This question is best explained by an example. Ignore the mathematical context, it doesn't really matter.     ... as x tends to 0, the point P slides towards P', so cos x (and hence 1/cos x) both have a limit equal to 1. ...   Given that parentheses are usually meant as an aside, if I read the text ignoring the parentheses:     ... so cos x both have a limit equal to 1 ...   the "both" here is grammatically incorrect (as, of course, cos(x) is a single "thing").  So here comes the question in the title: Do sentences need to remain grammatically correct if text in parentheses are ignored? And as a side question, what would be a better thing to use in the example?
If a set of parentheses lies between a subject and its verb, and the parentheses contain an substitutive subject whose singularity/plurality disagrees with the original subject, whose singularity/plurality should be chosen for the verb?  In other words, in the following example, should "questions" (and its verb "are") be singular, or should they remain plural as shown?     Many (if not every) questions on this StackExchange are answered.   My intuition tells me that the two words in question should remain in plural forms, since the text in parentheses only interrupts the sentence (and the sentence would be grammatically incorrect if everything in parentheses were removed and the words were in singular form).  On the other hand, when read aloud (assuming one reads the text in parentheses), this has an uncomfortable sound to it, and I've seen others write in what would be the above example's singular-form case, so I'm curious to find out which is correct.  And, thinking about it, I suppose the same question would apply when commas are used in place of parentheses.
How do I run Command & Conquer Gold on Windows 7 64-bit (in XP mode)? I downloaded the first Command &amp; Conquer game  and burnt some CDs. I couldn't get the Setup.exe program to run in Windows 7 64-bit, as it must need some old DLLs. So I ran up the Windows XP Mode virtual machine, and was able to install it fine.   However, when I try to run the program, I just get an empty message box with an "OK" button. I've set the compatibility to Windows 95, and checked all of the options in the Compatibility tab, but it's not running. I also downloaded the patch suggested by EA, which is an updated version of the THIPX32.DLL file (copied into the C&amp;C installation folder).  Has anyone managed to get this working? Have Blender on about 4 machines rendering animations. Just spotted on one of the machines its rendering something different from the actual scene that I have setup.    Top window shows a different set of layers objects to whats actually being rendered in the rendering window below.  In my scene contents, layers objects 1-5 are not visible, but these are the ones that look like they are being rendered.  The only thing I can assume is that perhaps it might be because I did not save the document before clicking render, but I would not have expected that behaviour (you dont need to save your word document before printing it).  Can anyone confirm why this is happening? Area of a weird ellipse shape. A propeller has the shape shown below. The boundary of the internal hole is given by $r = a + b\cos(4α)$ where $a &gt; b &gt;0$. The external boundary of the propeller is given by $r = c + d\cos(3α)$ where $c - d &gt; a + b$ and $d &gt; 0$.  Calculate the total area of the propeller as shown by the shaded region and calculate the average temperature of the propeller, given by $T (r, α) = C/r$, where $C$ is a constant.     Have absolutely no idea how to solve this. How could I go about detecting (returning true/false) whether an ArrayList contains more than one of the same element in Java?  Many thanks, Terry  Edit Forgot to mention that I am not looking to compare "Blocks" with each other but their integer values. Each "block" has an int and this is what makes them different. I find the int of a particular Block by calling a method named "getNum" (e.g. table1[0][2].getNum(); Thomson et al. provide a proof that $\lim_{n\rightarrow \infty} \sqrt[n]{n}=1$ in . It has to do with using an inequality that relies on the binomial theorem:  I have an alternative proof that I know (from elsewhere) as follows.  Proof. \begin{align} \lim_{n\rightarrow \infty} \frac{ \log n}{n} = 0 \end{align} Then using this, I can instead prove: \begin{align} \lim_{n\rightarrow \infty} \sqrt[n]{n} &amp;= \lim_{n\rightarrow \infty} \exp{\frac{ \log n}{n}} \newline &amp; = \exp{0} \newline &amp; = 1 \end{align}  On the one hand, it seems like a valid proof to me. On the other hand, I know I should be careful with infinite sequences. The step I'm most unsure of is: \begin{align} \lim_{n\rightarrow \infty} \sqrt[n]{n} = \lim_{n\rightarrow \infty} \exp{\frac{ \log n}{n}} \end{align} I know such an identity would hold for bounded $n$ but I'm not sure I can use this identity when $n\rightarrow \infty$. Question: If I am correct, then would there be any cases where I would be wrong? Specifically, given any sequence $x_n$, can I always assume: \begin{align} \lim_{n\rightarrow \infty} x_n = \lim_{n\rightarrow \infty} \exp(\log x_n) \end{align} Or are there sequences that invalidate that identity?  (Edited to expand the last question) given any sequence $x_n$, can I always assume: \begin{align} \lim_{n\rightarrow \infty} x_n &amp;=  \exp(\log \lim_{n\rightarrow \infty} x_n) \newline &amp;=  \exp(\lim_{n\rightarrow \infty} \log x_n) \newline &amp;=  \lim_{n\rightarrow \infty} \exp( \log x_n) \end{align} Or are there sequences that invalidate any of the above identities? (Edited to repurpose this question). Please also feel free to add different proofs of $\lim_{n\rightarrow \infty} \sqrt[n]{n}=1$. Poisson / exponential distribution Next weekend you will be participating in 12km cross country race on a mountain.The average time between  two successive wild animal sightings on the mountain is reported to be 5 minutes  (a) What is the probability that you see at least one wild animal in the 11th minute of the     race given that you will see 3 wild animals since the start of the race?  (b) What is the probability that it will take more than a quarter of a hour before you see a wild animal after ten minutes of running?  Now I have attempted (a) , but I don't know whether my thinking is correct. (b) on the other hand makes little sense to me.  My attempt:  (a)$ X~ Poisson(\frac{1}{5})$ and $Y~Exponential(\frac{1}{5})$  $Pr(X&gt;4) = Pr(X&gt;1)$  (I am thinking that this is some variation of the memoryless property)  $Pr(X&gt;1) =Pr(Y&lt;1)$  $Pr(Y&lt;1)= 1 - (e^{(\frac{-1}{5})})$  Perhaps, I was a bit to vague in my attempt of (a). So here goes my attempt of(b).From my understanding of the question , it is asking what it the probability that the time between events(in this case animal sightings) is more than 25 minutes given you have been running for ten minutes  Now from what I know the fact that you have been running ten minutes is irrelevant this is due to memory-less property of the exponential  distribution   so without further ado  I present my attempt at (b)   let $X $ be exponentially distributed random variable with $\lambda = 1/5$  then  $Pr(X &gt;15) = 1 - Pr(X &lt;= 15)$ I am considering buying a Dell XPS 15 laptop. The laptop has a Nvidia 420m card which should work with Linux but I keep reading that the Nvidia Optimus technology isn't supported on Linux. I am not really interested in switching from Nvidia to Intel to save power but need to know that the Nvidia card will in fact work if I installed Ubuntu.  If anyone has experience using a Nvidia card with Optimus technology or even better the exact laptop in question (Dell XPS 15 with 1GB NVIDIA® GeForce®  GT 420M) it would be great.  A major problem holding people back from adopting Linux is this sort of hardware issue. I am a long term Ubuntu user and supporter who can't afford to make a mistake with a purchase like this. I don't want to spend £500+ to find I have no graphics acceleration because Windows 7 is not an option. Stuck in a loop at login prompt after changing shell to zsh Linear mixed effect model vs. Ordered Probit vs. Ordered Logit with ordinal response I have a set of data with an ordinal response ranging from 1-5 (worst to best) and a categorical predictor with five unordered levels. The experiment is a language experiment whereby subjects are asked to rate different sentence types. In the literature it seems that people fit lmer() most of the time by scaling the ordinal response per subject (i.e. taking the mean response and standard deviation of that subject and dividing the every single response by it.). On the other hand, it seems a reasonable approach to use ordered linear mixed effects probit models or ordered linear mixed effects logit models as implemented in e.g. MCMCglmm() or clmm().  (1) I find myself asking what the best method would be. When is one method to be prefered over the other in an experiment as I have sketched above?  (2) Why do people prefer fitting an lmer() model with a scaled response? What is the advantage?  (3) If it is advisable to use an ordered probit or logit model, how do I decide between an ordered probit or ordered logit model?  Thanks for any help! How do you iterate through every day of the year? I would like to insert the below mathematical symbol, it looks like a big Delta but different. Is there command to obtain a similar shape? Console.WriteLine and generic List I frequently find myself writing code like this:  List&lt;int&gt; list = new List&lt;int&gt; { 1, 3, 5 }; foreach (int i in list) {     Console.Write("{0}\t", i.ToString()); } Console.WriteLine();   Better would be something like this:  List&lt;int&gt; list = new List&lt;int&gt; { 1, 3, 5 }; Console.WriteLine("{0}\t", list);   I suspect there's some clever way of doing this, but I don't see it. Does anybody have a better solution than the first block? Youths can teleport, they are chased by the government Git ignore file for Xcode projects how to change a pose lib using script I want to make a button that changes the active poselib to another one from the list, a specific one. I look in the console and can't see any operator. any ideas? Troubleshooting for biber Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$. Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$. Is the converse true? I.e., if $g \circ f$ is invertible, does it follow that $f$ and $g$ are both invertible?  I know that if $f$ and $g$ are invertible, then they are both injective and surjective. Therefore, I assume from this that I have to show $g \circ f$ is injective and surjective as well, thus proving it is invertible. However, I don't know how to show $g \circ f$ is bijective based only on the information I have. Are there ways to determine if a wall is load bearing? Other than looking up blue prints, which many homeowners may not have, are there ways to determine if a wall is load bearing?  Methods I can think of might include:   Going up in the attic to check if ceiling trusses run perpendicular to the wall If the wall is an exterior wall   Any others? Draw somewhat random function I am trying to reconstruct this image here    I am not very happy with the code, as it uses hacking and adding white boxes and alike. My problem is now how do I draw the somewhat arbitary function in the figure? I tried to do a polynomial fit, but that did not work. I got dimensions to large, would a spline solution work better?    \documentclass{standalone}     \usepackage{tikz}     \usetikzlibrary{patterns}     \usepackage{pgfplots}     \pgfplotsset{compat=1.6}     \begin{document}     \begin{tikzpicture}      \begin{axis}[         xmin=-0.1,xmax=5,         xlabel={z},         ymin=0,ymax=4.5,     xtick={2.5,4},     xticklabels={$v_1$,$v_2$},     ytick={2.5,3.5},     yticklabels={$u_1$,$u_2$},     xlabel={$u$},       ylabel={$v$},     axis lines=middle]  \draw [fill=gray!40!white,thick,dashed] (axis cs:0,0) rectangle (axis cs:4,3.5); \draw [color=black,fill=white,thick,dashed] (axis cs:0,0) rectangle (axis cs:2.5,2); \draw [fill=black] (axis cs:0,0) rectangle (axis cs:0.01,4.45); \addplot+[black,thick,domain=0:5,no marks] {0}; % \node at (axis cs:2.5,0)    [anchor=south west] {$A$}; \node at (axis cs:4,0)      [anchor=south west] {$A'$}; \node at (axis cs:2.8,2.2)  [anchor=north]      {$B$}; \node at (axis cs:4.2,4)   [anchor=north]       {$B'$}; \node at (axis cs:0.25,2.5) [anchor=north]      {$C$}; \node at (axis cs:0.25,4)   [anchor=north]      {$C'$}; \node at (axis cs:0,0)     [anchor=south west]  {$O$}; % \end{axis} \end{tikzpicture} \end{document} The square of an integer is congruent to 0 or 1 mod 4