit While I was reading the book Exploratory examples for real analysis, I came across this:     to show that : $$\lim_{x\rightarrow x_o}\frac{1}{h(x)} = \frac{1}{\lim_{x\rightarrow x_o}{h(x)}} = \frac{1}{M}$$      Discussion:Let $\epsilon \gt 0$.we want to find $\delta \gt 0$ such that       if  $0 \lt |x-x_0| \lt \delta $,then $\Big|\frac{1}{h(x)}-\frac{1}{M}\Big|\lt \epsilon$.      In order to get expression involving $|h(x)-M|$,we first find the common denominator:        $\Big|\frac{1}{h(x)}-\frac{1}{M}\Big|=\Big|\frac{M-h(x)}{M~h(x)}\Big|$      $~=\Big|\frac{h(x)-M}{|M|~|h(x)|}\Big|$.      As we have to deal with variable term $|h(x)|$ in denominator.We can construct bound .Let $\epsilon =\frac{|M|}{2}$ ,since lim$_{x\to x_o}h(x)=M$,there exists $\delta_1\gt 0~~$ s.t.       if $0 \lt |x-x_0| \lt \delta_1 $,then $|h(x)-{M}|\lt \frac{|M|}{2}$.      As you study steps below,identify that step where $h(x)\neq 0$ for all $0 \lt |x-x_0| \lt \delta_1 $ plays a critical role:      $|M|=|M-h(x)+h(x)|$      $~~~~~~\leq |M-h(x)|+|h(x)|$      $~~~~~~= |h(x)-M|+|h(x)|$      $~~~~~~\lt \frac{M}{2}+|h(x)| \implies$      $\frac{|M|}{2} \lt |h(x)| \implies$      $\frac{1}{h(x)}\lt \frac{2}{|M|}$,where $0 \lt |x-x_0| \lt \delta_1 $.      Now that we've bound for $1/h(x)$,we can apply the definition to term $|h(x)-M|$.      Since     lim$_{x\rightarrow x_o}h(x)=M$,we can find $\delta_2 \gt 0$ such that,       $~~~~~~~~~~~~~~~~~~~~~~~~~~~~$if  $0 \lt |x-x_0| \lt \delta_2$, then $|h(x)-M|\lt \frac{|M|^2 \epsilon }{2}$   The thing I can't understand is for what purpose did the author work with such complicated expression involving $\epsilon $ in the end of the discussion? Stop the Ubuntu updater from nagging about Firefox English Language pack even after uninstalling Firefox I have run sudo apt purge firefox, and I have gone through all of the /.config files, etc., and Software Updater is still asking me daily if I want to install the &quot;English Language Pack for Firefox&quot;. I don't have Firefox installed. How can I stop the updater from asking to update something on a program that doesn't exist? Output of dpkg -l | grep firefox: ii  firefox-locale-en                          88.0+build2-0ubuntu0.18.04.2        amd64        English language pack for Firefox Ready-to-Use Database models example Where can I find ready-to-use database models ?  I don't need a database with data in it, but only schemas (UML diagrams). Perhaps something like the , but much more complex and real world. How to find the sum of all the numbers that can be formed using the digits 2,3,3,4,4,4.. What should be the way of doing this type of problem?? Please guide