Number of onto functions from set A to B
Calculating the total number of surjective functions
The uniform limit of Continuous Functions is continuous.   Proof Let $\varepsilon &gt; 0$. There exists $N$ in natural numbers such that $n&gt;N$ implies  $|f_n(x)-f(x)| &lt; \frac{\varepsilon}{3}$ for all $x$ in $S$. In particular $|f_{N+1}(x)-f(x)| &lt; \frac{\varepsilon}{3}$ for all $x$ in $S$. Since $f_{N+1}$ is continuous at $x_0$ there is a $\delta&gt;0$ such that, $x$ in $S$ and $|x-x_0| &lt; \delta$ imply $|f_{N+1}(x)-f_{N+1}(x_0)|&lt; \frac{\varepsilon}{3}$ Now we conclude $x$ in $S$ and $|x-x_0| &lt; \delta$ imply $|f(x)-f(x_0)|&lt; 3 \cdot \frac{\varepsilon}{3} = \varepsilon$.  Can someone explain what is happening here? I don't follow it all. Group Membership Test for Permutations Number of functions from n-element set to {1, 2, …, m} I've gotten stuck at the following exercise;     There are m functions from a one-element set to the set {1, 2, …, m}.   How many functions are there from a two-element set to {1, 2, …, m}?   From a three-element set? Give a recurrence for the number of T(n) of   functions from an n-element set to {1, 2, …, m}. Solve the recurrence.   I'm not sure how to begin solving it? How can I detect if I'm in a subshell? Colorimetry is not the same I used the following code to list my java code, but the it looks like there's too much space between words. What can I do?  % source code listing \usepackage{listings} \usepackage{color} \usepackage{xcolor}  \usepackage{caption}  % citation style \usepackage{apacite} \DeclareCaptionFont{white}{\color{white}} \DeclareCaptionFormat{listing}{\colorbox{gray}{\parbox{\textwidth}{#1#2#3}}}  \begin{document} \begin{lstlisting}[label=some-code,caption=bind to service call] bindService(new Intent(this, Recognizer.class), recConnection, Context.BIND_AUTO_CREATE); \end{lstlisting} \end{document}   The snapshot of what I got. The code not completely shown, and space too wide, in function bindService. What's the name of each pseudo-rectangle in a spherical surface? Are recommendation questions an acceptable kind of list-type question or should they be closed? Recommendations are a recurring topic on multiple Stack Exchange (SE) sites. Some sites allow recommendations (ex: ), some do not (ex: ). There are many reasons for that and I can still remember animated discussions on this subject on the Gaming meta. Then there is that existential problem with Sci-Fi SE, &quot;What problems does answering a question on this site solve?&quot;  The only common problem I can think of is What to read/watch next?, which obviously led to a big number of recommendation questions, later slightly disguised as list question. And the main trouble with these questions isn't objectivity at all, some of them aren't even subjective. It's the fact that they don't have an answer - they are open ended. -  Those questions are monstrously popular because:  There's an actual problem to be solved,  or  This problem is quite common.  In view of the  blog post, a recommendation question fails the &quot;real questions have answers, not items or ideas or opinions.&quot; criteria. But it's still a &quot;practical, answerable questions based on actual problems that you face. &quot; and it requires expertise to answer. The problem is that there are multiple acceptable answers, and the asker is not the best person to evaluate the best answer because he doesn't know which one is the best compared to the others, and he cannot test it in short term. Even the need to accept an answer is questionable. So, is a recommendation question an acceptable kind of list-type question or should it be closed just like any other list-type questions? Newer "mainline" versions of the kernel are available from the , e.g. 3.4 and 3.5, while Ubuntu 12.04 is on 3.2.   What are the mainline kernels? Are they better than my existing kernel? What are the pros and cons of upgrading to a mainline kernel? Will I easily be able to go back? I'm a bit annoyed with the typesetting of citations that biblatex deems "ambiguous". In the following example, I have two papers with the same first author, but a different second author in two different years. When citing in the main text, the second author is included before "et al", since biblatex deems these references to be ambiguous. However, the references were published in different years, so I cannot see why these are ambiguous. Is it possible to get these citations referenced using only the first author?  MWE  \documentclass{article}  \usepackage{filecontents} \usepackage[hyperref,style=authoryear,natbib=true,maxbibnames=10,maxcitenames=2,useeditor=false,url=false,useprefix,giveninits=false]{biblatex} \addbibresource{ref.bib}  \begin{filecontents}{jobname.bib} @book{author_book, title = {Book's title}, author = {Author, Some and Better, Some and Cetter, Some}, location = {The City}, publisher = {Publisher}, date = {2005}, } @book{author_book2, title = {Book's title}, author = {Author, Some and Getter, Some and Cetter, Some}, location = {The City}, publisher = {Publisher}, date = {2006}, } \end{filecontents}  \bibliography{jobname} % \bibliography{ref}  \begin{document} Hello world \citet{author_book} \citet{author_book2} \printbibliography \end{document} I need a number of different full-page DOM samples for my qUnit test suite $x^3-9=y^2$ find integral solutions Find all integral solutions  $x^3-9=y^2$  I tried many times but still no idea how to solve it. I will be grateful for any help. Can an integrity check be run against a USB boot disk? "In the case of medical diagnostics, there is a cost associated with each medical procedure that provides additional information (blood test, x-ray, etc.)."   Should that end with "etc.).", "etc)." or "etc.)"? I searched around, and currently there are two methods suggested; installing an enhancement for Windows Subsystem for Linux and installing an XServer.  I want to know which method is the most hassle-free (easy to install AND to use), and which one is less memory-heavy.  I just want Synaptic and CMake. Why couldn't that be a builtin feature? Question about repeating decimal? For simple fraction, we can easily convert it to repeating decimal by calculator. Ex. $\frac 1 3 = 0.33333\ldots$, $\frac 1 7=0.(142857),\ldots$ But some fraction fraction like $10/29, 1/97,...$ The repeating part of them are too long, so it can't fully show on the calculator. So is there any algorithm  to find the repeating part for that fraction? Conky does not work properly on Ubuntu 16.04 GNOME I have this strange problem with conky. It doesn't show properly on the desktop:    I've tried everything from editing conky widget file to reinstalling conky and conky manager (v.2.4). Who knows how to fix it? I have encountered this question while tring to figure out why every sequential space $X$, is a quotient spaces of a metric space. If I understand correctly, given a sequential space, every sequence (including it's limit) can be identified with the space $Y=\{0\} \cup \{\frac1{n+1}|n \in N\}$. So The space $X$ can viewed as a quotient space of $\bigoplus_{(x_n) \in C} \{(x_n) \} \times Y$ where $C$ is the set of all converges sequences in $X$. My question is, How can I show that this space is metrizable?  Thank you! Shir How do I install KDE? I want to have both KDE and Gnome shells on Ubuntu. Ubuntu only has Gnome installed by default. How do I install KDE? The difference between two periodic functions converges to zero, is this two functions identical? If $f(x)$ and $g(x)$ are two periodic functions, that is, $f(x+T_1)=f(x)$ and $g(x+T_2)=g(x)$ for every $x \in \Bbb R$. Now that $\displaystyle\lim_{x\to\infty}(f(x)-g(x))=0$.  Conjecture: $f(x) \equiv g(x)$.