The most precious thing for me was .... a) my brother-in-law guitar b) my brother’s-in-law guitar c) my brother-in-law’s guitar d) my brother’-in-law guitar e) my brother’s-in-law’s guitar
I need a bit of help with this.      She is a photographer but that camera is her brother's-in-law     or:        She is a photographer but that camera is her brother-in-law's   I am aware that I could change the construction to make things easier, like:      She is a photographer but that camera belongs to her brother-in-law       However, I would really like to find out what's the correct way to write the sentence.
proving that elements of a sequence are pairwise coprime For the sequence $a_n = 6^{2^n} + 1$:   How can I prove that the elements of this sequence are pairwise coprime, i.e. prove that if $m$ is not equal to $n$ then $\gcd(a_m, a_n) = 1$. (begin by proving that $a_n∣ (a_{n+1} - 2)$) Finding the error in this proof that 1=2 I have a "proof" that has an error in it and my goal is to figure out what this error is. The proof:  If $x = y$, then  $$ \begin{eqnarray} x^2 &amp;=&amp; xy \nonumber \\ x^2 - y^2 &amp;=&amp; xy - y^2 \nonumber \\ (x + y)(x - y) &amp;=&amp; y(x-y) \nonumber \\ x + y &amp;=&amp; y \nonumber \\ 2y &amp;=&amp; y \nonumber \\ 2 &amp;=&amp; 1 \end{eqnarray} $$    My best guess is that the error starts with the line $2y = y$. If we accept that $x + y = y$ is true, then   $$ \begin{eqnarray} x + y &amp;=&amp; y \\ x &amp;=&amp; y - y \\ x &amp;=&amp; y = 0 \end{eqnarray} $$  Did I find the error? If not, am I close? R script line numbers at error? Writing a function inside the main method - Java Which props in Star Trek: Picard are reused from the original TNG show and films (if any)? Why can we treat quantum scattering problems as time-independent? From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this:   Solve the time-independent Schrodinger equation to find the energy eigenstates.  There will be a continuous spectrum of energy eigenvalues. In the region to the left of the potential, identify a piece of  the wavefunction that looks like $Ae^{i(kx - \omega t)}$ as the incoming wave. Ensure that to the right of the potential, there is not piece of the wavefunction that looks like $Be^{-i(kx + \omega t)}$, because we only want to have a wave coming in from the left. Identify a piece of the wavefunction to the left of the potential that looks like $R e^{-i(kx + \omega t)}$ as a reflected wave. Identify a piece of the wavefunction to the right of the potential that looks like $T e^{i(kx - \omega t)}$ as a transmitted wave. Show that $|R|^2 + |T|^2 = |A|^2$.  Interpret $\frac{|R|^2}{|A|^2}$ as the probability for reflection and $\frac{|T|^2}{|A|^2}$ as the probability for transmission.   This entire process doesn't seem to have anything to do with a real scattering event - where a real particle is scattered by a scattering potential - we do all our analysis on a stationary waves.  Why should such a naive procedure produce reasonable results for something like Rutherford's foil experiment, in which alpha particles are in motion as they collide with nuclei, and in which the wavefunction of the alpha particle is typically localized in a (moving) volume much smaller than the scattering region? Changing password? I would like to change my password.  I have followed the instructions in  but I cannot find the "my logins" hyperlink. Equifax credit score discrepancy in 1 month, why? I just went to Citi Bank's website (which gives free FICO scores from Equifax for users of some credit cards) and I realized that the score I saw there was a whopping ~50 points higher than the number I saw on Mint.com, despite the fact that they both claim to have received the number from Equifax. The only difference is the fact that Mint checked my score at the end of February 2015, whereas Citi checked it at the end of January 2015.  However, nothing unusual has happened to my credit history in between these two. I can confirm on Mint's credit report that nothing seems wrong, so I'm quite confused:   What can cause such a discrepancy? Whom should I contact to understand what is going on -- Mint, Citi, Equifax, or other? How should I contact them -- file a dispute, call them, or go somewhere in person?   Note that I don't feel I'm "disputing" anything, since I don't know if there is any cause for a dispute, and hence I'm not sure it makes sense to open a dispute with Equifax. I just want to know what is going on and why two third-party agencies claim to have received such wildly different numbers from the same agencies in the span of 1 month. I have been learning English for 7 years now, and I have read so many grammar books with rules, telling the difference between Present Perfect and Past Simple and I still find it hard to distinguish them.   On paper, it is easy, if it is not a certain (exact) time in the past without any time markers (yesterday, a month ago, etc) it is past simple. Yes, but outside the classroom it is really harder than this . I have heard many people speaking how they want to, mixing the tenses.   So, I will give these sentences which i have heard to be constructed differently, please, if someone can explain the difference to me.     Have you enjoyed the party? / Did you enjoy the party?      I have given the documents today. / I gave the documents today.      I have done this when I have revised it. / I did it when I revised it      What did you do today? / What have you done today ?   Is it possible to use past simple without mentioning a definite time in the past  (without the time markers)?     It has been 3 years since we moved house. / It has been 3 years since we have moved house.      I know him since we met each other/ I know him since we have met each other   Correct me if some of the sentences are grammatically wrong! Are $T\mathbb{S}^2$ and $\mathbb{S}^2 \times \mathbb{R}^2$ different? I have seen the claim that $T\mathbb{S}^2$ and $\mathbb{S}^2 \times \mathbb{R}^2$ are not diffeomorphic, but I have only ever seen the proof that they are not isomorphic as vector bundles (which is a cute application of the hairy ball theorem). How would I prove that they are indeed not diffeomorphic (or better, not homeomorphic)? Why are C character literals ints instead of chars? In C++, sizeof('a') == sizeof(char) == 1. This makes intuitive sense, since 'a' is a character literal, and sizeof(char) == 1 as defined by the standard.  In C however, sizeof('a') == sizeof(int). That is, it appears that C character literals are actually integers. Does anyone know why? I can find plenty of mentions of this C quirk but no explanation for why it exists. Is a "split plot" ANOVA with two factors the same as two-way ANOVA with repeated measures in one factor? Is a "split plot" ANOVA with two factors identical to two-way ANOVA with repeated measures in one factor? if not, what is the distinction? How can I convert byte size into a human-readable format in Java? How do I choose between "as to", "on", "of", and "about"? What's the best way to parse an XML dateTime in Java? Area enclosed between the curves $y=x^2$ and $y=60-7x$ What library do I have to use such that the document can render \lt and \gt as less than and greater than signs, respectively? \documentclass{article} %\usepackage{amsmath} It does Not work ! \begin{document} \[ x\lt y \gt z \] \end{document}  What library do I have to use such that the document can render \lt and \gt as less than and greater than signs, respectively? Edit I am using MathJax library in my site under Asp.net Mvc 3. Web application is vulnerable to XSS and XSRF attacks so &lt; and &gt; should be avoided as the input from the users. My database will save LaTeX commands that can be rendered by both LaTeX compiler and MathJax. Therefore, I need \gt and \lt that already work in MathJax. Source:  Rendered: How can I increase my Vault Dweller's Happiness? Is a join optimized to a where clause at runtime? What are the alternatives to OS X's Spotlight?