I have a specific sentence in which I feel inclined to use "your's" but in not sure if it's correct. Then sentence is:  "Every story has a beginning - This is your's."  What "your's" stand for here is simply "this is your story's beginning" but to spell it out like that doesn't create the same feeling.   Albeit, is this a correct usage of "your's"?  Edit: This is not a duplicate of "Yours vs your's" as I'm asking for a situation in which "yours" can't be used since it would mean their beginning, not their stories' beginning.
Which is correct “Is that yours?” or “Is that your’s?”?  I ask because it is possessive, so I would think it would be the latter, but I typically use and see the former usage.  Are there particular cases in which one should be used instead of the other? Or is one simply correct and the other not?  This is one of the few things that still confuse me, so help is greatly appreciated.
How to change the name of a thread List comprehension with expensive computation Can you recommend a Java library for reading (and possibly writing) CSV files? Proving complex series $1 + \cos\theta + \cos2\theta +... + \cos n\theta $ So I have this result  $1 + z + z^2 + ... + z^n = \frac{z^{n+1}-1}{z-1}$  which I proved already. Now I am supposed to use that result and De Moivre's formula to establish this identity     $1 + \cos\theta + \cos2\theta +... + \cos n\theta = \frac{1}{2} + \frac{\sin[(n+\frac{1}{2})\theta]}{2\sin(\frac{\theta}{2})}$   Can anyone help me? How to install Windows 7 after Ubuntu and dual boot? I just installed Ubuntu, a full install removing the prior OS. I was forced to remove  from my  because of the max four partitions already being there. I didn't lose anything, all backed up. However, now I am looking to create another partition and install Windows&nbsp;7 on it.   Do I also need some sort of boot loader that lets me choose which to boot? Viewing all my questions from Android app Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$ Let $\phi: R \to S$ be a surjective homomorphism. Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$ for an ideal $J$ of $R.$  Obviously, $S \cong R/ \ker \phi$(first isomorphism theorem) and $\phi(J)$ is an ideal of $S$, since $\phi$ is surjective( $\forall s \in \phi(J), s = \phi(j)$ for some $j \in J, \forall s' \in S, s' = \phi(r)$ for some $r \in R$, so $ss' = \phi(j)\phi(r) = \phi(jr) \in \phi(J)$, and $ss' = \phi(r)\phi(j) = \phi(rj) \in \phi(J)$ ).  However, I'm having trouble with going on. If it's important, I mean a unitary ring by a ring. How to evaluate the limit of this expression?  $$\lim_{x\to\infty} \frac{\sin^2\left( \sqrt{x+1}-\sqrt{x}\right)}{1-\cos^2\frac{1}{x}}$$  I managed to simplify the denominator into a sinus form by the Pythagorean formula, and also modified the argument of the sinus in the numerator by dividing with a conjugate which I think is necessary, into this final form:  $$\lim_{x\to\infty} \frac{\sin^2\left(\frac{1}{\sqrt{x+1}+\sqrt{x}}\right)}{\sin^2\frac{1}{x}}$$  And that's where I got stuck. So far I've tried to come up with some solution to eliminate the sinus from the denominator, without success. I'm sure the solution is pretty obvious but I don't quite know how to modify the trigonometric functions in this fashion, so any help would be most appreciated. Typing at symbol (shift+2) displays double quote (") and Typing at symbol (shift+') attherate (@) in ubuntu 16.04 I am working with ubuntu16.04. While working with terminal i had seen that my keyboard keys typing different signs. For example   Typing at symbol (shift+2) displays double quote (")  Typing at symbol (shift+') atTheRate (@)  Typing at symbol (shift+3) Euro (£)   .  I restarted my system but still it's showing same. How are we able to calculate specific numbers in the Fibonacci Sequence? I was reading up on the Fibonacci Sequence,  $\text {{1,1,2,3,5,8,13,....}}$ when I've noticed some were able to calculate specific numbers. So far I've only figured out creating an array and counting to the value, which is incredibly simple, but I reckon I can't find any formula for calculating a Fibonacci number based on it's position.  Is there a way to do this? If so, how are we able to apply these formulas to arrays? How to fix "Package is in a very bad inconsistent state" error? I can't update my system because it freezes while installing a third-party update (zramswap-enabler)! Sometimes I get the following message in Update manager:  Could not initialize the package information An unresolvable problem occurred while initializing the package information. Please report this bug against the 'update-manager' package and include the following error message: E:The package zramswap-enabler needs to be reinstalled, but I can't find an archive for it.  I tried to remove the zramswap-enabler, but it's impossible because I get the following message: dpkg: error processing zramswap-enabler (--remove):  Package is in a very bad inconsistent state - you should  reinstall it before attempting a removal. Errors were encountered while processing:  zramswap-enabler E: Sub-process /usr/bin/dpkg returned an error code (1)  Actually I would really reinstall that package, but it is unable to do it! If I remove this third-party PPA then the system is warning me about a very very serious problem. So why can I not install/reinstall/remove/update this package and why freezes the updater if I try to update? What is an effective way to level Archery? How to encrypt in VBScript using AES? I am looking to encrypt some data using  in  using a specific key and  value. Are there any good function libraries or COM components that would be good to use?  I looked at ; it allows a passphrase only, and won't allow setting specific key and IV values. Why haven't I received the "Curious" badge? As you can see in the picture, I have 13 out of 5. But it's been like this for about two months! What's the reason for that? $L^p$ spaces and counting measure currently I am working on the following two exercises as a revision for my exam.  Let $\mu$ be the counting measure on $\mathbb N$.   Show that if $1 \le p &lt; s &lt; \infty$ then $f \in L^p$ implies $f \in L^s$ and $\|f\|_s \le \|f\|_p$. Show that if $f \in L^p$ for some $p \ge 1$ then $\lim_{s \to \infty} \|f\|_s = \|f\|_\infty$.   My attempts so far:   It is $f \in L^s$ iff $\sum_{k = 1}^\infty |f(k)|^s$ converges. Since $f \in L^p$ we know that $\sum_{k = 1}^\infty |f(k)|^p$ converges. Thus for any $\varepsilon &gt; 0$ there is $N \in \mathbb N$ s.t. \begin{align*} k \ge N \Longrightarrow |f(k)|^p &lt; \varepsilon \Longrightarrow |f(k)| &lt; \varepsilon^{1/p} \end{align*} We have $\forall k \ge N$ that $|f(k)|^s &lt; \varepsilon^{s/p}$. Originally I wanted to use the comparison test now, showing that \begin{align*} \sum_{k = N}^\infty \varepsilon^{s/p} &lt; \infty, \end{align*} but that does not work since \begin{align*} \sum_{k = N}^\infty \varepsilon^{s/p} = \varepsilon^{s/p} \underbrace{\sum_{k \ge N} 1}_{= \infty},  \end{align*} so I don't know how to go on here. Let $K := \|f\|_\infty$. We need to show that $\forall \varepsilon &gt; 0$ $\exists M \in \mathbb N$ s.t. \begin{align*} s \ge M \Longrightarrow \left|\left(\sum_{k = 1}^\infty |f(k)|^s\right)^{1/s} - K\right| &lt; \varepsilon. \end{align*} Choose $M$ s.t. $M &gt; p$. Then $s &gt; p$ and from part (i) we know that \begin{align*} \left(\sum_{k = 1}^\infty |f(k)|^s\right)^{1/s} \le \left(\sum_{k = 1}^\infty |f(k)|^p\right)^{1/p}. \end{align*} But how can I use this? I'm used to doing all my coding in one C file. However, I'm working on a project large enough that it becomes impractical to do so. I've been #including them together but I've run into cases where I'm #including some files multiple times, etc. I've heard of .h files, but I'm not sure what their function is (or why having 2 files is better than 1).  What strategies should I use for organizing my code? Is it possible to separate "public" functions from "private" ones for a particular file?   question precipitated my inquiry. The tea.h file makes no reference to the tea.c file. Does the compiler "know" that every .h file has a corresponding .c file? One frequent aspect of pdflatex output that could be improved is to what extent one can select text output from the generated pdf-file and copy-and-paste it. This is essentially an issue of having the right output encoding. There are at least two important aspects to this:   In the ideal case, Unicode would be the output encoding. Ligature glyphs (such as ﬁ) are ideally de-ligated in the output (here: "fi").   It seems that output encodings are specified through the fontenc package. What is the range of possible output encodings, and most importantly: Is there a way to specify a Unicode output encoding and one that deals with ligatures in the intended way?  (Note: It is important to distinguish output from input encodings. How to use different input encodings in LaTeX has been documented widely. My understanding is that this is best handled by the inputenx package, as it supersedes the inputenc package.)    Quick guide to the solutions: The information in the answers and answer threads is a bit distributed, so here the short summary: one approach is to use \input glyphtounicode together with \pdfgentounicode=1; the other approach is to use cmap/mmap.  Addendum: Sometimes one will need to load the package accsupp and enclose one's macro definition in \BeginAccSupp{method=hex,unicode,ActualText=&lt;codepoint&gt;}[...]\EndAccSupp{} to generate a specific code point. See the caveat about non-BMP code points  and the fix (starting from accsupp version v0.4, 2012/11/18) , which provides the new unichar package option. How do I build a SOQL query for records in a list of IDs? Can some one correct my soql? I need to export records in data loader like:  WHERE Id IN ('123123123','123123fsdf')   But this following query does not work for me:  SELECT Id, Syndication_Documents__c FROM ContentVersion  WHERE Syndication_Documents__c in : 'a4fa0000000KzbV','a4fa0000000KzbW' I am looking for idioms or informal/slang/colloquial expression for some people that make you think that they are able of building a skyscraper, constructing a spaceship, playing the piano better than Mozart or something very fancy that requires remarkable skills, but when it comes to practice they prove to be completely inadequate. Probably a basic issue, but still something that irks me and I can't find an answer online. I want to change the default folder for saving new shapes/processing outputs from &quot;last used folder&quot; to &quot;project folder&quot; or &quot;something in relation to project folder&quot; - is this possible? If so, how can I achieve this?