In:     a choice between one of two options   I would like to know if this is correct grammatically. I came across it in a scientific paper. I think the “one of ” part should be removed. Am I correct?
I need backup in pressing my case that the phrase “choose from one of four options” is grammatically incorrect. Is there some resource that can prove my case, that the incorrect phrase should be replaced with one of the two following ones?        Choose one of four options   Choose from four options
How do you prove that $e=\sum_{n=0}^{\infty}\frac{1}{n!}$? Here I am assuming $e:=\lim_{n\to\infty}(1+\frac{1}{n})^n$. Do you have any good PDF file or booklet available online on this? I do not like how my analysis text handles this... I am looking for a YA book about a boy who learns to use powers from a mind-adept, in a seemingly abandoned house. The adept helps him open his mind by using a cube. One of his powers, I believe, is to go into dreams of people that  he knows. He helps his young female neighbor friend by doing this, opening a door in her mind. He tries to open the mind-door of a local older bully, but finds out the young man can't be helped because he has been abused mentally and physically. I don't believe the book I read is past 1995. It might have the word "adept" in it. More than one 'Open xxxxx here as Administrator' I want the option to open a Command window or Powershell window as Administrator from the drive and directory context menus in Windows.   I can have either by creating and populating the special 'runas' registry keys shown below, but is there a way I can have both listed on the context menu and have both run as Administrator?  [HKEY_CLASSES_ROOT\Drive\shell\runas] ... [HKEY_CLASSES_ROOT\Drive\shell\runas\command] ... [HKEY_CLASSES_ROOT\Directory\shell\runas] ... [HKEY_CLASSES_ROOT\Directory\shell\runas\command] ... [HKEY_CLASSES_ROOT\Directory\Background\shell\runas] ... [HKEY_CLASSES_ROOT\Directory\Background\shell\runas\command] ... Why is "the set of all sets" a paradox, in Layman's terms? I've heard of some other paradoxes involving sets (i.e., &quot;the set of all sets that do not contain themselves&quot;) and I understand how paradoxes arise from them.  But this one I do not understand. Why is &quot;the set of all sets&quot; a paradox?  It seems like it would be fine, to me.  There is nothing paradoxical about a set containing itself. Is it something that arises from the &quot;rules of sets&quot; that are involved in more rigorous set theory? LCM is associative: $\ \text{lcm}(\text{lcm}(a,b),c)=\text{lcm}(a,\text{lcm}(b,c))$ Definition: The least common multiple of $a.b\in\Bbb{Z}$ is the smallest  $k\in\Bbb{N}$ that is divisible by both a and b.         Proposition: $\text{lcm}(\text{lcm}(a,b),c)=\text{lcm}(a,\text{lcm}(b,c))\tag{2}$    Proof: We want to show $\text{lcm}(\text{lcm}(a,b),c)\mid\text{lcm}(a,\text{lcm}(b,c))$ and $\text{lcm}(a,\text{lcm}(b,c))\mid \text{lcm}(\text{lcm}(a,b),c)$ such that $\text{lcm}(\text{lcm}(a,b),c)=\text{lcm}(a,\text{lcm}(b,c))$.  Let $k=\text{lcm}(\text{lcm}(a,b),c)$, then $c\mid k$ and $\text{lcm}(a,b)\mid k$, but if we let $l=\text{lcm}(a,b)$, then $a\mid l\,\,\text{and}\,\, b\mid l$. Therefore $c\mid k\,\,,a\mid k\,\,\text{and}\,\, b\mid k$, but then $\text{lcm}(b,c)\mid k$. Thus $\text{lcm}(a,\text{lcm}(b,c))\mid k$      Question: Does this makes sense, ifso can I do the same for $\text{lcm}(\text{lcm}(a,b),c)\mid \text{lcm}(a,\text{lcm}(b,c))$? plotting discrete signals I`m using the Newton-Raphson method for obtaining MLE for parameters for maximizing my objective function. At each iteration, I want to check that is the Hessian matrix negative definite or not and I see the Hessian matrix is not negative definite at some iterations. So, I want to use the Fisher scoring algorithm ( of derivation) In this situation, the Fisher information matrix is indefinite!! Is it possible? What are the reasons for this? Are the second-order derivatives wrong? Or are values of expectations incorrect? Permutation with prime order, fixed point Let $M$ be a finite set and $\varphi$ a permutation of this set with prime order $q$. How do I show that $\varphi$ has a fixed point if $q$ is not a divisor of $|M|$? For some results returned in Google Search, on the right side it displays the company details, logo, contact numbers, etc...   For example, see the following screenshot:    I'd like to know what contributes to this so that I can try to achieve it for my site too. Which package to use for presentations? Beamer, Prosper, or Other This is a general, community wiki  question to address non-specific "I need a CMS or Wiki that does x, y, and z..." questions.  If your question was closed as a duplicate of this question and you feel that the information provided here does not provide a sufficient answer, please open a discussion on .    I have a list of features that I want for my website's Content Management System (CMS) - where can I find a [free] script that includes all of them? Doubles rules in table tennis Edits on closed posts Should questions or answers on questions that are closed be edited, even if the question is closed and the edit does not change anything about the reason it's closed? Example:  was just edited, which I saw in the review queue. It certainly improves the answer, but since the answer doesn't really have to exist on SE at all (because the question is off-topic), should this edit be made? In my understanding, the only reason that the edit option for a closed question is not greyed out is so that it can be edited to make it comply with the SE rules. I am trying to understand an example from my textbook.  Let's say $Z = X + Y$, where $X$ and $Y$ are independent uniform random variables with range $[0,1]$. Then the PDF is $$f(z) = \begin{cases} z &amp; \text{for $0 &lt; z &lt; 1$} \\ 2-z &amp; \text{for $1 \le z &lt; 2$} \\ 0 &amp; \text{otherwise.} \end{cases}$$  How was this PDF obtained?   Thanks Given the following problem     Let $U$ and $V$ be finite dimensional vector spaces, such that $\dim(U) = \dim(V)$. Prove that $U$ and $V$ are isomorphic.   I was just wondering if somebody could critique and validate my proof.  Proof  Two vector spaces $U$ and $V$ are isomorphic if and only if there exists a bijection $\phi: U \to V$. That is, an invertible linear map between the two. Let $\dim(U) = \dim(V) = n$ and let $\left\{u_1, \dots, u_n\right\}$ and $\left\{v_1, \dots, v_n\right\}$ be bases for $U$ and $V$, respectively. It follows that any vector $u \in U$ can be written as  $$ u = c_1u_1 + \cdots + c_nu_n $$  We define $\phi: U \to V$ as  $$ \phi(c_1u_1 + \cdots + c_nu_n) = c_1v_1 + \cdots + c_nv_n $$  Observe that $\phi$ is invertible. That is, given a vector  $$ v = d_1v_1 + \cdots + d_nv_n $$  in $V$, we define $\phi^{-1}: V \to U$ as  $$ \phi^{-1}(d_1v_1 + \cdots + d_nv_n) = d_1u_1 + \cdots + d_nu_n $$  Since there exists a bijection between $U$ and $V$, they are isomorphic. We are using .Net to make web service calls the Salesforce API. Is there a way to know for sure that the calls are using TLS 1.2? Are there any API logs or records of the protocol is use in Salesforce we can review to be confident the change is working? Is there a limit as to how fast a black hole can grow? To evaluate limit of sequence $\left(\left( 1 + \frac1n \right) \left( 1 + \frac2n \right)\cdots\left( 1 + \frac nn \right) \right)^{1/n}$ How do I evaluate the limit of the following sequence $$a_n  = \left(\left( 1 + \frac1n \right) \left( 1 + \frac2n \right)\cdots\left( 1 + \frac nn \right) \right)^{1/n}$$   I tried to take log and then using cauchy $1^{st}$ theorem of limits but I coudn't do it.  Could someone kindly help? How do the Flashes breathe utilizing their super speed? The air pressure would be extreme. Do they run in a pressurized bubble? throwing a $k$-sided dice until you get every face the same number of times