For example, current time is 10:10.  then when will the train leave?   The train will leave in 10 minutes. The train will leave in 10 minutes' time. The train will leave after 10 minutes.   If the train leave at 10:20, what can we say?
The class will be over in 10 minutes. The class will be over after 10 minutes.  I know the first is correct but why?
Does pointwise convergence of continuous functions on a compact set to a continuous limit imply uniform convergence on that set? The problem is in Marsden - Elementary Classical Analysis 2nd ed. Ch.5.  My approach was   Condition : $f_k, f(\in\mathcal C) : A\to N$, $f_k \to f \ \text{(pointwise)}$ and $A$ is compact. Since $A$ is compact, the range of $f_k, f$ are all compact, so bounded. Since $f_k, f\in\mathcal C_b$, if $\|f_k-f\|\to 0$ in $\mathcal C_b$ then $f_k\to f \ \text {(uniformly)}$.   when the norm of $\mathcal C_b$ is defined by $\|f\|=\sup\{\|f(x)\||x\in A\}$.  I got stucked in 3, showing $\|f_k-f\|\to 0$. I don't even know the proposition is true. Can anyone give me some hint to solve this or a counterexample for this? Why is diamond transparent while graphite is not? Diamond and graphite are both made of the same atom, carbon. Diamond has a tetrahedron structure while graphite has a flat hexagonal structure. Why is diamond transparent while graphite is not (at least not with more than a couple of layers)? Hello I'm writing a beamer presentation and I would like to change the colour of the text in the theorem block from one place and it will affect my whole presentation.  Is this possible?  My example:  \documentclass{beamer}   \usetheme{Madrid}   \usecolortheme[RGB={201,20,35}]{structure}   \setbeamercolor{background canvas}{bg=black}  \setbeamercolor{normal text}{fg=white}   \setbeamercolor{theorem text}{fg=black}    %\useoutertheme{shadow}  \useinnertheme{rounded}   \usepackage[utf8]{inputenc}  \usepackage{default}   \begin{document}   \begin{frame}{Primul Slide}   Bla bla bla    Bla bla bla   \begin{theorem}  This is a theorem it is very important!!  \end{theorem}   \end{frame}   \end{document} I have a common scenario in app design, where I need to store an ordered list, and make the ordering easily accessible and adjustable via an application UI.    The ordering operations are simple and operate on only one item at a time - move to top, move to bottom, move up one position, or down one position.  These positioning operations may be interspersed in with typical add / edit / delete list operations.  For discussion, this is a single-user app and db store.  Because the objects can be highly complex, I'd like to avoid caching the entire list client-side, and tracking newly created objects in memory until a big save operation occurs.    I am using MS-SQL almost exclusively on these projects, and I'm wondering if there are db features, SQL features, or design patterns I should be using to better support the management of ordered lists.    My current approach is to use a DECIMAL column to store the list positions, which become fractional during the item move process.  Then I sort the list and re-generate integer positions to normalize list.  Following this operation, it's ready for another item move.   In an example implementation, I create a column named Seq for position tracking.  Once decimal place is enough for the .5 storage.   [Seq] [decimal](10, 1) NOT NULL   When an item is re-positioned in the app UI,    I UPDATE that record with new Seq value I retrieve the full table, sorted ascending by Seq and regenerate all Seq values in the table from a 1-based integer series   The new Seq value is easily calculated-    Move to top = 0 Move to bottom = MAX(Seq) + 1 Move up = subtract 1.5 from the current Seq value Move down = add 1.5 to the current Seq value   As lists get longer, updates get slower, since I'm doing N UPDATE statements, where N is the number of rows in the table, so it seems only suitable for small tables.    Is there some kind of in-built capability for managing an ordered list in SQL or MS-SQL? Is there a means to update multiple rows in one call?    A far more performant approach would be to allow more decimal places, and then position at the median of the two adjacent items, with no re-sequencing on the list.     Move to top = Min(Seq) - 1 Move to bottom = MAX(Seq) + 1 Move up = median of the 2 previous item Seq values Move down = median of the 2 following item Seq values   This approach only requires one SELECT (containing 2 rows max) and one UPDATE.    However with enough re-positions I imagine the field would run out of decimal places. For example, if I start with items at positions 10 and 11, and keep moving items down the list from position 9, they'd be given sequences of 10.5, then 10.25, then 10.125.  After 10 moves, the positions get lengthy... 10.0009765625.    UPDATE #1 - IMPROVED RE-SEQUENCING OF THE LIST  Regarding re-sequencing, I'm more caught up on row_number(), OVER, and WITH capabilities in MS-SQL.  It's nice to find that there's a much smoother way to re-sequence the list in a single UPDATE operation;  with OrderedItems as  (     select         ItemID,         Seq,         row_number() over (order by Seq asc) NewSeq     from          Items ) update OrderedItems set Seq = NewSeq Simplifying the integral $\int\frac{dx}{(3 + 2\sin x - \cos x)}$ by an easy approach login and payoff are nouns. But can they be used as verbs? I know that words like login and payoff are properly nouns but I increasingly notice many (not at all uneducated) people use them as verbs:     Will you payoff your credit card this month?   and     Please check this when you login.   To me (a non-native English user), that seems incorrect because separating the core noun from a preposition is what I was taught: Please check this when you log in. (My emphasis)  Is this use proper or not? Alternate property name while deserializing Why must a planet be in a star's "habitable zone" to have life? Analytic solution for $x=\ln(x+1)$ Finding the limit of $\frac{Q(n)}{P(n)}$ where $Q,P$ are polynomials Suppose that $$Q(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0} $$and $$P(x)=b_{m}x^{m}+b_{m-1}x^{m-1}+\cdots+b_{1}x+b_{0}.$$ How do I find $$\lim_{x\rightarrow\infty}\frac{Q(x)}{P(x)}$$ and what does the sequence $$\frac{Q(k)}{P(k)}$$ converge to?  For example, how would I find what the sequence $$\frac{8k^2+2k-100}{3k^2+2k+1}$$ converges to?  Or what is $$\lim_{x\rightarrow\infty}\frac{3x+5}{-2x+9}?$$   This is being asked in an effort to cut down on duplicates, see here: Coping with  duplicate questions.  and here: . How does "virus been detected" on android pop up on chrome when visiting some sites? What is the cause of this chrome bug on android? The last site I went to was www.destructoid.com and all of a sudden it gets redirected to the following url. This happened previously awhile back, but I didn't document everything as I did today. I'm also on android chrome canary if that matters.   I took some screenshots before closing out of that tab. But my question is:   What chrome bug or malware is causing these random redirects? How can one detect if they have this vulnerability?   The url is: I have, not one but two microSD cards that my phone (Samsung Galaxy Young, Gingerbread OS) seem to have broken. One is 1GB and the other is 2GB. The 1GB one won't be formatted.  When I put the 1GB one into the computer the computer prompts for a formatting. I don't care for the content so I tried to format it, but to no avail; the format fails and I have no idea what to do to make it work again.  I tried using the SDformatter software, but it can't format the card as it is write protected. I'm googling to solve it but so far no success.  My computer OS is win7 if that's of any relevance. Why does bool(xml.etree.ElementTree.Element) evaluate to False? Install CentOS 7 on HP dl120 gen9 server with b140i raid controller I'm trying to install CentOS 7 on a HP DL120 gen 9 server with a b140i controller. I have 4 1TB HDD setup in a raid 1+0 and the CentOS installer doesn't seem to recognize the logical drive created from the storage utility.  From my understanding i need some drivers for CentOS 7 to recognize the B140i controller. Also, the driver seems to be closed source by HP.  What is my approach here? Is there any other free linux OS that i can use on this server and that would recognize the raid controller?  Thank you. Is there a way to mix LIKE operator with IN ? Something Like  SELECT Id FROM Account WHERE Name LIKE IN:nameList   Where nameList is list of String? Is this is possible ? (I can make a dynamic query by doing OR with all the elements, but was looking for a more elegant way to do this) I am trying to do a new environment or command (i tried both) where i can put in the name, description and code of a Method in c++ and it gives me a new section with the MethodName, the code listed and the description below. But i am not able to use the listings environment in a new command or new environment.. Consider my MWE   \documentclass[a4paper,11pt]{article} \usepackage{listings}  \newcommand{\method}[3] { \section{#1}\label{#1} \begin{lstlisting} #2 \end{lstlisting} #3 }   \begin{document}  \method{MethodName}{Method Void MethodName()}{Description of the Method blablabla}  \end{document}   How can I fix this?   I would prefer to do it using a macro since I don't need an ending. Did Voldemort die or stay in limbo after the final battle? In Harry Potter and the Deathly Hallows, while Harry is in Kings Cross he sees something like a small child, which is the fragment of Voldemort's soul that was attached to him.     He recoiled. He had spotted the thing that was making the noise. It had   the form of a small, naked child, curled on the ground, its skin raw and rough, flayed-looking, and it lay shuddering under a seat where it had been left, unwanted, stuffed out of sight, struggling for breath.      He was afraid of it. Small and fragile and wounded though it was, he did not want to approach it. Nevertheless he drew slowly nearer, ready to jump back at any moment. Soon he stood near enough to touch it, yet he could not bring himself to do it. He felt like a coward. He ought to comfort it, but it repulsed him.      Harry Potter and The Deathly Hallows   Once Harry returns to the world of the living, that part of Voldemort's soul stays in limbo. Is this what happens to all fragments of someone's soul if he has divided his soul by creating a Horcrux? Does that mean that Voldemort's soul however crippled will stay in limbo or when all parts of his soul die, so does he? Intuition about Herbrand Models. I'm having trouble understanding how Herbrand models work. I feel like there is a bigger picture to it which I'm not understanding. Why does every satisfiable first order formula have a herbrand model at all ? Can I somehow construct a Herbrand model from a normal model ? My book also says that : a formula is unsatisfiable iff the Herbrand expansion is unsatisfiable. The book I'm using &quot;Mathematical Logic for computer science by Mordechai Ben-Ari&quot; has all the proofs of the above but its not very intuitive to me. Could somebody share their point of view? Help me understand the proof for Bolzano-Weierstrass Theorem! Group by alias (Oracle) How to 'group by' a query using an alias, for example:  select count(*), (select * from....) as alias_column  from table  group by alias_column   I get 'alias_column' : INVALID_IDENTIFIER error message. Why? How to group this query?