C# implementing IDisposable just to clean up event handlers
Should I always disconnect event handlers in the Dispose method?
Suppose that $V, W$ are closed in $X$ and that $V\cap W, V\cup W$ are connected. Show that $V$ and $W$ are connected.  My attempt: Suppose that $V=U_1\cup U_2$ where $U_i$ are open in $V$, not empty and $U_1\cap U_2=\emptyset$. This induces a separation for $V\cap W$: $$ V\cap W = (U_1\cap W)\cup(U_2\cap W).$$  $U_i\cap W$ is open in $V\cap W$  $(U_1\cap W)\cup (U_2\cap W)=\emptyset$ as otherwise $U_1\cap U_2 \ne \emptyset$.  Now, I need to show that both sets are not empty. We know that $V\cup W$ is connected and closed in $X$. So, for all $x\in V\cup W=U_1\cup U_2\cup W$ and all neighborhoods $Z$ (in $X$!) of $x$ we have that $Z\cap (V\cup W) \ne \emptyset$. We can choose $x\in U_1 \subseteq V\cup W$. But then I would have to find a neighborhood of $x$ in $X$. I can't find one... How can I complete this bullet point?   Thanks. What do you call someone who has extensive knowledge but won't share it? Find the domain of composition of two functions Let $$f(x)= \frac{x}{x-9} \text{ and } g(x) = \frac{-6}{x+5} $$   Find the domain of $f \circ g.$    Please show the steps and substitution/algebra to the problem. Thank you. How to resolve the C:\fakepath? This is trigonometry from double angles and compound angles. Thus far I've simplified it up to this point. $$2 \sin^2θ – 3\sinθ +1 = 0$$  I'm trying to factorize this to solve for General Solution. I tried taking out a common but that +1 is giving me a problem. I used the quadratic equation to get 1 and 0.5 as an answer, but i don't know how to write it in terms of 2sin(squared)θ and -3sinθ.  Any help will be appreciated. Error-Handling in Swift-Language Can I use a HDD on my PS3 if I have already used another on the same console? I'm thinking of changing the Hard Disk of my PS3 (Slim 120GB), but I am unsure of what will happen to the data on the one I previously had if I do this:   PS3 has some data in the HDD. I turn off PS3, change HDD, install OS on new HDD. I download some data on new HDD from PS Plus.   Let's imagine I forgot to back something up...   I turn PS3 off, change HDD back.   Can I still use the old hard drive without needing to format it again? If the edges of the complete graph $K_{17}$ (on 17 vertices with no three collinear) are each colored one of three colours can it be proven to have two or more monochromatic triangles? Shape gets distorted when adding stroke in Illustrator CS6 I very recently started learning how to use Adobe Illustrator (CS6), and just now I noticed something strange. When I add a 1pt stroke to my shape, it gets slightly distorted. This distortion does not disappear if I remove the stroke. (But only if I remove the stroke by setting its weight to 0. Using CTRL+Z does return the shape to its former state.)  After adding and removing the stroke a few times, the difference becomes quite noticable:   Am I doing something wrong? Is it a bug? I can't imagine this being the expected behaviour.  EDIT: I think I figured it out. Appearantly, turning 'Align to pixel grid' off doesn't affect previous shapes. If I turn it off and then recreate my shape from scratch, the problem is fixed.   However, I was wondering if their is a way to disable the effect for existing shapes. In other words, can I 'fix' the shapes I created while 'Align to pixel grid' was still on? Reference to the Table of Contents page I thought that someone must have asked this, but my searches didn't find it.  I am looking to refer back to the table of contents from places in my document. How can I do this? Let a,b,c be positive real number, such that  $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=a+b+c$. Prove that :  $\frac{1}{(2a+b+c)^2}+\frac{1}{(2b+c+a)^2}+\frac{1}{(2c+a+b)^2} \leq \frac{3}{16}$  Can anyone help me how to deal with it? Why is compactness in logic called compactness? In logic, a semantics is said to be compact iff if every finite subset of a set of sentences has a model, then so to does the entire set.   Most logic texts either don't explain the terminology, or allude to the topological property of compactness. I see an analogy as, given a topological space X and a subset of it S, S is compact iff for every open cover of S, there is a finite subcover of S. But, it doesn't seem strong enough to justify the terminology.   Is there more to the choice of the terminology in logic than this analogy? My GNU/Linux system (Arch) now has libncurses.so.6 rather than libncurses.so.5. But I have upstream's vanilla TeX Live (fully updated) and xindy wants libncurses.so.5:    xindy --version   produces the following error  xindy release: 2.5.1 xindy script version: 1.18 /usr/local/texlive/bin/xindy.run: error while loading shared libraries: libncurses.so.5: cannot open shared object file: No such file or directory   And ldd can confirm the problem:  ldd /usr/local/texlive/bin/xindy.run    gives      linux-vdso.so.1 (0x00007ffc07997000)     libm.so.6 =&gt; /usr/lib/libm.so.6 (0x00007fab4d1b1000)     libcrypt.so.1 =&gt; /usr/lib/libcrypt.so.1 (0x00007fab4cf79000)     libncurses.so.5 =&gt; not found     libdl.so.2 =&gt; /usr/lib/libdl.so.2 (0x00007fab4cd75000)     libc.so.6 =&gt; /usr/lib/libc.so.6 (0x00007fab4c9d1000)     /lib64/ld-linux-x86-64.so.2 (0x00007fab4d4af000)   How can I use xindy without changing my operating system, while using vanilla TeX Live?  2 strategies have occurred to me:   compile xindy from sources against libncurses.so.6; compile and install libncurses.so.5 alongside libncurses.so.6.   Option (2) can be dodgy or can be fine, depending on the details. My suspicion is it may be dodgy for this library, simply because no packages are available for the old version of the library, which might mean there are problems having both installed. Moreover, since everything else is compiled against the new version, I'm not sure whether this would be enough for xindy anyway.  Option (1) I have no idea about. I don't know if this is even vaguely doable or, in fact, where the sources are or what might be required to compile them. (I don't suppose there's any chance a pre-compiled binary is available somewhere? But that is probably hoping for too much ;).)  What is the most practicable approach? Defining scalable "white curly brackets" {| and |} (⦃ and ⦄) I would like to construct what Unicode calls "white curly brackets" that are in addition scalable. They look like ⦃ (≈{|) and ⦄ (≈|}) and have Unicode codepoints U+2983 and U+2984.  unicode-math has them as \lBrace and \rBrace, but (1) I don't presently use XeTeX or LuaTeX and (2) their design (shown in  on pages 3-4) is not to my liking: the brace part is too fat for my taste, and I would like the vertical bar to not leave any protrusions. I am trying to have them visually match the parentheses \llparenthesis, \rrparenthesis, \llbracket, and \rrbracket from stmaryrd.  Right now I am using a makeshift definition, which is sufficient for now, but the symbols don't scale (in general or with \left/\right). Here is sample code:  \documentclass{article} \usepackage{amsmath} \usepackage[only,llbracket,rrbracket,llparenthesis,rrparenthesis]{stmaryrd} % for comparison with 4 similar parenthesis symbols \usepackage{accsupp} % for ensuring the right Unicode codepoint upon pasting  \newcommand*{\llbrace}{%   \BeginAccSupp{method=hex,unicode,ActualText=2983}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char102}%     \mathchoice{\mkern-4.05mu}{\mkern-4.05mu}{\mkern-4.3mu}{\mkern-4.8mu}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char106}%   \EndAccSupp{}% } \newcommand*{\rrbrace}{%   \BeginAccSupp{method=hex,unicode,ActualText=2984}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char106}%     \mathchoice{\mkern-4.05mu}{\mkern-4.05mu}{\mkern-4.3mu}{\mkern-4.8mu}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char103}%   \EndAccSupp{}% }   \begin{document}  \noindent ok: \(\displaystyle\llbrace abc \rrbrace\) \(\textstyle\llbrace abc \rrbrace\) \(\scriptstyle\llbrace abc \rrbrace\) \(\scriptscriptstyle\llbrace abc \rrbrace\)  \noindent ok: \(\displaystyle \llbrace \frac{a}{b} \rrbrace\) \(\textstyle\llbrace \frac{a}{b} \rrbrace\) \(\scriptstyle\llbrace \frac{a}{b} \rrbrace\) \(\scriptscriptstyle\llbrace \frac{a}{b} \rrbrace\)  \noindent incorrectly scaled (\verb|\scriptsize|): {\scriptsize\(\llbrace abc \rrbrace\)} (large magnification required)  \noindent incorrectly scaled (\verb|\tiny|): {\tiny\(\llbrace abc \rrbrace\)}  \noindent \verb|\left| and \verb|\right| not possible before \verb|\llbrace| and \verb|\rrbrace|: \\ \indent \(\llbrace \left\llbracket\left\{\left[(a) \cdot bc^{2^3}\right]^4\right\}^5\right\rrbracket \rrbrace\) % Note: This is also not possible with \llparenthesis and \rrparenthesis from stmaryrd.  \noindent for comparison: \(\llparenthesis x \rrparenthesis, \llbracket x \rrbracket, \llbrace x \rrbrace; (x), [x], \{x\}\)  \end{document}   Lines 1 and 2 look just right with the present setup. Lines 3 and 4 demonstrate that my definitions don't scale. Lines 5a/b gives an example of where I would like to be able to use \left and \right. Line 6 juxtaposes different types of parentheses for visual comparison.  Is there an easy way to scale the glyphs I have constructed myself? Or is designing new glyphs the only way? While the vertical part of my glyphs doesn't leave any protrusions, the "brace part being too fat" part of my problem isn't being addressed by my code. With this in mind: I recognize that it might not be that easy to make the brace part of the glyph thinner (though if you can, more power to you), but I think that any solution that addresses the scaling problem for any manually constructed glyph cluster will be a valuable contribution to the community.    For a slightly different setup (original example code) with  \RequirePackage{fix-cm} \documentclass[12pt]{memoir} \usepackage{fixltx2e}[2006/09/13] \usepackage{amsmath} \usepackage{txfonts} \usepackage[only,llbracket,rrbracket,llparenthesis,rrparenthesis]{stmaryrd} \usepackage{accsupp}   in the preamble, one needs \mkern-5.7mu in the fourth argument to \mathchoice for "correct" scaling. To see what goes wrong in that case, it's best to include a line such as discontinuous small symbols in a footnote\footnote{\(\scriptscriptstyle\llbrace \frac{a}{b} \rrbrace\)}. This might help a potential answerer test things out. Is it possible to add a list of hosts that are only specific to a certain user? Perhaps a user-specific hosts file?  This mechanism should also complement the entries in the /etc/hosts file. Nesting HTML- anchor tags Derive a formula to find the number of trailing zeroes in $n!$ Possible Duplicate:          I know that I have to find the number of factors of $5$'s, $25$'s, $125$'s etc. in order to do this. But how can you derive such a formula for any number $n$? Invertibility of the Product of Two Matrices I have shown that if two $n\times n$ matrices $A$ and $B$ are invertible, then $AB$ is also invertible. I am having problems though with showing that $(AB)^{-1}=B^{-1} A^{-1}$. I thought of using their left-multiplication transformations but it seems that this is only associative and not commutative so I can reverse $L_A L_B$ Where $\phi(n)$ is the Euler phi function, how do you find all $n$ such that $\phi(n)|n$? What is the current URL to create a new Google Document please? Since Google last updated their Docs the old URL does not work.