A friend has written me a message in which she tells me that she is leaving tomorrow from Italy. I want to say that I hope that she had/ has had a great time here in Italy. What is the right way to say it? "I hope you enjoyed staying in Italy" or "I hope you have enjoyed etc.." Thanks.
Non-na­tive speak­ers of­ten get con­fused about what the var­i­ous tens­es  and as­pects mean in English. With in­put from some of the folk here I've put to­geth­er a di­a­gram that I hope will pro­vide some clar­i­ty on the mat­ter.  I of­fer it as the first an­swer to this ques­tion. Con­sid­er it a liv­ing doc­u­ment. In­put is wel­come, and good sug­ges­tions will be  in­cor­po­rat­ed in­to the di­a­gram.    No­ta bene: What this is not is a dis­cus­sion of whether there are  more than two tens­es in English. , to which this ques­tion is not in­tend­ed to sup­ply ar­gu­ments one way or the oth­er.  Here, the aim is to pro­vide an overview of what con­struc­tions English-speak­ing peo­ple use for con­vey­ing in­for­ma­tion about ac­tions re­fer­ring to past, present, and fu­ture, and to pro­vide it first and fore­most to pre­cise­ly the peo­ple who are like­ly to use "tense" as a catch-all term in their search, rather than to lin­guists who know bet­ter.  Break­ing News There is now an ex­cel­lent ELU blog ar­ti­cle ti­tled  . It is high­ly rec­om­mend­ed read­ing.
What do you call the process of combining two words to create a new one? How was this answer posted after this question was closed? Question:   Answer:   The question was closed at 11:57:57 (according to the hover-over-"x-mins-ago" bar) and the answer was posted at 12:16:35. It's a fairly lengthy answer, so it's possible that it was started to be written before it was closed but I swear I've started to answer a question then I got a banner along the top saying "this question has been closed" and the answer was no longer post-able. How would I create an arch? Why don't we consider centrifugal force on a mass placed on earth? Framing a question whose answer is an ordinal number I am the third daughter (or son) of my parents.   OR      How should a question that is answered with the above sentences be framed? Polynomial divisibility is unchanged by coeff. field extension I would like to verify the validity of the following line of thought:  Let $K \subset E$ be a field extension. Let $K[x]$ be the polynomial ring over $x$ and denote $K(x)$ its field of quotients (the rational functions over $K$).  Now assume $f(x)=g(x)h(x)$ with $f(x),g(x) \in K[x]$ and $h(x) \in E[x]$ and all $f$, $g$, $h$ are different than zero. Then $\frac{f(x)}{g(x)} = h(x)$ in $E(x)$. So $h(x) \in K(x)$. But $h(x)$ is a polynomial, so $h(x) \in K[x]$.  Is there any other simpler argument than that?  Added:  Let me be more specific. Let $x^p - a \in K[x]$, with $p$ being prime and $char(K)=p$. Let $b$ be the unique root of $x^p - a$ in its splitting field $K(b)$. Then $x^p - a=(x-b)^p \in K(b)[x].$ Let $m_b(x) \in K[x]$ be the minimal polynomial of $b$ over $K$. Then $m_b(x)$ divides $(x-b)^p$ and so $m_b(x)=(x-b)^l$ and $l$ is the smallest positive integer for which $(x-b)^l \in K[x]$. Let $p = lq+r$ where $0 \ge &lt;l$. Then $x^p-a=(m_b(x))^q (x-b)^r$. Can i conclude that $(x-b)^r \in K[x]$ and so $r=0$ by the minimality of $l$?  Thanks. I'm not sure how to solve this problem. Can you guys provide some input/hints?      Let $A=(x_1,y_1)$, $B=(x_2,y_2)$ and $C=(x_3,y_3)$ be three points in $\mathbb{R}^{2}$.      Show that the area of $\Delta ABC$ is given by   $\frac{1}{2}\left| \det(M) \right|$, where   $$M = \begin{pmatrix} 1 &amp; 1  &amp; 1\\  x_1 &amp; x_2 &amp; x_3\\  y_1 &amp; y_2 &amp; y_3 \end{pmatrix}$$ $\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$ I was thinking about something the other day (that is probably stupid), and thought this would be a good place to talk about it.  If someone wanted to draw its family tree over the last 1000 years, he'd write a binary tree with a depth of about 40 (counting 25 years on average between each generations). This tree would have 240 leaves, or about 1012 ancestors on the deeper level. That is obviously much more than the total world population and a stupid figure when you think about it.  The only explanation that I can think of is that a real genealogy tree must have "linked" branches at several levels that change the actual number of ancestors. Anyway, for an average person, how many ancestors would that make? Could one assume that all or nearly all of the persons that lived in its country or world region a 1000 years ago would be part of its ancestors? "Where" exactly are complex numbers used "in the real world"? How can I intercept XMLHttpRequests from a Greasemonkey script? Do Hutts find humanoid females attractive, and if so why? Jabba the Hutt kept scantily clad humanoid slaves.  Jabba even tried to kiss Leia.  But IIRC Hutts are hermaphrodites and of course should by all biological reasoning not be attracted to creatures of a specific sex (don't recall sexy dudes hanging around) with radically different body design.  So do Hutts find humanoid females hot, and if so why?  Or do they just do this for status and to show off to the largely humanoid populations that surround them? resetPassword problem for enterprise users when called from a community? I'm working within a custom application in a customer community that is used by both community-license users and Salesforce enterprise users.  There is a custom Visualforce page where an application admin can select a user and reset the password.  The VF Controller is using the standard System.resetPassword() method.  We are finding that when an enterprise user receives this password reset email, the user can't get to the expected password reset page.  Instead, it eventually redirects to the community login screen.  The password reset URL for these enterprise users is based on the community's URL, and it seems that these users cannot change password through the community -- it has to be through the enterprise URL, like what you get when you reset password via Setup.  Has anyone run into this and found a workaround?  (Of course community users have no trouble with password resets through this Visualforce page.) I'm stuck in full screen in the node editor. Escape isn't working, and I have no menus and no idea how to leave except to quit Blender and reopen the program. Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$ For the finite-dimensional case, we have a canonical isomorphism between $\mathbf{V}$, a vector space with the usual addition and scalar multiplication, and $(\mathbf{V}^*)^*$, the "dual of the dual of $\mathbf{V}$." This canonical isomorphism means that the isomorphism is always the same, independent of additional choices.   We can define a map $I : \mathbf{V} \to (\mathbf{V}^*)^*$ by $$x \mapsto I(x) \in (\mathbf{V}^*)^* \ \text{ where } \ I(x)(f) = f(x) \ \text{for any } \  f \in \mathbf{V}^*$$  My Question: what can go wrong in the infinite-dimensional case? The notes I am studying remark that if $\mathbf{V}$ is finite-dimensional, then $I$ is an isomorphism, but in the infinite-dimensional case we can go wrong? How? How to increase the Java stack size? Special Relativity - Regarding the Simultaneity of Events During the Train Paradox How to deal with travel excitement? How does one usually deal with excitement about travel, prior to travel ? A lot of people feel them butterflies in their stomach before a big travel is coming up. Is there an effective way to put these feelings away ? Or how can one best deal with such excitement/feelings (which almost cause interference with day to day activities) ? help with some Hilbert style proofs in a propositional logic axiom system. I'm very new to classical propositional logic, and my lecturer is using a system with the following axioms:  A1. X→(Y→X)  A2. (X→(Y→Z))→((X→Y)→(X→Z))  A3. (¬Y→¬X)→(X→Y)  Use uniform substitution and Modes Ponens (MP) as rule of inference. Deduction Theorem also allowed.  I'd like to deduce the following:  (a) X, Y ⊢ ¬(X→(¬Y)) (conjunction, but expressed in terms of NOT and IMPLIES)  (b) X→((X→Y)→Y)  (c) (X→Y)→(((¬Y)→X)→Y)  (d) (((¬Y)→X)→Y)→(X→Y)  Remark: The last two are to show that the axiom (A3) can be replaced with a different axiom:  B3. (¬Y→¬X)→(((¬Y)→X)→Y).  Solution: Bram28 proves (b) and (c) below. I demonstrate (a) and (d).  (d) is alright; first, I claim that X, ((¬Y→X)→Y) ⊢ Y.  Axiom (A1) gives ⊢X→(¬Y→X) so that ((¬Y→X)→Y)⊢X→Y by Hypothetical Syllogism (HS), which Bram28 shows to be valid.  Now that we have ((¬Y→X)→Y)⊢X→Y just apply the deduction theorem to get what we want: ⊢((¬Y→X)→Y)→(X→Y).  (a) is slightly trickier. Axiom (A1) gives ⊢ Y→(X→Y) so that X, Y ⊢ (X→Y).  Next, by part (b), we have as a theorem that ⊢X→((X→¬Y)→¬Y).  Therefore X, Y ⊢(X→¬Y)→¬Y.  But ⊢(¬¬(X→¬Y))→(X→¬Y) by DN Elim, which Bram28 shows to be valid.  By HS, X, Y ⊢(¬¬(X→¬Y))→¬Y.  By Axiom (A3) and MP, X, Y ⊢(Y→¬(X→¬Y)).  Also, rather trivially X, Y ⊢Y.  Finally by MP we conclude X, Y ⊢¬(X→¬Y) as required. 1099 for settlement what about lawyer fees? I am getting a settlement from a business over a suit but most of the settlement will go to the attorney to cover their fees incurred on contingency.  If the 1099 reports the full settlement, will I have to pay taxes on the full amount or if not, how do I tell the IRS it is not all taxable. Otherwise, I could easily end up owing more in taxes than I get for my small portion.