Why does the converse of the Isomorphism Theorem in first-order logic not hold?
Example of non-isomorphic structures which are elementarily equivalent
How can I visualize boxes? This question led to a new package:      Some of you may know the Web Developer Toolbar for Firefox that can outline the block level elements of a page like this:  Is there a way to do something similar with TeX boxes for a complete document? Import users from CSV file Is it possible to import users by using CSV file? or something like a LDAP connection to import all users? Removing lines from text file that contain string at beginning and string at end - and keep one It took me a while to word this best.  Problem 1:  Is there a way to find lines in a text file that have the same string at the beginning and the same strings at the end?   Beginning and end strings not necessarily equal to each other.  Text between the two strings is not consistant in number of characters or number of hyphens.  A hyphen is in between notable strings (which I added to my large text file).  For example:  File:    AAAAA-tjhut-ghyut-FILE1.txt   BBB-fhuj-dnbhg-frt76-FILE2.txt   AAAAA-ghtujukr-hgute7gr-xhyutt-FILE1.txt   AAAAA-VGYT-4d7tt-xhyutt-FILE1.txt   CCCC-fjuk-dryy-fhuj-FILE3.txt   Lines to detect:    AAAAA-tjhut-ghyut-FILE1.txt   AAAAA-ghtujukr-hgute7gr-xhyutt-FILE1.txt   AAAAA-VGYT-4d7tt-xhyutt-FILE1.txt   Problem 2:  Is there a way to remove all but one of the lines containing the duplicate strings at the beginning and end from above?  Before:    AAAAA-tjhut-ghyut-FILE1.txt   AAAAA-ghtujukr-hgute7gr-xhyutt-FILE1.txt   AAAAA-VGYT-4d7tt-xhyutt-FILE1.txt   After:    AAAAA-tjhut-ghyut-FILE1.txt   Big thanks for any advice.  Note: I think using the occurances of the first hyphen and last hyphen can be used to locate the duplicate strings. How can I convert a hex string to a byte array? Why doesn't the definition of a category require an explicit notion of morphisms equality? I am learning basics of the category theory (CT).  I do understand that CT is a modern powerful framework to describe various branches of mathematics in a unified way.  I do admit that category's definition tells a lot about the whole thing and focuses on the most important properties, shadowing unnecessary details. However, the more I go forward, the more it feels like it should explicitly require a notion of morphisms equality (like it does with morphism composition). It feels so because equality or inequality of morphisms arises everywhere, since the very beginning: any commutative diagram eventually reduces to an equality of two different paths and many other things involve equality as well. Even composition is defined grounding upon an (implicit) equality!  I'll try to give an example of my concern. Consider $\mathbb{SET}$. Its objects are sets and morphisms are functions. Now, let's recall that functions are sets as well - to be more precise, a function $f : A \mapsto B$ is a subset of a $A \times B$ obeying certain properties, which I omit. Thus, one could argue that $f$ is both a morphism between objects $A, B \in Obj(\mathbb{SET})$ and an object defined as a set of pairs $\{ (a_1 \in A, b_1 \in B), ..., (a_n \in A, b_n \in B) \}$ and those are equal because both are essentially exactly the same thing.  I hope my concern is clear and I need some kind of "conceptual insight" from knowledgeable people to move forward. Please give me the right perspective. $$\lim_{x\to 0} \frac{\ln(1+x)}x$$  The process I  want to take to solving this is by using the definition of the limit, but I am getting confused. ( without l'hopitals rule)   $$\lim_{h \to 0} \frac{f(x+h) - f(x)}h$$  $$\lim_{h \to 0} \frac{\frac{\ln (1+x+h)}{x+h} - \frac{\ln(1+x)}x}h$$  $$\lim_{h \to 0} \frac{x\ln(1+x+h) - (x+h)\ln (1+x)}{hx(x+h))}$$  At this point I get confused because I know the answer is $1$, but I am not getting this answer through simplification of my formula. Can the union axiom be weakened? I'm not a git master, but I have been working with it for some time now, with several different projects.  In each project, I always git clone [repository] and from that point, can always git pull, so long as I don't have outstanding changes, of course.  Recently, I had to revert to a previous branch, and did so with git checkout 4f82a29.  When I was again ready to pull, I found that I had to set my branch back to master.  Now, I can not pull using a straight git pull but instead, have to specify git pull origin master, which is annoying, and indicates to me that I don't fully understand what is going on.  What has changed which does not allow me to do a straight git pull without specifying origin master, and how to I change it back?  UPDATE:  -bash-3.1$ cat config [core]     repositoryformatversion = 0     filemode = true     bare = false     logallrefupdates = true [branch "master"] [remote "origin"]     url = git@github.com:user/project.git     fetch = refs/heads/*:refs/remotes/origin/*   UPDATE 2: To be clear, I understand that my original method may have been incorrect, but I need to fix this repo so that I can simply use git pull again.  Currently, git pull results in:  -bash-3.1$ git pull You asked me to pull without telling me which branch you want to merge with, and 'branch.master.merge' in your configuration file does not tell me either.  Please name which branch you want to merge on the command line and try again (e.g. 'git pull  '). See git-pull(1) for details on the refspec.  If you often merge with the same branch, you may want to configure the following variables in your configuration file:      branch.master.remote =      branch.master.merge =      remote..url =      remote..fetch =   See git-config(1) for details.   I can tell git pull which branch to merge, and it works correctly, but git pull does not work as it did originally before my git checkout. Adverb sentence query He is arguably the best actor of his generation   In the above sentence the adverb is placed just after "be" Can we use adverb after "be"? If we can use then please explain properly because I have studied that adverb can be used before adjective and adverb . This is a really trivial question, but I've seen different conventions and some edits regarding which is correct, so I'm curious:  Should question titles be title-cased or sentence-cased? I am trying to follow Blender Guru's beginner tutorial. He went to the Compositor tab and was using it to Denoise an image but when I got there, no nodes show up. Can you guys help? How to debug EntityMalformedException? I've got fatal error EntityMalformedException: Missing bundle property on entity of type node. in entity_extract_ids() (line 7700 of .\includes\common.inc) when trying to access user/xyz.  I tried to retrieve info about the malformed node at line 7700, where the error message is built, thinks like :  if (!isset($entity-&gt;{$info['entity keys']['bundle']}) || $entity-&gt;{$info['entity keys']['bundle']} === '') {  dpm($info);// or dpm($entity);  throw new EntityMalformedException(t('Missing bundle property on entity of type @entity_type.', array('@entity_type' =&gt; $entity_type))); }   dpm($entity) returns an unexpected user object, and $info a huge qty of things.   Could somebody put me on the right way ?  I already read whatever I could find about Missing bundle property errors, but none helped solving.  dpm($entity) returns  uid (String, 2 characters ) 70 name (String, 9 characters ) John pass (String, 55 characters ) $S$DUwPuOuDPiDL4nRTYXqc7a5uOfMKey7pyhOFUEKka1XM... mail (String, 30 characters ) john@example.com theme (String, 0 characters ) signature (String, 0 characters ) signature_format (String, 13 characters ) filtered_html created (String, 10 characters ) 1396286331 access (String, 10 characters ) 1397146661 login (String, 10 characters ) 1396513460 status (String, 1 characters ) 1 timezone (NULL) language (String, 2 characters ) fr picture (NULL) init (String, 30 characters ) john@example.com data (Array, 5 elements) roles (Array, 1 element) og_user_node (Array, 0 elements) message_subscribe_email (Array, 1 element) field_bio (Array, 0 elements) field_name_first (Array, 1 element) field_name_last (Array, 1 element) field_facebook_url (Array, 0 elements) field_linkedin_url (Array, 0 elements) field_twitter_url (Array, 0 elements) user_trusted_contacts (Array, 1 element) group_group (Array, 1 element) group_access (Array, 1 element) metatags (Array, 0 elements) rdf_mapping (Array, 3 elements) realname (String, 13 characters ) John Doe content (Array, 13 elements) entity_view_prepared (Boolean) TRUE privatemsg_disabled (Boolean) FALSE Why can't Chromium suddenly access any partition except for /home? What is the sign of the work done on the system and by the system? What is the sign of the  done on the system and by the system?  My chemistry book says when work is done on the system, it is positive. When work is done by the system, it is negative.  My physics book says the opposite. It says that when work is done on the system, it is negative. When work is done by the system, it is positive.  Why do they differ? Passing HTML to template using Flask/Jinja2 I`m using the Newton-Raphson method for obtaining MLE for parameters for maximizing my objective function. At each iteration, I want to check that is the Hessian matrix negative definite or not and I see the Hessian matrix is not negative definite at some iterations. So, I want to use the Fisher scoring algorithm ( of derivation) In this situation, the Fisher information matrix is indefinite!! Is it possible? What are the reasons for this? Are the second-order derivatives wrong? Or are values of expectations incorrect? How does the post-2.0 Puzzle Ring work? Patch 2.0.1 introduced a lot of significant changes to the loot system in the game. One of the significant ones was the revamp to the , which now has a new effect:      Summon a treasure goblin who picks up normal-quality items for you. After picking up 12–16 items, he drops a rare item with a chance for a legendary.    What is the cooldown on the goblin item drop? Does the effect stack if you have one on your character and another on your follower (i.e. two goblins)? Is the drop chance for the rare/legendary affected by increased Magic Find? If so, approximately how much? Is there a cap on them max item level of the dropped item? (While &lt; lvl 60, at lvl 60, and when the level cap is raised in the expansion.) Does the item counter reset when you leave the game, change acts, or die? Rotating image / marker image on Google map V3 How to add n hours to a specified time? copy ssh private keys to another computer