Go + to + noun phrase
Is there a reason the British omit the article when they "go to hospital"?
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$? I'm trying to show that $\langle1-i\rangle$ is a maximal ideal of $\mathbb{Z}[i]$.  I started by assuming there is some ideal $A$ that properly contains $\langle1-i\rangle$, and then I want to show that $1 \in A$, and then I will have that $A= \mathbb{Z}[i] $, so $\langle1-i\rangle$ is maximal.  Is this the right approach?  Thanks  Second Attempt: Because $\forall a+bi \in \mathbb{Z}[i]$, we have $a+bi = (a+b) -b(1-i)$, then we have $a+bi - (a+b) = -b(1-i) \in \langle1-i\rangle$, which implies $a+bi +\langle1-i\rangle = a+b +\langle1-i\rangle$.  So every coset is of the form $c +\langle1-i\rangle$, where $c\in \mathbb{R}$.  Furthermore, $-i(1-i)^2=2 \in \langle1-i\rangle$. Write $c = 2q + r$, where $q,r\in \mathbb{R}$ and $r=0,1$.  Then because $2 \in \langle1-i\rangle$, we have $2q\in \langle1-i\rangle$ and therefore $2q= 2q+r-r = c-r\in \langle1-i\rangle$, so $c+\langle1-i\rangle = r+\langle1-i\rangle$, and every coset is of the form $0 + \langle1-i\rangle$ or $1 +\langle1-i\rangle$. Thus, $1 +\langle1-i\rangle$ is the only nonzero element, and is invertible with itself as its inverse.  Thus, $\mathbb{Z}[i]/\langle1-i\rangle$ is a field with two elements, and by a theorem, $\langle1-i\rangle$ must be maximal.  Is this correct? If someone who is otherwise healthy decided to drink fairly heavily and consistently over a long period of time, what is the healthiest way to do so?  Example: Stay extra hydrated by drinking more water, take a multivitamin, get more sleep, etc.  Obviously the best solution would be to cease drinking, but IF that person is stubborn and won't quit - what's the best way to go about it? Is there a way to add a timer to a Beamer presentation? in elisp's let, how do you reference a variable bound in the same let while binding another variable? Labelled in-line equation How can I make an overset symbol at the same size and height as \bar except with a different symbol? Apologies for the cryptic title, but I was not sure how best to phrase the question in one sentence. I am essentially trying the create a vector symbol with \rightharpoonup as the top instead of the arrow.  The output to the following code will feature an overset harpoon over x, next to a simple \bar{x}. Observe that on the left, the top symbol is significantly higher and bigger than on the right one.  \documentclass{article}  \usepackage{amsmath,amsfonts,amsthm,amssymb}  \newcommand{\vect}[1]{\overset{\rightharpoonup}{#1}}  \begin{document} $$ \vect{x} \quad \bar{x} $$ \end{document}   I would like to create something that looks in every way like the right hand symbol, except using something that looks like \rightharpoonup at the top.  If this command sequence already exists in LaTeX, please use that as an answer, because I have searched for and failed to find it so far. Identify this novel: youngsters psychologically tested for abilities/profession, hero wants to author the tests, society uses moving walkways How come Mortarboard is bronze and Enthusiast is silver? :   Silver  Enthusiast    Visited the site each day for 30 consecutive days   56.9k awarded Bronze  Mortarboard   Earned at least 200 reputation in a single day      15.4k awarded    It would seem that earning Enthusiast requires almost no effort while Mortarboard is highly non-trivial. This appears to be reflected in the award count (almost 4:1 in favor of enthusiasts).  So, why is the first one silver and the second one bronze?  (A similar question can be asked about Epic vs Fanatic and probably many other). Fingerprint activation in Dell Vostro 14 in Ubuntu 18.04 I have Dell Vostro 14 with OS Ubuntu 18.04.  I tried   sudo apt install -y fprintd libpam-fprintd   but not able to use fingerprint reader of my laptop. The number of books in economics that we need to buy (is/are) three 1) The number of books in economics that we need to buy (is/are) three.   or       2) A number of books in economics that we can buy for the course (is/are) available in the college book store.   Possible answers:  a)is  b)are  My approach:  I am confused here why is and are are used in the 1 and 2 sentence.  What they exactly mean according to subject verb agreement rules. I'm using the package braket for my physics notes, and this speeds things up a great deal but I'm constantly writing \ket{\psi} or \bra{\psi}, and because this specific pair of bra and ket appears so often, this gets repetitive and I would like a macro to speed this up.  However since the braket package works only in math mode, my attempt \newcommand{\ketp}{$\ket{\psi}}$ work when I'm writing in text mode, but when I'm writing in mathmode it breaks (unsurprisingly).  Is there any way I can get this command to work in both mathmode and textmode without having to define two different macros, one for each?    Thanks in advance for any help.  P.S. I'm certain this is a very simple question but I could find little to no explanation of this feature. Since Ubuntu 18.04 I can't drag a file e.g. image file to an open application such as Inkscape or  email message window. In Ubuntu 17.10 I was able to select the image file by clicking on it, and while holding down left mouse button I would hit the supper key displaying all open windows where for there I could then drop the file in any open app or folders. This is no longer possible/default behaviour since Ubuntu 18.04. Is there a workaround that would allow me to achieve this or even a way to recreate the same behaviour like in 17.10? Is my processor 64 or 32 bit? Is there any easy LINQ expression to concatenate my entire List&lt;string&gt; collection items to a single string with a delimiter character?  What if the collection is of custom objects instead of string? Imagine I need to concatenate on object.Name. If $R$ is an integral domain and a subring $S$ has identity $1_S$, how would you show that $1_S=1_R$ (here $1_R$ is the identity of the ring $R$)? I am unsure about what an integral domain really is and how the subring comes into play here. What graduation gown should a PhD-holder wear when later receiving a Master's in another field? Creating surface from points in ArcGIS for Desktop? how to create surface from points in ArcGis? I have a points (centroids of the neighbourhood and number of people living in every neighbourhood) and i would like to create surface that would present density of population. Maximum value of $\sin A+\sin B+\sin C$? I would like to know how can I customize the Ubuntu installer NOT customize Ubuntu, I just want to modify the installer.  We have a large environment here with lots of developers and since we don't use Windows, I want to customize the installer to automatically set the timezone to NYC, the keyboard layout to English USA, put the company logo in the installer etc... Space Expansion vs. Relative Motion Given 2 objects moving at some velocity $v$ relative to one another, is it possible to determine whether they are moving or whether the space between them is expanding?