Should I use '' I had been listening to this concert since it started snowing, at seven.'' or ''I have been listening to this concert since it started snowing, at seven.'' I never know when to use present perfect or past perfect.
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.
How can I utilize the whole terminal, like htop or emacs do? I want to write a program that can "draw" in the terminal the same way as htop or emacs. By that I mean "get rid of the prompt and make the output dependent on the current size of the terminal".   To make this a bit more clear:   I want to use the terminal this way:     in stead of this way: Is it possible to load a raster file (e.g. geotiff or erdas img) directly into a Leaflet map? If so, can you guide me to the correct documentation or method to do this? I am trying to do this with the imageOverlay() function in Leaflet currently.   var imageUrl = 'http://localhost/test/my_raster.tif',         imageBounds = [[30.430224, -87.193133], [30.435867, -87.185944]];         L.imageOverlay(imageUrl, imageBounds).addTo(map);    I am new to Leaflet. Help with completing the proof: Any unbounded sequence is either infinitely large or has a convergent subsequential limit Given $\{x_n\}$ is an unbounded sequence, prove:   $$ \lim_{n\to\infty}x_n = \infty\ \  \text{or}\ \ \lim_{n_k \to \infty} = A $$   In other words any unbounded sequence either infinitely large or has a convergent subsequence.     Everything before udpate section is wrong.  Part 1. Proving $|x_n| &gt; M \implies \lim_{n\to\infty} x_n = \infty$  $\Box$ Start with the definition of an unbounded sequence: $$ \forall M &gt; 0 \in \Bbb R \ \exists N \in \Bbb N: \forall n &gt; N\implies |x_n| &gt; M $$  Suppose that: $$ \lim_{n\to\infty}x_n \ne \infty $$ That means: $$ \forall n\in\Bbb N\ \exists C &gt;0 \in\Bbb R : |x_n| &lt; C $$  Now taking $M^\prime = \max\{M, C\}$ we have that: $$ \begin{cases} \begin{align} \exists N \in \Bbb N : &amp;\forall n&gt;N \implies &amp;|x_n| &gt; M^\prime \\ &amp;\forall n \in \Bbb N: &amp;|x_n| &lt; M^\prime \end{align} \end{cases} $$  So we have arrived to a contradiction which means the assumption is wrong and: $$ \lim_{n\to\infty}x_n = \infty $$ $\Box$     Part 2. It's not clear to me how to prove that if unboundedness does not imply infinity limit then it must imply the existence of a convergent subsequence.   Two questions is my mind:   Is part 1 correct?  How do I proceed with the second part?     I'm using the following definition. $$ \lim_{n\to\infty}x_n = +\infty \stackrel{\text{def}}{\iff} \forall \epsilon &gt; 0 \exists N \in \Bbb N :\forall n &gt; N \implies x_n &gt; \epsilon \\ \lim_{n\to\infty}x_n = -\infty \stackrel{\text{def}}{\iff} \forall \epsilon &gt; 0 \exists N \in \Bbb N :\forall n &gt; N \implies x_n &lt; -\epsilon \\ $$ A sequence is considered infinitely large when: $$ \lim_{n\to\infty}x_n = \infty\ \ \text{when}\ \ \lim_{n\to\infty}x_n = + \infty \ \ \text{or} \ \ \lim_{n\to\infty}x_n = - \infty $$    Update.   Looks like i've messed up a lot of things. I will try once again. As shown in comments and answers the statement holds only in case: $$ \lim_{n\to\infty} |x_n| = \infty \iff \forall \epsilon &gt; 0 \exists N \in \Bbb N: \forall n &gt; N \implies |x_n| &gt; \epsilon $$  Consider the following: $$ \lnot P = \lnot\left(\lim_{n\to\infty}|x_n| = \infty \right) \iff \exists \epsilon &gt; 0\ \forall N_1 \in \Bbb N : \exists n &gt; N_1 \land |x_n| &lt; \epsilon $$  But on the other hand it is given that $x_n$ is unbounded: $$ Q = \forall M &gt; 0\ \exists N_2 \in \Bbb N : |x_{N_2}| &gt; M $$  Construct a negative expression for boundedness: $$ \lnot P = \exists M &gt; 0\ \forall N_2 \in \Bbb N : |x_{N_2}| &lt; M $$  If $S = \lnot P \implies \lnot Q$ then $S = P \lor \lnot Q$  Let $\epsilon = M$, choose $N = \max\{N_1, N_2\}$ then both statements are true and: $$ \exists \epsilon &gt; 0\ \forall N = \max\{N_1, N_2\}: \exists n &gt; N \land |x_n| &lt; \epsilon $$  Now either $P$ is true, which would mean $\lim |x_n| = \infty$, or $\lnot Q$ is true which would mean the sequence is bounded and hence contains a convergent subsequence. Why does inductor current lag the applied voltage at its terminal by 90 degrees? I studied electromagnetism and I am currently working with Inductors.  I could not figure out the physical reason based on electromagnetics on why inductor current lags the applied voltage by 90 degrees?  Everywhere I find the Formula as the starting point of explanation which is partially satisfying.    Induced EMF =L di(t)/dt    From the above equation, I understood that when there is a change in current there will EMF induced in the coil terminals. But How this induced EMF makes the current to lag the supply voltage V(t) = Vm*sin(wt)? (Please don't just differentiate and say there is a lag, I am looking for a physical sense on why this happens)  Lets us consider the AC voltage is applied across the terminal at time t=0; At this time there is almost no current. From this transient state how the steady-state is reached where the current is delayed with respect to the voltage?  Can someone help me to figure out why the current lags the Supplied voltage by using electromagnetism, the motion of Charges or any other basic concepts? Before the seasonal flu vaccine was recommended for all healthy adults, people in developed countries might get vaccinated against on the order of 10 different pathogens and develop immunity for some more via natural exposure.  Now the same person is expected to take a seasonal flu vaccine for a new strain every year - won't this put them in an uncharted territory as far as effects on the immune systems are concerned within a couple of decades? Java Serialization with non serializable parts I have:  class MyClass extends MyClass2 implements Serializable {   //... }   In MyClass2 is a property that is not serializable. How can I serialize (and de-serialize) this object?  Correction: MyClass2 is, of course, not an interface but a class. What is a suitable image resolution for canvas prints? I would like to create a 60 inch x 20 inch canvas print using an image with a resolution of 4759x1798 (240 pixels per inch) and I would like to know if the image quality will still be good at that size.  To generalise the question, what is the recommended maximum size of an enlargement at varying image resolutions?  e.g. 3 megapixel, 5 megapixel, 8 megapixel, etc We have a webservice that our application uses and the developers require https connections to the webservice.  Since this is an internal webservice would you use a self signed cert? Why exactly can't a single resistor be used for many parallel LEDs? Why can't you use a single resistor for a number of LEDs in parallel instead of one each? Why does println(array) have strange output? ("[Ljava.lang.String;@3e25a5") How can I be a good reviewer? Someday, as strange as it feels to me right now, I might be asked to review an article for publication. A while ago my advisor and I were talking about this, and it hit me that I don't really know how to be a good reviewer, beyond the basics:   Respond timely to things, Make your report clear and detailed, Have actually read the paper, Etc.   Beyond this, though, I'm completely in the dark. So I'd like to ask:     What's some good advice for a first-time reviewer?   My field is math, but I'm really interested in general advice (although advice specific to math, or another field, would also be interesting and useful).    I'd like to make this question "community wiki" or analogous, but I can't seem to figure out how - if someone can do so, please do, and then I will delete this paragraph. I saw a thing called VPN connections under the Internet button at the top of my screen.   So I would like more info on this, and possibly instructions on how to set one up. Thanks! Update Windows 8 Enterprise to Windows 8.1 Enterprise KMS activation So it is shown that volume license packages of Windows 8, like Pro and Enterprise, are unavailable for upgrading.  I received a link last night to download the Windows 8.1 Enterprise 90-day Evaluation, but it will replace my current Windows 8 Enterprise version.  Is it known when these versions will become available for upgrade? I've been waiting patiently for weeks to get this upgrade.  Thanks. Can any one tell me the advantage of synchronized method over synchronized block with an example? Draw Vertices of Regular Polygon I am trying to draw just the nodes (no sides) at the vertices of a regular hexagon.  should be easily modified to accomplish what I want, but I am such a novice that I have difficulty understanding the example. Ideally, each vertex would be a separate named node so that I can easily draw edges between them (I will be making several different graphs using these same nodes). I'm working on the question     Let $G$ be the group of invertible real matrices of the form $\left [\begin{array}{c c}a &amp; b\\ &amp; a^2\end{array}\right ]$. Determine the Lie algebra $L$ of $G$, and compute the bracket on $L$.   I'm familiar with how to derive the Lie algebra for a linear group like $U_n$, $SU_n$, etc. but I'm not sure what to do in a more explicit case like this. wp_delete_auto_drafts() deletes links in menus Since yesterday the wp_scheduled_auto_draft_delete cron job somehow deletes all page entries from our menus. All entries in the table wp_postmeta with meta_key = '_menu_item_object' and meta_value = 'page' get deleted in the process. By tracing back the DELETE query I found out that the menu entries are deleted by a function called _wp_delete_post_menu_item. I got the following stacktrace for that function:  #0  _wp_delete_post_menu_item(3244) #1  call_user_func_array(_wp_delete_post_menu_item, Array ([0] =&gt; 3244)) called at [/srv/www/htdocs/biva/wp-includes/plugin.php:470] #2  do_action(delete_post, 3244) called at [/srv/www/htdocs/biva/wp-includes/post.php:2483] #3  wp_delete_post(3244, 1) called at [/srv/www/htdocs/biva/wp-includes/post.php:5645] #4  wp_delete_auto_drafts() #5  call_user_func_array(wp_delete_auto_drafts, Array ()) called at [/srv/www/htdocs/biva/wp-includes/plugin.php:546] #6  do_action_ref_array(wp_scheduled_auto_draft_delete, Array ()) called at [/srv/www/htdocs/biva/wp-cron.php:100]   But I'm stuck here, I'm not a wordpress developer and I have no clue why deleting old drafts results in deleting attached menu entries although the main pages still exist.  Workaround: As a workaround we added the following to the top of wp-config, wich will disable wp-cron:  /** Disable wp-cron to prevent menu from getting deleted. Detailed Bug description: http://wordpress.stackexchange.com/questions/145953 **/ define('DISABLE_WP_CRON', true);   If you are experiencing similar difficulties you might try locking the rows in the table wp_postmeta with meta_key = '_menu_item_object' and meta_value = 'page' and then tracing back the error message when WP trys to delete these rows, that's how we nailed down our error.  Reproduce the Error: It is definitely the stealth publish plugin that is causing our error, one can easily reproduce it, by doing the following:   Install a fresh Wordpress 3.9.1. Install the stealth publish plugin . Create a few test pages and add them to a new menu. Create a new page, with some dummy content, but do not save it!. Leave the page without saving. Change the system time 8 days into the future. The wp_scheduled_auto_draft_delete cron job will run because it runs daily and it hasn't run for 7 days as soon as you visit your page. It will then find your never saved dummy page delete it as it is older than 7 days and the menu will vanish. You might need to refresh the page a few times till the effect becomes visible.   I've recorded a screencast on how to reproduce the error (but I took not the time to comment it): Can I choose which records are copied in a Partial Copy sandbox? We have a partial copy sandbox that we're using for development and testing.  This is really helpful as some of our applications internally store Salesforce id's.  However, there is a limitation with the partial copy as it only brings in 10,000 records per object from the production environment.  Unfortunately some of the id's we internally store are not being brought down into our partial copy which causes errors.  The 10,000 records that it did copy over aren't needed; I realistically only need 1 or 2.  Is there any way I can achieve copying over a specific record from the production environment? LaTeX Editors/IDEs I have already bought the PC version on minecraft for my account. However, when attempting to change my skin, the game simply states:"You have to buy the PC edition of Minecraft."   Which is odd because I already have.  Why is this happening? How can I fix it?