In an e-mail to a superior, should I write "I shall create a page", or "I will create a page"?
Which is the correct use of these two words, and in which context should one be used rather than the other?
I looked up a few grammar-teaching websites (in Chinese language). The website says many people do not use the phrase "A xxx of" correctly because they do not identify the subject of the phrase correctly.   The website says phrases like "A range of; A high percentage of" is singular, while "a number of; a group of; a couple of; a total of" is plural.  Therefore according to the website, the correct sentences should be as follows.     A wide range of courses is available. ("A wide range" is the subject)      A high percentage of peptides that are made of amino acids is present   in the sample. ("A high percentage" is the subject)      A number/ group/ couple of people were killed in the earthquake.("people" is the subject )       A total of 230 employees were laid off. ("employees" is the subject)   I don't get the pattern here. All of this looks (or should I use "look"?) arbitrary to me. In fact I thought this phrase is supposed to be arbitrary and whether the phrase is plural or singular should depend on the the person's own judgment.   How do I identify the correct subject in the "A xxx of" phrase? List of Stored Procedure from Table I have a huge database with 100's of tables and stored procedures. Using SQL Server 2005, how can I get a list of stored procedures that are doing an insert or update operation on a given table. Price Optimization I ran linear regression on my hotel reservation data and obtained the following model fit in R:  Sales = 170.2 + 3.6*Days_left_to_checkIn + 7.6*Revenue - 9.6*Room_Rate -7.67*cancellation_price + 4.8*Number_of_cancelled_Room -8.9*Online_reputation_of_Hotel  After this, I used the Optimize function to optimize the equation for maximum revenue (Revenue = Room_Rate* Sales)  after substituting all the values of variables I got this equation  f=-9.6*Room_Rate^2 + Room_Rate*253.56  Optimize(f, lwr=10, upr=524)  What is the next step to calculate Room_Rate to maximize the revenue (revenue = Room_Rate * Sales)? Is there any better way to optimize the function of demand? I've read that it is possible to add a method to an existing object (i.e., not in the class definition) in Python.   I understand that it's not always good to do so. But how might one do this? A $60\times 60$ board is partitioned into rectangles of size $2\times 5$ (or $5\times 2$). Is it true that there always exist another partition into rectangles of size $1\times 3$ (or $3\times 1$) such that any $2\times 5$ (or $5\times 2$) rectangle contains a $1\times 3$ (or $3\times 1)$ rectangle?  For the "simple" partition into $2\times 5$ rectangles, this is certainly true: use the simple partition into $1\times 3$ rectangle.  Another way to partition is to first partition the $60\times 60$ board into $12\times 10$ boards, and then for each such board, put two $2\times 5$ at the top and ten $5\times 2$ below. It is not hard to tile each such $12\times 10$ board with $1\times 3$ (or $3\times 1)$ rectangles so that each $2\times 5$ (or $5\times 2$) contains a $1\times 3$ (or $3\times 1)$ rectangle.  (I'm assuming that an $m\times n$ rectangle has $m$ rows and $n$ columns.) Say I want to book a flight from Fort Lauderdale to Chicago.  Say the airline also flies to St. Louis from Fort Launderdale but has a connecting flight through Chicago.  If I book that flights from FLL->ORD->STL and just get off in Chicago, what possible problems can I run into, assuming I didn't check any bags and only have carry on?  This scenario exist for Southwest, but I wanted this be more of a general question that would apply to all airlines. Extract all string from a java project IndentationError: unindent does not match any outer indentation level How to use enum values in f:selectItem(s) A is similar to $A^k$, then each eigenvalue of $A$ is a root of unity Let $A \in \mathbb{C}(n,n)$ and $k \geq 2$ be an integer such that $$A \sim A^k$$. Show that if $A$ is non-singular then each eigenvalue of $A$ is a root of unity.   Attempt: Since $A \sim A^k$, $$PA = A^kP$$ where $P$ is an invertible matrix. Since $A$ is invertible, $0$ cannot be an eigenvalue of $A$. Suppose $$Av = \lambda v \quad v \neq 0$$ then $$PAv = \lambda Pv$$ $$\therefore A^k(Pv) = \lambda (Pv) $$ but this implies that $Pv$ is an eigenvector of $A$. But the eigenvalues of $A^k$ are $\lambda^k$ $$\therefore \lambda^k=\lambda$$ which gives the conclusion required.   My questions is: Is the logic correct? If so, Am I missing any details? If not, then how could I approach this?   Thanks! Why is the $S_{z} =0$ state forbidden for photons? $\sum_{n=1}^\infty \log \frac{n+1}{n}$  $\sum_{n=1}^\infty \log \frac{n+1}{n}$ =  $\displaystyle\lim_{n \to{+}\infty}(\log2 - \log1)+(\log3-\log2)+...+(\log(n+1)-\log n)$=$\displaystyle\lim_{n \to{+}\infty}\log(n+1)\to \infty$. So, the series diverges.  Is my procedure correct? How can I write a spiral symbol? How can I get a spiral like    There seems to be a spiral-like unicode codepoint:   I tried  \documentclass[varwidth=true, border=2pt]{standalone} \usepackage[ngerman]{babel}  \usepackage[utf8]{inputenc} % Color \usepackage{color} \definecolor{lightgray}{gray}{0.95}  \DeclareUnicodeCharacter{43612}{\spiral}  %document \begin{document}{\textcolor{lightgray}{a}}\spiral{\textcolor{lightgray}{b}} \end{document}   but I got  ! Undefined control sequence. l.13 ...document}{\textcolor{lightgray}{a}}\spiral                                               {\textcolor{lightgray}{b}}   edit: I know . None of the answers gave me a spiral symbol. Can I charge computers by inducing 5-volt into their USB connectors? Is this possible? I noticed that when my EeePC 900 is off but plugged in charger, there is power coming out of the USB port. Can this be a sustainable way of charging a PC, or a flaw in design? Merging two incoming broadband lines for faster Internet Make clear which profile data is visible to whom Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge? Does the following series converge or diverge? $$ \sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}} $$ The methods I have at my disposal are geometric and harmonic series, comparison test, limit comparison test, and the ratio test. Why use sucrose rather than glucose in an injectable vaccine? I want to show that the two annuli $$A=\{r&lt;|z-z_0|&lt;R\} $$ $$A'=\{r'&lt;|z-z_0'|&lt;R'\} $$ are conformally equivalent (i.e. there exists a biholomorphic map between the two) iff $$\frac{R}{r}=\frac{R'}{r'}. $$  Sufficiency:  Suppose the ratios of the radii are the same. A suitable scaling (by $\frac{r'}{r}$) will make $A$ congruent to $A'$, and a translation will map the scaled $A$ onto $A'$. This is clearly a conformal homeomorphism.  Necessity:  The annulus $A$ has the following set of periods $$\left\{ \pm \frac{2 \pi}{\log (R/r)} \right\} $$ (this step required some computations which I will omit)  Similarly $A'$ has   $$\left\{ \pm \frac{2 \pi}{ \log(R'/r')} \right\}$$ as its set of periods. Since the set of periods is a conformal invariant. The ratios of the radii must indeed by the same.  Is this proof correct?   Thanks! Do reactions interrupt their triggers or not? In the Player's Handbook, it is pretty clear that reactions normally interrupt the thing that they are reacting to.    Xanathar's Guide to Everything, however, has explicitly changed all reactions to occurring after their triggers have finished resolving unless the ability specifies otherwise, and is reliant on that implicit assumption for several reaction abilities already.  This leads to contradictory interpretations of reactions that take implicit timing. How should this be resolved?   I'm particularly interested in how to resolve this in Adventurers League games, where players show up with perfectly legal characters reasonably expecting their abilities to work either way on account of owning or not owning XGE.