I need your help please. How can I typeset this set (in the picture blew) in Latex. I even failed to write an attempt. I appreciate your help. Thanks in advance.
I was wondering what the proper LaTeX code would be to display something like this:    You don't have to include the mathematical symbols, what is important is the structure.
My kids are playing Minecraft on 2 PCs, creative mode.  They are connected by the way of one of them starts a single player game on the other one than joins that game over the LAN.  Can I, using Minecraft PE on my iPad, join their game as well? Why must a singularity form inside a black hole? I am currently looking at the various libraries that I can use to show a map in my custom Android App. I have found several like Mapsforge, OSMDroid, ArcGIS runtime for Android, Google Maps for Android and so on. I'm sure that I am missing a few.   Is there a comparison chart somewhere about the differences in functionalities and pros and cons of each one?   If there isn't one, we could make this question community wiki, to serve alongside  &amp; . D+ and D- on USB I'm making a small project which will take +5v from USB, What should I do with the D+ and D-, keep it open or short them to ground or do I have to add some components?  I want to run ATMEGA168 and 16x2 LCD with back light. Why does a Tesla car use an AC motor instead of a DC one? I was just watching a mega factory video and wondered why they use an AC motor which requires a power inverter instead of DC which may be powered directly from their DC battery? Introducing an inverter means more cost (weight, controller, etc).  Are there any reasons for that? What are the differences between an AC and DC motor that may have lead to this decision? Also does anyone know what kind of motor is used in other electric cars? Is $x^3+y^3+z^3-1$ irreducible over a field $k$ of characteristic $\neq 3$? Is $x^3+y^3+z^3-1$ irreducible over a field $k$ of characteristic $\neq 3$?   If I can show that $y^3+z^3-1$ is irreducible, I believe I can use Eisenstein's criterion. But I don't see how to show even this.  The other approach on my mind is to show that $k[x,y,z]/(x^3+y^3+z^3-1)$ is an integral domain, but this doesn't seem particularly promising either. How can I prove that if $n$ is even then $n^2$ is even and if $n$ is odd then $n^2$ is odd? what is the difference between IBE and ABE schemes Can somebody explain in simple words. real life example light help and limitations of these schemes etc. Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$ My application got crashed because of not initializing the view Proof that in a field $x=0$ is equivalent to $x=-x$ When installing Wine on 64-bit Ubuntu 12.04, both 64-bit support and 32-bit support get installed. If I run wine foo.exe where foo.exe is a 64-bit-aware installer, it thinks it's on 64-bit Windows. This would be fine if this mode didn't fail, but in my case, it does (yet the Wine database suggests the app I'm trying to install should work, presumably as a 32-bit app).  How do I tell Wine (and Winetricks) to use Wine in 32-bit-only mode? For example, if I have a lens that is 16mm-50mm, which focal length would be the closest to the human eye's view? (I don't have a camera yet, so I'm just curious.)   Would 50mm be more zoomed in than "normal"?  I imagine 16mm would be wider than the normal human point of view? Difference between declaring variables before or in loop? I have always wondered if, in general, declaring a throw-away variable before a loop, as opposed to repeatedly inside the loop, makes any (performance) difference?  A (quite pointless) example in Java:  a) declaration before loop:  double intermediateResult; for(int i=0; i &lt; 1000; i++){     intermediateResult = i;     System.out.println(intermediateResult); }   b) declaration (repeatedly) inside loop:  for(int i=0; i &lt; 1000; i++){     double intermediateResult = i;     System.out.println(intermediateResult); }   Which one is better, a or b?   I suspect that repeated variable declaration (example b) creates more overhead in theory, but that compilers are smart enough so that it doesn't matter. Example b has the advantage of being more compact and limiting the scope of the variable to where it is used. Still, I tend to code according example a.  Edit: I am especially interested in the Java case. Difference between Loading a class using ClassLoader and Class.forName This question led to a new package:      I'm giving my students an old exam and barely remembered to change the date at the top. A colleague and I joked about how long we could reuse the same exam, and it made me wonder if I could use LaTeX to create an exam that looked like it was written in 1963 on a typewriter.  Here's what I'd like to see:   Typewriter font even in math mode. (Several ways to accomplish this; is there a "best" way?) Slight inconsistencies in the printing of each letter. I attempt this below adapting code taken from . Each word has a random vertical shift, though I'd like to see it reduced to each letter having its own vertical shift. Other typewriter-like irregularities would be great. It would be great if math-mode delimeters \left(, \right}, etc., can be created in a piece-meal fashion as they did in days of old. Fraction bars, tops of square-root symbols -- any horizontal line, really -- is made up of a series of en-dashes that don't quite match up.   Here is what I've come up with so far:  \documentclass[10pt]{article}% This is a document class providing more font size options \usepackage{graphicx} \usepackage{ifthen} \usepackage[textwidth=7.5in,textheight=9.5in]{geometry} \pagestyle{empty}  % thanks to Bruno Le Floch: https://tex.stackexchange.com/q/9331/4012 % and in his comments to https://tex.stackexchange.com/a/29458/4012 \usepackage[first=-1,last=1]{lcg}% you can play around with these values \makeatletter \newcommand{\globalrand}{\rand\global\cr@nd\cr@nd} \makeatother  \newcommand{\randomvshift}[1]{\globalrand\raisebox{\value{rand}pt}{#1}}  %%% thanks to Martin Scharrer: https://tex.stackexchange.com/q/11598/4012 \makeatletter \def\typewriter#1{%     \@typewriter#1 \@empty } \def\@typewriter#1 #2{%    \randomvshift{#1}\space    \ifx #2\@empty\else     \expandafter\@typewriter    \fi    #2% } \makeatother \begin{document}\tt  \typewriter{Math 101 Fall 1963}  \begin{enumerate} \item   \typewriter{$\frac{\texttt{d}}{\texttt{dx}}\texttt{(x)}^2$}  \item \typewriter{State the Fundamental Theorem of Calculus.}  \end{enumerate}  \end{document} Forbid links to open new tabs in Google Chrome Proving a vector space is infinite-dimensional Let $S$ be a vector space. Suppose that for any positive integer $n$, there exists a linearly independent subset $S_n ⊆ V$ of size $n$.   How do you show that $S$ is not finite dimensional but infinite-dimensional.  I understand that to be finite dimensional then it must have a finite then  there exists a finite set that such at $\operatorname{Span}(T)=S$. So would it be right to prove by contradiction that there is not a finite spanning set that satisfies $\operatorname{Span}(T)=S$, and hence I could argue that the vector space $S$ is infinite dimensional.  How would I show that $S$ does not have a spanning set $T$, such that $\operatorname{Span}(T)=S$? Manually installing a program on Debian How To Use DateTimePicker In WPF? I have no idea how to use the DateTimePicker control in WPF. It is not available in the Toolbox.