Varying spacing after line break Before line break  After line break   An empty line between two sentences usually gets me a line break without any additional spacing. For some reason, on the second page of the same chapter, there is additional spacing after each line break and also more spacing after \\.  Why is that? Is TeX somehow trying to fill the page before the following section? I'd like to constantly have no extra spacing after line breaks and \\.
Best choice between using \\ or leaving space after each paragraph to end the paragraph Here is the thing, I have always used a blank space between paragraphs in order to tell latex that there is a new paragraph. But there is someone I work with very often that keeps using \\ to break a line after a paragraph...  This is really annoying so I wanted to know if there is a real advantage of using \\ over just leaving a space.  Note that I am not referring to the paragraph environment, but to the simple term paragraph.
Using Leibniz Integral Rule on infinite region I am trying to take the derivative with respect to $a$ of some function $I(a)=\int_{0}^{\infty}f(a,x)dx$.  I would like to make sure that I am using the  correctly.  Various web sources indicate a set of conditions that must hold for $f(x,a)$ and $\frac{\partial f(x,a)}{\partial a}$ when integration is done over infinite region.  From reading  (see Theorem 10.3 on page 13) the conditions that $f(x,a)$ and $\frac{\partial f(x,a)}{\partial a}$ must obey are:   $f(x,a)$ and $\frac{\partial f(x,a)}{\partial a}$ are continuous over $x\in[0,\infty)$ and around $a$ that we are interested in. There exists an integrable function (over $x$) $g(x)$ such that $|\frac{\partial f(x,a)}{\partial a}|\leq g(x)$. There exists an integrable function (over $x$) $h(x)$ such that $|f(x,a)|\leq h(x)$.   Integrable here means $\int_{-\infty}^{\infty}g(x)dx&lt;\infty$.  However,  seems to omit condition 3 above.  I am wondering which source is correct.  If there are "both correct", when is condition 3 necessary? How to remove conference information from the ACM 2017 SIGCONF template? Extract float/double value How do I extract a double value from a string using regex.  import re  pattr = re.compile(???)     x = pattr.match("4.5") Configuring, compiling and installing a custom Linux kernel The existence of the empty set is an axiom of ZFC or not? I found in the Wolfram MathWorld page of the  that this is one of the Zermelo-Fraenkel Axioms, however on the page about these  I read that it is an axiom that can be deduced from the Axiom of Subsets and the Axiom of Foundation (or Axiom of Regularity), so, the existence of the Empty Set is an axiom of ZFC or not? I am a third year (starting fourth year in the fall) PhD student in mathematics. I've passed all qualifying exams and am currently doing research. As far as I can tell, I am not doing poorly. I have the good fortune of having a great advisor, being in a very supportive department, and having friends and family who genuinely care about my success.   The fact is research is hard. It appears to consist primarily of staring at a problem for days and days and days without getting anywhere. Sometimes, rarely, I do figure something out and that feels wonderful, but the overwhelming majority of my time appears to be spent banging my head against a mostly figurative wall. I am not complaining about the material being hard, and I am not averse to putting in hard work, but I get frequently discouraged when I realize the vast volumes of mathematics that I yet know nothing about (and probably never will). It's very hard to quantify progress - in particular, there are too few tangible returns after too many hours worked. I find myself thinking along the lines of "Oh, if only someone actually smart were thinking about this problem they would have solved it in moments" and so on.   I've talked about this to some number of people; here is some advice I have received:   Take a day off. Putting in hours upon hours of trying things doesn't magically lead to a solution, particularly if the brain is tired and just wants to sleep. Have a hobby. Since math research doesn't exactly provide instant gratification, a hobby might provide some instead.  Talk to other graduate students. Realize that many graduate students go through this.   I'm interested to know how other folks have dealt with being discouraged as a graduate student. Does it get better with time and experience? Is this a sign that research is not for me and that I should seriously consider a life outside academia? How do I remove the limit on PC keyboard button presses? Whenever I play a PC game with the directional keys, I can only press two buttons at a time.  For instance if I am playing a shooter like R-Type, I cannot hold down the fire button while moving diagonally at the same time.  The computer simply ignores the extra button press.  How do I remove this limit so I can shoot while moving diagonally?  This limitation seems to apply for every game.  I am running Windows 7 if it makes any difference.  I noticed the same problem back when I used Windows XP. Where Can I Give Feedback on Ubuntu? I'm running Ubuntu 11.04 Beta 2. Is there a way, or a place, to give feedback on this system? Not file bugs, just give feedback. How to remove configuration files completely Recently I uninstalled some software using sudo apt-get --purge autoremove, thinking that this would remove all traces of it including unused dependencies and configuration files. However I discovered that a configuration file was left behind in my home folder.  Is there a more powerful command which would remove even that?   Also, is it safe to delete the hidden files and folders under home, if they are merely configuration files, or are there other kinds of files? Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$ I have the following homework problem:  Let $B$ be the set of rational numbers in the interval $[0,1]$, and let $\{I_k\}_{k=1}^n$ be a finite collection of open intervals that covers $B$. Prove that $\sum_{k=1}^n m^*(I_k) \geq 1$.    This is my approach, First we have that $B = \mathbb{Q}\cap [0,1]$. Now, $B \subset \bigcup_{k=1}^nI_k$, where $I_k$ are open intervals.In particular $0 \in B \wedge 1 \in B$.Now, since $B \subset \bigcup_{k=1}^nI_k$ then there exist positive numbers, $\epsilon_0, \epsilon_1$ such that: $$(0-\epsilon_0,0+\epsilon_0)\subset \bigcup_{k=1}^nI_k$$ $$(1-\epsilon_0,1+\epsilon_0)\subset \bigcup_{k=1}^nI_k.$$   Clearly, $-e_0 \notin [0,1]$ and $e_1 \notin [0,1]$.I am not sure, if so far I am in the right track. Can I transfer my Terraria character from one PC to another? Currently my map server is run on my laptop at home, and my brother and I play via LAN each on his desktop PC.  However, I'd like to transfer my character from the Desktop PC to my laptop in order to play on the go.  Can I do this? Where is the character information saved? Why does camera this tracking fail completely even when the solution value is very low? How to search for upcoming conferences that will be held in a specific subject What is the SE version of Seven Dirty Words? Caution: R-rated language  Some words, when present in a comment, make it eligible for instant, automatic one-flag deletion. Out of the , only      shit and fuck    appear to work this way. But then there are other, Stack Exchange-specific dirty phrases:    accept rate or accept-rate acceptance rate  what have you tried   whore    Are there other such words or phrases? Is there a complete list of them?     Some suspect words and phrases that do not suffice for automatic deletion:       accept an/the answer, thank you, voting to close, piss, bitch, idiot, cunt (often found on Stack Overflow as a misspelling of "count"). Easier/better way to compute and store a value that's accessed as a property? Is "guy" gender-neutral? How can I hire a professor to answer my advanced technical questions in a niche area? In short, How does one go about hiring a professor or someone really well established in their field for a private tutoring session?  I tried looking online but can’t find much, mainly websites for tutors that are practitioners or “experts” as in with with n years of experience at best. This doesn’t cut it at my level as I am a researcher with a PhD and already have published papers on my topic.   However, I am very passionate about my subject and always looking to grow. So I do have questions, very technical (in my case computer science) and would happily pay a fee for consulting with a professor in the field.  Any advice? How to move from screen 1 to screen 3 by moving cursor to the left and vice versa? If I have to move the mouse from the left screen all the way to the right screen, the distance is quite big.   Is there a way to virtually connect the sides of the screen as if they were arranged in a circle? I could then move from the left screen to the right screen, by simply moving the cursor to the left. In proof by induction, what does it mean when condition for inductive step is lesser than the propsition itself? My question is regarding the question posed at the end of the proof.  My answer is that the result does not hold for all $m \ge 7$ because when $m=7$, the result is $343 \le 128$, which is false.  Is there another way to answer this sort of question besides directly trying different values until you get a false result?  EDIT:  Another question I have regarding this solution is:  In the proof for the inductive step, we start by assuming $k \ge 10$. But along the way, the author mentions $k \ge 1$ and $k \ge 7$ to justify the inequality.  Why do we bother to do this instead of just sticking with $k \ge 10$? "Awesome" vs. "Awful"