The organ in Las Pinas Church is made entirely of bamboo. The organ in Las Pinas Church was made entirely of bamboo. Whic is more suitable,is made or was made?
Suppose a book consists of three sections:     The book is/was divided into three sections.   I am thinking the past tense option "was" should be used, because the act of dividing the book into three sections happened at the time of writing. Is my analysis good?
Keep box-shadow direction consistent while rotating Looking for solo (one person) RPGs - do they exist? I am looking to find out if solo RPGs exist, and which you'd recommend.  I do not mean "one-on-one" 1 player + 1 GM games. I really mean "1 person."  Update: After receiving two (fine, up-voted) answers that indicate Choose Your Own Adventure solutions (which rocks with nostalgia), I should add that I'm not looking for simple linear decision tree gaming. A counterexample: I've got my own little creative-writing mini-game where I write out a story, but once every 5 sentences a series of dice-rolls forces my written sentence into something else, and I have to adapt as writer. Not really an RPG, but also non-linear. I already found the radius of convergence of the power series $:$ $$\sum_{n=1}^{\infty} \frac {(-1)^n} {n} z^{n(n+1)}.$$ What happens at the boundary of disk of convergence?  I found that the radius of convergence to be $1$ and hence the disk of convergence is $|z|&lt;1$. Now I found at $z=1$ the series converges. Now how can I proceed? Please help me. Thank you in advance. For any real number $a \geq 1$ let $f(a)$ denote the real solution of the equation $x(1+\ln x)=a$ then the    question is to find out $$ \lim_{a \to \infty} \frac{f(a)\ln a}{a}$$.  It is clear that if we denote $h(a)$ by $h(a)=a(1+\ln a)$ then $f(a)$ is the inverse function of $h(a)$. Also $f(a)$ is increasing function in its domain. Also the limit persuades using lhospital's but I cannot see how to apply it here. Thanks. Recovering eigenvectors from SVD Problem recreating BCD on Windows 7 64bit - The requested system device cannot be found If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric How do I SOSL across objects, matching all records with FIND clause? How to understand degrees of freedom? From , there are three interpretations of the degrees of freedom of a statistic:     In statistics, the number of degrees of freedom is the number of   values in the final calculation of a statistic that are free to vary.      Estimates of statistical parameters can be based upon different   amounts of information or data. The number of independent pieces of   information that go into the estimate of a parameter is called the   degrees of freedom (df). In general, the degrees of freedom of an   estimate of a parameter is equal to the number of independent scores   that go into the estimate minus the number of parameters used as   intermediate steps in the estimation of the parameter itself (which,   in sample variance, is one, since the sample mean is the only   intermediate step).      Mathematically, degrees of freedom is the dimension of the domain of a   random vector, or essentially the number of 'free' components: how   many components need to be known before the vector is fully   determined.   The bold words are what I don't quite understand. If possible, some mathematical formulations will help clarify the concept.  Also do the three interpretations agree with each other? Evaluate $\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$ Evaluate $$\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$$  We can write as $\displaystyle\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$ $$= \lim_{n \to \infty}\left[\frac{(n +1)(n+2) \cdots (n+n)}{n^n}\right]^{\frac{1}{n}} = \lim_{n \to \infty}\left[(1+\frac{1}{n})(1+\frac{2}{n})\cdots (1+\frac{n}{n})\right]^{\frac{1}{n}}$$  I have used this result if $\{a_n\}$ is a sequence of positive term which is convergent to $l$ and $b_n = (a_1. a_2 . \cdots a_n)^{1/n}$ ,thhen $b_n$ converges to $l$  here $a_n = 2$, but i think it is not right,how to use this result in this question. Give me hint how to proceed . Thank you I'm working on an exercise from functional analysis.  Let $E$ be a vector space and $\|\cdot\|_1$ and $\|\cdot\|_2$ be two complete norms on $E$. Now suppose that $E$ satisfies the following property:  $\bullet$ if $(x_n)$ is a sequence in $E$ and $x,y\in E$ such that $\|x_n-x\|_1\to 0$ and $\|x_n-y\|_2\to 0$, then $x=y$.  Now we want to show that the norms $\|\cdot\|_1$ and $\|\cdot\|_2$ are equivalent.  My idea is as follows: If for any $n&gt;0$, there is an element $x_n\in E$ such that $\|x_n\|_1&gt;n\|x_n\|_2$. Then consider $(\frac{x_n}{\|x_n\|_1})_{n\geq 1}$. Clearly, $(\frac{x_n}{\|x_n\|_1})_{n\geq 1}$ converges to $0$. However, I cann't get a contradicition from this. Maybe my idea is wrong.   In fact, I even don't konw how to show that a Cauchy sequence in norm $\|\cdot\|_1$ is also a Cauchy sequence in norm $\|\cdot\|_2$.   Anyone can give me some hints or a counter example? Thank you very much. Microsoft.Office.Interop.Excel doesn't work on 64 bit Let $G = \mathbb{R} / \mathbb{Q}$. Is this an interesting group to study?  Is it isomorphic to any more natural mathematical objects? How to generate all permutations of a list? Why is the direct product of a finite number of nilpotent groups nilpotent? Positive operator has a positive spectrum? Let $T : \operatorname{dom}(T) \rightarrow H $ be a positive self-adjoint operator, is it then true that $\sigma(T) \subset [0,\infty)$? This is something that sounds natural and I guess that it is true. For bounded operator, this can be easily shown, but the only proof I know cannot be adapted to unbounded operator, so I was wondering if anybody here knows how to show this? How can I have a Linux machine join a Windows Domain? Sorry if I am misusing terms here; I actually don't know much about Active Directory and the related technologies.  Basically I have a Linux computer and I'd like it (or my user on that computer) to be associated with my user on the Domain, so that I can browse the network and all that stuff windows has.  Is this feasible?  What do I need to look into to do something like this? How to find Windows 7 File Transfer History? Suppose that $n \ge 2$. How to prove that the set $\mathcal D \subset M_n(\mathbb R)$ of the diagonalizable real matrices is not dense in $M_n(\mathbb R)$? I came across a reference to it recently on  and (as of now) it is not explained.  I suspect  might be it, but I don't know for sure.