Is 6:2(2+1)=1 or is 6:2(2+1)=9 ? I can't find any information regarding the order of multiplication without a sign. I'm sure that 6:2*(2+1) is 9, but I'm not sure about this.
Possible Duplicate:          Please, look at the picture?    Which calculator shows true result and how to prove achieved result?
The list view of Nautilus 3.6 shows the dates files were modified in a variety of ways: the hour and minute if modified on the current day, and the month and day if modified during the current year, and the year tacked on if modified during a previous year. I would like to see the entire date and time consistently on all the files (e.g.: Sat 20 Apr 2012 01:28:34 PM EDT).  I had this set up before, but I can't figure out how to do so with version 3.6. I did find this question, but the answers no longer apply to Nautilus 3.6:   How can I do so in Nautilus 3.6+? The equivalence between Cauchy integral and Riemann integral for bounded functions Definitions  Suppose $P\colon a=x_0&lt;x_1&lt;\dotsb&lt;x_n=b$ is a partition of $[a,b]$. Let $\Delta x_k=x_k-x_{k-1}$ and $\lVert P\rVert$ denotes $\max_{0&lt;k\le n}\Delta x_k$.  The Cauchy integral of a function $f$ on closed interval $[a,b]$ equals to $I$ if and only if for each $\epsilon&gt;0$, there's some $\delta&gt;0$, for each partition $P$ of $[a,b]$ such that $\lVert P\rVert&lt;\delta$, we have $\left\lvert\sum_{k=1}^nf(x_k)\Delta x_k-I\right\rvert&lt;\epsilon$.  Problem  If $f$ is bounded on $[a,b]$ whose Cauchy integral equals to $I$, then $f$ is Riemann-integrable and $\int_a^bf=I$.  Background  It's an exercise from our calculus(analysis) problemset book, and there's a hint: consider the partitions whose $x_k-x_{k-1}$ is a constant for different $k$'s, and try to estimate the Riemann sum for each of these partitions through the Cauchy integral.  I have no idea about such estimation. After drawing some pictures, I discouraged. I googled on the Internet and found an . I realized that it's a quite different approach and with some advanced techniques (such as the analysis of a positive measure set -- discontinuities). I hope there will be some simpler approachers, just as the hint says. I need a more detailed hint, or a solution. Can anybody help me? Thanks! Every partially defined isometry can be extended to a isometry I know that the following theorem holds true:  Let $S$ be a subset of $\mathbb R^n$, and let $f:S\to \mathbb R^n$ a map such that $d(p,q)=d(f(p),f(q))$ for every $p,q \in S$ (here $d$ is the usual euclidean distance). Suppose that $0 \in S$ and $f(0)=0$. Then $f$ can be extended to an orthogonal transformation of $\mathbb R^n$.  I have two questions:   Can someone give me a reference of a proof of this theorem? I believe that the previous theorem holds true also if we change $\mathbb R^n$ with $\mathbb C^n$ and "orthogonal" with "unitary", with nearly the same proof. Does it holds true also in the $ \ell^2$ space? With the same proof? Not flying the first leg of the journey – Company cancels the second-leg ticket I've a friend that booked a round-trip journey. He booked A-to-B and B-to-A. Somehow he needed to be earlier at location B, so he took a train and did not take the flight from A to B.  When he went to the airport to take the "back home" flight (B-to-A), he was informed that his ticket was canceled because he did not take the A-to-B flight. They canceled the ticket and sold it to someone else.  Is this normal? The company said it was their right to do so, and he could not get the flight back. The company was Iberia. How to delete GRUB entirely from GRUB rescue and boot Windows only Convergence of $U_n=\frac{1}{\sqrt{2n\sigma^2}}\left(\Sigma X_j-\Sigma Y_j\right)$ - central limit theorem Suppose that $U_n=\frac{1}{\sqrt{2n\sigma^2}}\left(\Sigma X_j-\Sigma Y_j\right)$,  where $X_1,X_2,\ldots$ and $Y_i,Y_2, \ldots$ are i.i.d. sequences of random variables with mean $\mu$ and variance $\sigma^2$ and the sequences $\{X_i\}$ and $\{Y_i\}$ are independent.  Then, for all real numbers $x$, show that, as $n\to \infty$,  $$\mathbb{P}(U_n\leq x) \to  \int_{-\infty}^{x} \frac{1}{(\sqrt(2\pi))} \:e^{-\frac 12{u^2}}\mathrm du $$ Approach  I tried to carry out the integration on the right, but this does not integrate nicely. It ends up involving an error function, so I figured this was the wrong was to go.  Should I be looking at convergence in probability to answer this question? Is Chebyshev's inequality relevant here? If so, how and how does that relate to the integral? The definite article implying the generic idea of something I know that the definite article "the" can be used to mean a generic idea of something as in "the lion is the king of the animals." In this sentence, the in "the lion" is used to imply the general image of lions, so not specifying a particular lion.   However, I am confused in identifying where a "the" in a sentence is used for a general idea or a specific reference. For example, in the sentence "the price of gas is soaring", I heard that "the" in the sentence is an example of the generic use of the. Although I can easily understand the generic use of "the" in the lion example, but I do not understand how there is an general idea about gas price. Soaring gas price is something real,and gas prices in different regions( in a hypothetical situation) can be different. So, if I say "the price of gas is soaring", do I mean the price of gas that is determined by the world's oil system or can I say "the gas price" even when I am indicating the state of gas price in "a particular region"?    I know it is even difficult to understand my question, but I hope someone could find what I am confused about and give an answer. How to set the close-laptop-lid-action? Is there a way to unfold a mesh? Is there a way to take a mesh, cut it with seams or sharp edges and flatten it, so that the faces stay the same shape and size?  Making paper models is one aspect, where you could use that technique.  No, I'm afraid SZ0Return is not going to do it properly.  And misusing the UV-unwrap is only a last option.    Note, while it's an option to revert to Blender 2.49 which had a script to do this, I'd like a solution that I can use inside the current workspace. This one seems to be a common question in most forums and all over the web, it is asked here in many formats that typically sound like this:  In SQL Server -  What are some reasons the transaction log grows so large? Why is my log file so big? What are some ways to prevent this problem from occurring? What do I do when I get myself on track with the underlying cause and want to put my transaction log file to a healthy size? I am working on Ubuntu 12.04 64bit.  I want to add "Open terminal here" to Nautilus context or right-click menu but it tries to download 32bit version from Internet. In order to show $e^{x+y}=e^{x}e^{y}$ by using Exponential Series, I got the following:   $$e^{x}e^{y}=\Big(\sum_{n=0}^{\infty}{x^n \over n!}\Big)\cdot \Big(\sum_{n=0}^{\infty}{y^n \over n!}\Big)=\sum_{n=0}^{\infty}\sum_{k=0}^n{x^ky^n \over {k!n!}}$$  But, where should I go next to get $e^{x+y}=\sum_{n=0}^{\infty}{(x+y)^n \over n!}$.  Thanks in advance. Let $L$ and $R$ be $n \times n$ matrices. I am trying to solve the following minimization problem  $$ L^{k+1} := \arg \min_{L} \lambda \|L\|_{\ast} + \frac{1}{2\mu}\|L-R^{k}\|_{F}^{2} $$ $$ \mbox{s.t.}\ L \succeq 0 $$  where $\|\cdot\|_{\ast}$ and $\|\cdot\|_{F}$ denote the nuclear and Frobenius norms, respectively. Also, $k$ expresses the $k$th iteration when solving an optimization problem successively.  I don't know how to solve this problem. Would you tell me the way? Write $\frac 11 + \frac12 + ...\frac1{(p-1)} =$ $\frac ab$.Such that $(a,b)=1$. Show that $p^2 \mid a$ $\text{if}$ $p\geq 5$.  I was trying to apply something with prime modulus, but I am unsure how exactly to go about it. Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$ Password Protect QGIS project On a shared computer, I have a QGIS project which links up to a PostGIS database that contains my data. If a user wants to access layers from the db, they have to enter the db credentials, so that's OK.   However, I have previously logged on and imported layers from my db into QGIS, and manipulated them in QGIS (styling options based on meta-data, etc.)... Anybody who opens my QGIS project can view these layers in QGIS, and can therefore see the data I wish to be protected in my db.  Is there a way to password protect my QGIS project? I'm aware there are been several similar questions, and some great answers with hints on how to prove this, for example  and .  But I've never really seen a detailed proof of the absolute convergence of the Riemann zeta function in the half-plane $\Re(s)&gt; 1$.  I hope there's interest on a detailed proof of this for reference. Here is my attempt. Please, fill in any detail that might be missing, or point out any mistake!  On $\Re(s)=\sigma&gt; 1$, we have  $$\sum_{n=1}^{\infty}\bigg|\frac{1}{n^s}\bigg|=\sum_{n=1}^{\infty}\frac{1}{n^\sigma}$$  and  $$\frac{1}{n^\sigma}\leq\frac{1}{n^{1+\epsilon}}$$  for any $\epsilon &gt;0$, so by the direct comparison test, if   $$\sum_{n=1}^{\infty}\frac{1}{n^{1+\epsilon}}$$  converges absolutely, then so do $\sum_{n=1}^{\infty}|1/n^s|$ and $\zeta(s)$.  By the integral test, the convergence of $\sum_{n=1}^{\infty}1/n^{1+\epsilon}$ is equivalente to the finitude of the integral  $$\int_1^\infty \frac{1}{n^{1+\epsilon}}=\bigg[-\frac{1}{\epsilon x^\epsilon}\bigg]=\frac{1}{\epsilon}$$  which holds for any $\epsilon &lt; \infty$.  Any correction or improvement is welcomed! Thanks in advance. What are C++ functors and their uses? I keep hearing a lot about functors in C++. Can someone give me an overview as to what they are and in what cases they would be useful? ON an American street, but IN a British one. Do the twain ever meet? In the United States, we say that someone lives on a street, whereas I've noticed that British people say in. For instance:     Bubba lives on Washington Street.   Colin lives in Cavendish Avenue.   I believe we both would use at when a number is given. For instance:     Bubba lives at 16 Washington Street.   Colin lives at 7 Cavendish Avenue.   I don't think it matters if it's a road, avenue, street, circle, or lane — as far as I know, in America, we always live on a street. Does it vary in British English, or is it always in? If it varies, what are the rules? If the center of a group $G$ is of index $n$, prove that every conjugacy class has at most $n$ elements. (This question is from Dummit and Foote, page 130, 3rd edition.)  Here is my attempt: we have  $|G| =|C_G (g_i)| | G : C_G (g_i)| $  $|C_G (g_i)| =|Z(G)| \cdot  |C_G (g_i):Z(G)| $.  Then   $|G|= |Z(G)|\cdot |C_G (g_i):Z(G)|\cdot | G : C_G (g_i)| $.  Then  $n = |C_G (g_i):Z(G)|\cdot  | G : C_G (g_i)| $.  But $|C_G (g_i):Z(G)|$ is positive integar as  $ Z(G)$ is   subgroup of  $C_G (g_i)$.  If $| G : C_G (g_i)|$ bigger than $n$, then $|C_G (g_i):Z(G)|\cdot | G : C_G (g_i)|$ is bigger than $n $.  But   $|C_G (g_i):Z(G)|\cdot | G : C_G (g_i)|=n$, contradiction.  Then $| G : C_G (g_i)|\le n$ and this completes the proof.   Is this proof right or not ??!!!