I'm new to LaTeX and I was wondering how to write a command that gives me \left\{A,B\right\}. I want to renew this command like \poisson, for example.  If someone could help me, I will be very grateful.  Sorry if the question is basic.  Thanks.
I have been using LaTeX for a long time now, and I find myself often going to this website to solve my problems. This often includes copy pasting codes which include \newcommand, \newenvironment and \def. I think it is time I start to learn how to use them so I can solve my problems myself! It is always better if you actually know what is going on inside your code.  I am wondering if there is any turtorial or book out there that handles how to use those commands. Or is the best way to learn to just mess with a random file?   Thanks in advance!  (Also this is my first time I post here after using this website for so long, I really appreciate everyone who posts and tries to help other people here!)
The main effect will be non-significant if the interaction is significant? Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$ Why is brace expansion not supported? Do I have to do any configuration to start brace expansion? When I run mkdir {1..10}, it just creates a dir naming {1..10}. Closure of a Ball is Contained in Closed Ball (usual metric) Let $\overline{B_d (x, r)}$ be the closure of an open ball, and let $\hat B_d (x, r)$ be a closed ball. Show that in any metric space $(X, d)$, $\overline{B_d (x, r)} \subseteq \hat B_d (x, r)$ for all $x \in X$ and $r &gt; 0$.    I used the definition of closure: $\overline{B}$ = $B \bigcup B'$. If $x \in \overline{B}$, then $x \in B$ or $x \in \overline{B}$, or both. If $x \in B$, then clearly $x \in \hat B$ since $B \subseteq \hat B$. But, if $x \in B'$, then $x$ is an accumulation point. Since $\hat B$ is closed, it contains all accumulation points of $B$. Thus, $x \in \hat B$.  Is this approach correct, or at least in the right direction? Should I be using the closure definition, or try another one? Thank you. How can I capture KeyDown event on a WPF Page or UserControl object? I have a Page with a UserControl on it.  If the user presses Esc while anywhere on Page I want to handle.  I thought this would be as easy as hooking up the PreviewKeyDown event, testing for the Esc key, and then handling it.  However, when I placed I breakpoint in the event handler I found it was never getting called.  I thought perhaps the UserControl might be getting hit, so I tried PreviewKeyDown there... same result.  Does anyone know the proper place to test for a KeyDown or PreviewKeyDown on a Page object? In my ~/.bashrc file reside two definitions:   commandA, which is an alias to a longer path commandB, which is an alias to a Bash script   I want to process the same file with these two commands, so I wrote the following Bash script:    #!/bin/bash  for file in "$@"     do     commandA $file     commandB $file done   Even after logging out of my session and logging back in, Bash prompts me with command not found errors for both commands when I run this script.  What am I doing wrong? Force a rebuild of the start menu program index/database in Windows 10 With Windows 10 Microsoft migrated to a database-ish solution for indexing programs in search and the start menu, rather than just using a /startmenu/ directory. AFAIK the exact implementation is still pretty unclear, but there is something along those lines.  Updating from 8.1 to 10 causes it to migrate everything from /startmenu/ to the new system, which ignoring issues such as a (seemingly arbitrary) cap of 500 applications, works fine.  However this failed for me, and from googling seems to be an issue from upgrading with an older dev build, which then carried on to RTM.  So does anyone know a way to force a rebuild/re-index of the program library? Rebuilding the system wide index through control panel (also in &lt;=8.1) has no effect. Cannot mount USB stick - errors out with "$MFTMirr does not match $MFT" If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed I'd like to know if the following proof is valid.  The only thing I'm not sure about (though I can't see why it's invalid if it is) is if we can always use the Hausdorfness of $Y$ to separate an open set from $f(C)=g(C)$.  "Let $X$ be a space, $Y$ a $T_2$-space, and $f,g:X \to Y$ continuous functions.  Prove that $C:=\{x \in \,|\,f(x)=g(x)\}$ is a closed subset of $X$."  Let $x \in X$ be such that $f(x) \ne g(x)$.  Since $Y$ is $T_2$, there are open sets $U_\alpha \ni f(x)$ and $V_\alpha \ni g(x)$ such that $U_\alpha \cap O_\alpha=V_\alpha \cap O_\alpha=\varnothing$ for all $\alpha \in A$ where $A$ is the set indexing the points of $f(C)=g(C)$, and $O_\alpha$ is an open set containing $x_\alpha \in f(C)=g(C)$.  Let $U:=\displaystyle\bigcap_{\alpha \in A} U_\alpha$ and $V:=\displaystyle\bigcap_{\alpha \in A} V_\alpha$.  Then $U \cap f(C)=V \cap f(C)=\varnothing$.  Therefore, since $f,g$ are continuous, $f^{-1}(U)$ and $g^{-1}(V)$ are open sets in $X$ disjoint from $C$.  Since $X\setminus A$ is the union of such open sets, it is open itself and therefore $C$ is closed.  Thanks. What equipment is necessary/preferred for real estate photography? What equipment is necessary for real estate photography, and what is preferred?  I'm starting into real estate photography, and I'm trying to figure out what I need and what I will want to plan on adding to my kit as I go.  I'm thinking especially along the lines of lighting equipment and lenses (focal lengths).  For example, is an ultra-wide actually necessary? Or is a general walk around sufficient. Let me use the following example to explain my question: public string ExampleFunction(string Variable) {     return something; }  string WhatIsMyName = &quot;Hello World&quot;; string Hello = ExampleFunction(WhatIsMyName);  When I pass the variable WhatIsMyName to the ExampleFunction, I want to be able to get a string of the original variable's name. Perhaps something like: Variable.OriginalName.ToString()  Is there any way to do this? How to convert decimal to hexadecimal in JavaScript Bayes' Theorem Intuition I've been trying to develop an intuition based understanding of Bayes' theorem in terms of the prior, posterior, likelihood and marginal probability. For that I use the following equation: $$P(B|A) = \frac{P(A|B)P(B)}{P(A)}$$ where $A$ represents a hypothesis or belief and $B$ represents data or evidence. I've understood the concept of the posterior - it's a unifying entity that combines the prior belief and the likelihood of an event. What I don't understand is what does the likelihood signify? And why is the marginal probability in the denominator? After reviewing a couple of resources I came across this quote:     The likelihood is the weight of event $B$ given by the occurrence of $A$ ... $P(B|A)$ is the posterior probability of event $B$ , given that event $A$ has occurred.   The above 2 statements seem identical to me, just written in different ways. Can anyone please explain the difference between the two? Command line move file with long directory path without repeating directory path Is there any way of executing a mv command without typing the full path in the second argument?  Example:  mv my/file/that/has/a/really/long/path/foo.bar some_magic_operator_that_means_the_same_directory/foo.baz Avoiding GeoServer/Java out of heap space error? I'm new to Geoserver, Ubuntu and Java, but have downloaded a virtual machine from gisvm.com and am getting up to speed. I got as far as configuring it with some fairly large shapefiles from a project I've worked on previously.  My question is related to a problem which I see if I show the shapefile using the OpenLayers layer preview option. I see an error:     OpenLayers map preview code="internalError" Rendering process failed.   java.lang.OutOfMemoryError: Java heap space   Googling has led me to plenty of Java command line options to increase heap space, but I have no idea if this should be applied to an environment variable, in a startup script or as a part of the Geoserver config.   Can you help me to understand what I need to edit to get this working?   I'm also wondering if I should be splitting my shapefile into smaller pieces. Cut part from video file from start position to end position with FFmpeg I have a video file of 30 minutes, but I want to extract a video from 00:09:23 to 00:25:33.   I can define the startposition with -ss, but I couldn't find one for the end position. Any help please? Does ClamAV Scan Windows virus? I'm new to Ubuntu.  I'm now setting up an OwnCloud server which supports ClamAV file scan.  Since most of the users connected to the server uses Windows OS, can ClamAV scan for Windows virus?  I also did some research that such as BitDefender. It clams that it scans real time, if someone upload files to the server, will BitDefender scan the file even OwnCloud doesn't support?  By the way, I heard that if I update the system frequently, I don't have to install any antivirus that scan for Linux virus. Is that right? 100% confidence interval for mean Is it possible to apply the law of the iterated logarithm (e.g. ) to derive non-trivial (i.e. bounded) 100% confidence intervals for population averages?  An abstract () gives at least such hint. However, its first reference by Robbins () does not seem to cover such result, as pointed out in @whuber's comment.  Edit: After justified comments by @whuber, I reformulated the question. What is the proof that the total number of subsets of a set is $2^n$? What is the proof that given a set of $n$ elements there are $2^n$ possible subsets (including the empty-set and the original set). Making image positioned on textbox clickable in case of ipad (Creating HTML5 Search input type for iOS)