use vs. used what is the correct usage?
What's the negation of "I used to be"? Surely not "I didn't used to be"?
Where can I find other RPG players? I'd really like to learn how to play pen-and-paper RPGs.  I know that it takes a few players to actually sit down and play, but I'm not at all sure where to find more gamers.  How do I find existing groups to join? Or, are there any resources online that may help me find existing RPG groups or players? Converting GeoPDF to vector format like CAD or shapefile? I want to convert a GeoPDF that has vectors entity in it to a vector format and preserve the real coordinates of these vectors. The GeoPDF has been exported from ArcMap and has layers in it.  I have try GDAL, but it rasterize the PDF before exporting it. Which is not good for me. Also I don't want a solution that would convert this image back to vectors, too complicated for the data I have.  Is someone aware of any tool that can do that? The resulting format can be a CAD file or a shapefile or anything that is a vector format. Let $X,Y$ be topological and $f:X \to Y$ be open and continuos.  I am studying Baire space and I would like to try the following facts :      $(i)$ The inverse image of dense set is dense.       $(ii)$ The inverse image of comeager set is comeager.   I am studying Baire space and I would like to try the following facts  Can we collaborate to verify the above claims?    Thanks. Continuous function does not map closed set to closed set Motivated by , can one prove that the order of an element in a finite group divides the order of the group without using Lagrange's theorem? (Or, equivalently, that the order of the group is an exponent for every element in the group?)  The simplest proof I can think of uses the coset proof of Lagrange's theorem in disguise and goes like this: take $a \in G$ and consider the map $f\colon G \to G$ given by $f(x)=ax$. Consider now the orbits of $f$, that is, the sets $\mathcal{O}(x)=\{ x, f(x), f(f(x)), \dots \}$. Now all orbits have the same number of elements and $|\mathcal{O}(e)| = o(a)$. Hence $o(a)$ divides $|G|$.  This proof has perhaps some pedagogical value in introductory courses because it can be generalized in a natural way to non-cyclic subgroups by introducing cosets, leading to the canonical proof of Lagrange's theorem.   Has anyone seen a different approach to this result that avoids using Lagrange's theorem? Or is Lagrange's theorem really the most basic result in finite group theory? Do film industries outside India use intervals/Intermission? Do Stack Exchange sites allow editing of comments and posts from other users? Finding the n-th lexicographic permutation of a string I have an ordered set of symbols S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }. I want to find the 1,000,000-th permutation in lexicographic order of S. It is a programming puzzle, but I wanted to figure out a way without brute-forcing the task.  So my thinking was like this:  For 10 variable symbol positions, we have 10! permutations, obviously. Now we want to find the first symbol.  If we fix the first symbol, then the remaining 9 symbols can have 9! combinations.  That means that 0 or 1 cannot be the first symbol, because the highest possible position is 2*9! = 725,760, which is lower than 1,000,000.  The lowest position for a leading 3 is 3*9! + 1 = 1,088,641, so it can't be 3 or higher, either.  Therefore, the first number must be 2. 2*9! is the largest multiple of 9! no greater than 1,000,000, so I need the 2nd symbol (zero-based) from the current set.  So now the question becomes, of the remaining S := S \{2}, which permutation of these symbols is at lexicographic position (1,000,000 - 2*9!) = 274,240?  6*8! = 241,920 is the largest multiple of 8! which is smaller than 274,240, so I need the 6th-smallest symbol of the remaining set, which is 7. So the prefix should be 27 by now.  That way, I keep going and finally arrive at: 1,000,000 = 2*9! + 6*8! + 6*7! + 2*6! + 5*5! + 1*4! + 2*3! + 2*2! + 0*1! + 0*0!  which results in "2783905614" as my solution.  However, according to the , (free reg. req.) that is incorrect.  Where did I go wrong in thinking or applying? Why is the gravitational force always attractive? Is there another way to explain this without the curvature of space time?   PS: If the simple answer to this question is that mass makes space-time curve in a concave fashion, I can rephrase the question as why does mass make space-time always curve concavely? Graphics crop in guest welcome window I don't expect that any user should have noticed this, since only guests will see them.  Well, it seems that the Stack Overflow welcome splash, containing the basic info of the site, is cropped from the bottom.    Please don't mind the sides, I cropped them to fit on the screen. Just on the bottom is my concern. Adding HTML5 placeholder to all drupal forms I'm trying to add the placeholder attribute to all textfields across my website, but I'm having no luck.  I've created a module that overrides hook_form_alter  function mymodule_form_alter(&amp;$form, &amp;$form_state, $form_id) {     foreach ($form as $key =&gt; $value) {         if ("textfield" == $value["#type"]){             $value['#attributes']["placeholder"] = t($value["#title"]);         }     } }   I should tell you that I'm also using the webform module. Why am I getting "line 1: $' :\r': command not found"? I use Cygwin on my laptop (DOS). I have a collection of scripts from my colleagues, and my own. I am not an IT person, not knowledgeable in Unix. I am following my colleagues' syntax and able to manage a few simple things. The scripts worked well on my old laptop. I just changed laptop and installed Cygwin. When I run my scripts, they do not work. Here is one example of the error message I get: line 1: $':\r': command not found line 5: syntax error near unexpected token `$'\r'' line 5: `fi  Here are the top 5 lines of my script : iter=1 if [ -f iter.txt ]    then rm ./iter.txt  fi    Can someone please explain how I can get around this problem? I understand there has been so much on this topic but I am still confused. I get that if the person is the subject it is who and anything else is whom. However, I'm really struggling to work out this rule for the following sentence:     The scope of which his account of morality applies to is therefore restricted to those whom/who the ‘notion of justification to a being of that kind makes sense.’   Should it be who or whom? I can't work out the subject and object. Can't connect to wireless 13.10 I have ubuntu installed as the sole OS on a T420. Before this I had installed the #! distro (and Xubuntu before that) and wireless worked seamlessly on either. My home hotspot shows up but when I click on it tries for a while before disconnecting.  Before going into the problem further, I wanted to double check that I entered the wifi password for my home network correctly. I went to Edit Connections >> Wi-Fi Security and changed the key, but it is still not able to connect. So I think the password is definitely correct. I don't understand why it can't connect now. UK PLAB Visa Refusal due to unexplained bank deposits I had applied for a PLAB (Doctors) Visa for the UK to appear in PLAB test. I got refused on the basis of two recent large deposits in the bank statement I provided (my mothers). In reality, these are my own savings which I had deposited in her account to make it more strong. The only objection I got was that I must provide evidence for the source of these deposits. Other than this, I have previously travelled to the UK and USA as well as other parts of the world and my travel history is fine. Can someone please advise on how to proceed and re-apply? Does Wolfram Mathworld make a mistake describing a discrete probability distribution with a probability density function? diagram software for Ubuntu? FireFox 66 Quantum disabled all my extensions at midnight! I have found that for only one page (so far) the spacing between the header and content is different from the spacing on all the other pages. You can see this behavior in the images below (from pages 2 and 3 of the document):     My .tex file contents are shown below.  \documentclass[a4paper]{report} \usepackage{fullpage} \usepackage{lipsum} \usepackage{fancyhdr} \pagestyle{fancy} \setlength{\headsep}{0.5cm}  \begin{document} \renewcommand{\headrulewidth}{0.4pt} \renewcommand{\chaptermark}[1]{\markboth{\thechapter. #1}{}} \fancyhead[L]{\bfseries \leftmark} \fancyhead[R]{\bfseries \rightmark}  \chapter{Version Control} \lipsum \lipsum \lipsum \lipsum  \end{document} NOTE: Signing up or Logging in via OpenID is no longer officially supported from any of our sites. Currently,  is still on the internet, but we are in the process of completely removing it.    Stack Overflow was an early and strong supporter of . We built our sign up/log in flow around it. We were idealistic and had , but these hopes weren't realized. Over the years people have wondered if  is . We've had to remove support as OpenID providers  or .  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