What does the black rectangle at the end of the line mean? It is overflow?     This writes overflow  \documentclass[12pt,a4paper]{report} \setlength\textwidth{145mm} \setlength\textheight{247mm} \setlength\oddsidemargin{15mm} \setlength\evensidemargin{15mm} \setlength\topmargin{0mm} \setlength\headsep{0mm} \setlength\headheight{0mm} \let\openright=\clearpage  \begin{document}  \begin{description}  \item [Epocha (ekvinokcium)] $T$ udává okamžik v čase. Je několik druhů epoch - referenční epocha (v případě světelných křivek udává, kdy je fáze 0), epocha maximální radiální rychlosti, epocha periastra, epocha primárního minima, apod. Udává se v různých časových jednotkách:   \begin{itemize} \item Juliánská data se hodí na analýzu dlouhých časových pozorování. Označují střední sluneční dny, které začínají v poledne světového času SČ, což je lokální čas na poledníku procházejícím observatoří v Greenwichi. Počátek těchto časových jednotek JD0 připadá na střední poledne v Greenwichi 1. ledna 4713 př. n. l.    \end{itemize}  \end{description}  \end{document}
Is it possible to make LaTeX mark overfull boxes in the output, for example by drawing red rectangles in the PDF where the boxes overflow? The purpose -- to more easily "see" where the problems are in the output.
Iterated self-composition of arbitrary function Does there exist some notation that represents the iterative composition of a single-input, single-output function with itself? As in, say, $f_5(x)=f(f(f(f(f(x)))))$.  In other words, going by the above (incorrect, I'm pretty sure) notation:  $f(x)=x+1$, $f_n(m)=m+n$  I'm looking for the correct way to express the notion of "$f_n(x)$" for any $f$. Column vs Field: have I been using these terms incorrectly? I feel kind of embarrassed here, I've always used the terms "column" and "field" completely interchangeably, which recently caused some confusion in a technical discussion.   I was told, though, that this wasn't correct, that it should be (translating each term into spreadsheet terminology, ignoring data types and all the other stuff that make databases useful):   Database Column: like a spreadsheet column  Database Record: like a spreadsheet row Database Field: like a spreadsheet "cell" (a specific column of a specific row)   Is this right? I could have sworn that column and field are used more interchangeably than that. I certainly have been.  So we don't add fields to a table, we add columns to a table, and fields are only relevant when talking about data within a record?  Other thoughts on column vs field?  Edit: to clarify, the current context is MS SQL Server. My background before SQL server was MS Access, which might influence my use of these terms. Why are Alkaline, NiMH, and Li-ion AA measured differently (mAh, mWh, etc)? Looking around Amazon, it seems that different types of batteries are measured differently:  Does anyone know why?   Li-ion are measured in mWh    (Cheap-Os)  3000mWh AmpTorrent  NiMH are measured in mAh      Alkalines are typically not measured   "Long Lasting" Duracell "Longest Lasting" Energizer    I assume that Alkalines are not measured for some sort of historical reason with marketing departments?  ... or is it that alkalines so mystical and unreliable that giving them a measurement is too aggressive? Or that switching to non-toxic / non-mercury was such a bad move in performance that measurements had to be removed in the 90s so people wouldn't know?  Perhaps NiMH are measured in mAh because the voltage can very so greatly and mWh doesn't make sense?  Are Li-ion measured in mWh because that's more consistent with non-battery measurements and they do deliver reliable voltage? I was able to post in chat with less than 20 rep by joining 20 sites I joined 20 other sites (out of the many) and even with 1 rep was able to post in any of the chatrooms. For example: In ELL, I have just 1 rep and have posted messages in its chat.  ell.stackexchange.com/users/18923/lamart This seems like a bug because I should have needed 20 rep to post. . EDIT: From , I got the idea to make this edit. To reproduce this bug/error:  Create a new SE account. Use it to make an account here. You will get 1 default rep. Choose a random SE site and use this account to get 1 rep on that random site. Repeat the above step 20 times. Now you have 1 rep on 20 network sites but the net SE rep is 20. Go to the ELL chat and ping me. (important step)  From my comment: I have now got 40 rep since people voted this question up. Initially I had net 20 rep gained by creating 20 accounts on 20 different SE sites. Those default 1rep added up to get me to 20rep and I was able to chat. The link says one needs 20 rep in any of the SE site to chat in &quot;all the other&quot; category chatrooms..... but I did not have 20 rep on ELL at that moment. I created a interior scene and  i don't know how to bake a texture using cycles bake. Why do we use von Neumann ordinals and not Zermelo ordinals? Why do we use von Neumann ordinals, $$ 0 = \emptyset $$ $$ n+1 = n \cup \{n\} $$  and not Zermelo ordinals? $$ 0 = \emptyset $$ $$ n+1 = \{ n \} $$ Differential form is closed if the integral over a curve is rational number. The following problem comes from do Carmo's book Differential Forms and Applications, Chapter 2, Exercise 4:  Let $\omega$ be a differentiable 1-from defined on an open subset $U\subset \mathbb{R}^n$. Assume that for each closed differential curve $C$ in $C$, $\int_C \omega$ is a rational number. Prove that $\omega$ is closed.   Can anyone give some hints? My idea was that we could try to show the integral vanishes if the curve lies in $N_\epsilon (p)$ (i.e. a small neighborhood around $p$) for any $p$ in $U$ and use the Poincare Lemma, but failed. How to implement a progress bar using the MVVM pattern When a vehicle makes a turn, the two front wheels trace out two arcs as shown in the figure below. The wheel facing towards the inside of the turn has a steering angle that is greater than that of the outer wheel. This is necessary to ensure that both front wheels smoothly trace out two arcs, which have the same center, otherwise the front wheels will skid on the ground during the turn.   During a turn, do the rear wheels necessarily trace out the same arcs as the front wheels? I put up  over on SO with the assumption that the text would be formatted like it is for a question or answer.  I'm not really sure if I was incorrect in my assumption, or if I just formatted my text improperly, as I can't go back and edit what I put in.  Am I missing an obvious feature?  If not, would it be reasonable to request bounty-text edits—perhaps with moderator-approval to prevent abuse?  Edit: I was trying to use markdown to produce an unordered list as part of my bounty.  What you see in the link is a blob of text with dashes separating phrases limsup of intersection of events as a subset of intersection of limsups Let $A_1, A_2, \ldots$ and $B_1, B_2, \ldots$ be two sequences of events in some probability triple $(\Omega, \mathcal{F}, \mathbf{P})$. Now, it is true that $\left(\limsup_n A_n\right) \cap \left(\limsup_n B_n\right) \supseteq \limsup_n (A_n \cap B_n)$, and I can think of many different cases where this relation holds true for equality (e.g., let $A_n = B_n$, or $A_n = B_n^c$, or $B_n = \emptyset$, or $B_n = \Omega$). However, I cannot think of any case where $\left(\limsup_n A_n\right) \cap \left(\limsup_n B_n\right) \supset \limsup_n (A_n \cap B_n)$ holds for strict inclusion.  My proof for the relation is simple. Since $A_n \cap B_n \subseteq A_n$ and $A_n \cap B_n \subseteq B_n$, then we can perform some set algebra as follows:  $$\bigcup_{k=n}^\infty (A_k \cap B_k) \subseteq \bigcup_{k=n}^\infty A_k$$ $$\bigcap_{n=1}^\infty \bigcup_{k=n}^\infty (A_k \cap B_k) \subseteq \bigcap_{n=1}^\infty \bigcup_{k=n}^\infty A_k$$  Then we can use the same logic for $B_n$, and come to the conclusion as stated in the beginning. Ubuntu 11.10 is installed, and I have updated my system via Ubuntu Software Centre, and after the update 3 updates remain in the list. But I am unable to select them, the tickboxes cannot be checked and Ubuntu Software Centre gives no error when I try to check.  Also, below it says "There is no update to be installed" and even though there seems to be updates Install Updates button is unclickable.  What should I do in order to install these updates? Is there a general way to change the font of a particular symbol without switching packages?  For example, suppose I'm using Computer Modern for my entire document, but I want the "subset" operator to look as it does in mathabx.  How can I redefine it to appear in this way? This poor creature is taken aboard the spaceship and the humans do not know that it is intelligent.  The alien can repeat what it hears, e,g, "pass the sugar".  It is able to escape at night and it communicates messages to its fellow aliens.  It directs that they turn up the heat of the atmosphere (somehow they can do this) so as to force the humans to leave.  The alien protagonist states that it will die w/ the humans or leave with them. Given $a_1, a_2, a_3, \ldots , a_n$ not all zero, show $\gcd(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$. Also deduce $a_1x_1+a_2x_2+ \ldots +a_nx_n = b$ has solutions $\iff \gcd(a_1, a_2, a_3, \ldots , a_n)|b$.   I know that $ax+by=n$ has integer solutions $\iff \gcd(a,b)|n$. I'll need to use induction to show $a_1x_1+a_2x_2+ \ldots +a_nx_n = \gcd(a_1, a_2, a_3, \ldots , a_n)$ has solutions, and then I will be able to say that as $\gcd(a_1, a_2, a_3, \ldots , a_n) | a_1x_1+a_2x_2+ \ldots +a_nx_n $ for any $x_1,x_2, x_3 \ldots x_n$ then $c \leq \gcd(a_1, a_2, a_3, \ldots , a_n)$ and $c \geq \gcd(a_1, a_2, a_3, \ldots , a_n)$, and thus $c=\gcd(a_1, a_2, a_3, \ldots , a_n)$. How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$? I would like to find the apothem of a regular pentagon. It follows from   $$\cos \dfrac{2\pi }{5}=\dfrac{-1+\sqrt{5}}{4}.$$  But how can this be proved (geometrically or trigonometrically)? What's the point in adding a new line to the end of a file? Some compilers (especially C or C++ ones) give you warnings about:  No new line at end of file   I thought this would be a C-programmers-only problem, but github displays a message in the commit view:  \ No newline at end of file   for a PHP file.  I understand the preprocessor thing explained in , but what has this to do with PHP? Is it the same include() thing or is it related to the \r\n vs \n topic?   What is the point in having a new line at the end of a file? Here is some information we got : We know the value of $n$, with size $1043$. We know the value of $p$ (size $20$) and $q$ (size $1023$) as the factors. $e = 65537.$ $\varphi(n)$ = $(q-1)(p-1)$ When I calculated $\gcd$ and $\text{modinv}$, I got : $\gcd(e,\varphi(n)) = 65537$ $modinv(e,\varphi(n)) = 1 $ So we can tell that they are not relatively prime. So, how to compute the d, and get the value of m? I'm not that good with math, so I cant understanding well the theory. so can anyone please make an example implementation or write a clear formula? Could the granting lag for each badge be added to the FAQ? On my fully updated Ubuntu 18.04.3 system, audio doesn't work unless I switch between outputs. When I boot my PC, the right output (stereo speakers) is already selected by default, but there is no audio from Chromium, Firefox, VLC or any other program. However, the GNOME speakers test works. I can hear "front left" and "front right" from there, but no audio from other programs. In order to fix that, I can simply switch to another audio output (e.g. HDMI out) and then switch back to the stereo speakers, and the audio will magically work. Any idea why? It's not a big deal because it takes a couple of seconds to switch between outputs, but it's kind of annoying to do that after every reboot.