Here's my code. I would like to not show the equation numbers to the right of the equations. Is that possible?  \frame[t]{ \frametitle{An Example} \vspace{0.1in} \begin{itemize} \item Since $A= ABUAB^c$ with $AB$ and $AB^c$ being mutually exclusive events, by Axiom 3,  \begin{align} P(A) &amp;= P(AB)+P(AB^c) \\ &amp;= P(A|B)P(B) + P(A|B^c)P(B^c) \\ &amp;= P(A|B)P(B) + P(A|B^c)\lbrace1-P(B)\rbrace. \end{align} \end{itemize} }
I have an equation like this:     \begin{align}       P(A \cup B) = \sum_{\omega \in A \cup B} P(\omega) = \sum_{\omega \in A} P(\omega) + \sum_{\omega \in B} P(\omega)       = P(A) + P(B)     \end{align}   For some reason, LaTeX is automatically labeling the equation. How do I turn that off? Secondly how do I write something in LaTeX on this site. I tried enclosing in '$' but it doesn't work.
I have from Exercise 1 pg 33 - "Algebra - T. W. Hungerford" following:      Question to proof: Show by example that the first conclusione may be false if $G,\, H$ are monoids that are not group.   I thinked:     Proof: let be for example two monoids $(G:=\{\emptyset\}, \bot)$ and $(H:=\{\emptyset, \{\emptyset\}\}, \top)$ with: $$\begin{array}{c|c} \bot &amp; \emptyset \\ \hline \emptyset &amp; \emptyset \end{array} \, \, \, \,\, \,\, \,\, \,\, \,\, \,\, \,\, \,\, \, \begin{array}{c|cc} \top &amp; \emptyset &amp; \{\emptyset\}\\ \hline \emptyset &amp; \emptyset &amp; \emptyset \\ \{\emptyset\} &amp; \emptyset &amp; \{\emptyset\} \end{array}$$ $G$ with $e_G:=\emptyset$ like neutral element and $H$ with $e_H:=\{\emptyset\}$ like neutral element. Let be $f$ a function from $G$ to $H$ with $\emptyset \mapsto \emptyset$ (namely $x \mapsto x$), the function is Homomorphismus in fact $$ \begin{align} {\color{Red}f}{\color{Red}(}{\color{Red}x}{ \color{Red}\bot }{\color{Red}y}{\color{Red})}=&amp;f( \emptyset \bot \emptyset)= {\color{Green}f}{\color{Green}(}{\color{Green}\emptyset}{\color{Green})}= \emptyset \\ {\color{Red}f}{\color{Red}(}{\color{Red}x}{\color{Red})} {\color{Red}\top} {\color{Red}f}{\color{Red}(}{\color{Red}y}{\color{Red})}=&amp;f(\emptyset) \top f(\emptyset)= \emptyset \top \emptyset= \emptyset \\ &amp;\text{with }x,y \in G \end{align}$$ but it means that $$ \begin{align} f(e_G)&amp;\neq e_H \\f(e_G)={\color{Green}f}{\color{Green}(}{\color{Green}\emptyset}{\color{Green})}=\emptyset &amp;\neq \{\emptyset\}= e_H \end{align}$$ Therefore $f$ ist Semigroup-Hom but not Monoid-Hom...   Is it correct? How do I get the Minecraft GUI scale to go back to Auto? I have been playing Minecraft, and I went into the settings to see what could be changed. I was in display and I saw the GUI scale was set to "Auto", which was fairly large. I cycled through the scales until I got back to auto, but the GUI scale was stuck at normal size and wouldn't allow me to make it large again. I know this isn't such a big problem, but I really like big font and this is a constant bother to me. Double booked - User bookmarking question recorded twice Why doesn't Cantor's diagonal argument also apply to natural numbers? Distribution of sum of exponentials Let $X_1$ and $X_2$ be independent and identically distributed exponential random variables with rate $\lambda$. Let $S_2 = X_1 + X_2$.  Q: Show that $S_2$ has PDF $f_{S_2}(x) = \lambda^2 x \text{e}^{-\lambda x},\, x\ge 0$.  Note that if events occurred according to a Poisson Process (PP) with rate $\lambda$, $S_2$ would represent the time of the 2nd event.   Alternate approaches are appreciated. The approaches provided are commonly used when learning queueing theory &amp; stochastic processes.     Recall the Exponential distribution is a special case of the Gamma distribution (with shape parameter $1$). I've learned there is a more general version of this  that can be applied. What's the fixed size of the suggested edit queue? We know that Stack Overflow has a suggested edit queue, visible to the users who have the  privilege. Someone said the queue has a fixed size.  What's the fixed size of the suggested edit queue?  Is it often that the queue gets filled up and users can no longer suggest edits? I have a basic grammar question about the past tense. If I met a guy yesterday, which tense should I use about his name today?  For example,     "Yesterday I met a guy, his name is/was John." Windows Metro apps have wrong icon in search UI I'm creating a composite image, in order to create a timeseries. I've already created the composited image, but i am having difficulty masking the clouds of the composite image. I've followed the code from a page having similar problems, however when I run the code (after replacing all the l8_mayo to composite as that is the name of my composite var), I get the error code of composite.map not a function. This error does not come up when I run the exact same code from the previous answer. Can someone explain how to overcome this problem? Here is the page I used:  here is my code and the link to my code:  (point is the long, lat for Lake Manyara, Tanzania)  //load images for composite var sr14= ee.ImageCollection('LANDSAT/LC08/C01/T1_SR') .filterBounds(point) .filterDate('2014-01-01','2014-03-01') .select(['B4','B3','B2']);  // Temporally composite the images with a maximum value function. var composite = sr14.max(); Map.setCenter(35.8244, -3.5799); Map.addLayer(composite, {}, 'max value composite');  var getQABits = function(image, start, end, newName) { // Compute the bits we need to extract. var pattern = 0; for (var i = start; i &lt;= end; i++) {    pattern += Math.pow(2, i); } // Return a single band image of the extracted QA bits, giving the band // a new name. return image.select([0], [newName])               .bitwiseAnd(pattern)               .rightShift(start); };  // A function to mask out cloudy pixels. var cloud_shadows = function(image) { // Select the QA band. var QA = image.select(['BQA']); // Get the internal_cloud_algorithm_flag bit. return getQABits(QA, 7,8, 'Cloud_shadows').eq(1); // Return an image masking out cloudy areas. };  // A function to mask out cloudy pixels. var clouds = function(image) { // Select the QA band. var QA = image.select(['BQA']); // Get the internal_cloud_algorithm_flag bit. return getQABits(QA, 4,4, 'Cloud').eq(0); // Return an image masking out cloudy areas. };  var maskClouds = function(image) { var cs = cloud_shadows(image); var c = clouds(image); image = image.updateMask(cs); return image.updateMask(c); };  var composite_free = composite.map(maskClouds);  Map.addLayer(composite_free, 'composite collection without clouds'); dpkg-divert: error: rename involves overwriting `/usr/lib/xorg/protocol.txt' with different file `/usr/lib/xorg/protocol-precise.txt', not allowed Editing Photoshop (PSD) files on Ubuntu? I was wondering that is it possible to edit PSD files on Ubuntu (like with Gimp). Actually, I need to edit layers. I haven't managed to do it. It would be nice if there is a chance! :) Is there any way to tinker with the iPhone SDK on a Windows machine? Are there plans for an iPhone SDK version for Windows?  The only other way I can think of doing this is to run a Mac VM image on a VMWare server running on Windows, although I'm not too sure how legal this is. Random plot based on a specific random seed Python 3 with QGIS on Mac? Consider the following code:  foo () {     echo $* }  bar () {     echo $@ }  foo 1 2 3 4 bar 1 2 3 4   It outputs:     1 2 3 4       1 2 3 4   I am using Ksh88, but I am interested in other common shells as well. If you happen to know any particularity for specific shells, please do mention them.  I found the follwing in the Ksh man page on Solaris:     The meaning of $* and  $@  is   identical  when  not  quoted  or  when  used  as a parameter   assignment value or as a file name. However, when used as  a   command argument, $* is equivalent to ``$1d$2d...'', where d   is the first character of the IFS variable,  whereas  $@  is   equivalent  to  $1 $2 ....   I tried modifying the IFS variable, but it doesn't modify the output. Maybe I'm doing something wrong? Is the integral $\int_0^\infty \frac{\mathrm{d} x}{(1+x^2)(1+x^a)}$ equal for all $a \neq 0$? Let $a$ be a non-zero real number. Is it true that the value of $$\int\limits_0^\infty \frac{\mathrm{d} x}{(1+x^2)(1+x^a)}$$  is independent on $a$? What is the best technique for long-exposure photography in good light? Prove that a graph with the same number of edges and vertices contains one cycle Recall the definition of the Weyl Chambers: A Weyl Chamber is a region of $V \setminus \bigcup_{\alpha \in \Phi} H_{\alpha}$, where $V$ is underlying Euclidean space, and $H_\alpha$ the hyperplane that is perpendicular to $\alpha$ the elements of  $\Phi$ in $V$.   I want to show that:   The Weyl chambers are open, convex and connected.   My attempts:   A single hyperplane $H_\alpha$ separates the space $V$ into two half-spaces: positive half-space $H_\alpha^+=\{x \in V \mid (\alpha,x)&gt;0\}$ and negative half-space $H_\alpha^-=\{x \in V \mid (\alpha,x)&lt;0\}$. It is clear that $V \setminus H_\alpha = H_\alpha^+\cup H^-_\alpha.$ As the result, the Weyl chambers can be regarded as components of  $$V \setminus \bigcup_{\alpha \in \Phi} H_{\alpha}= \bigcap_{\alpha \in \Phi} \left( V \setminus H_{\alpha} \right)= \bigcap_{\alpha \in \Phi} \left( H_\alpha^+\cup H_\alpha^- \right).$$ By the discussion above, a Weyl chamber is simply a $\textbf{intersection}$ of finite half-spaces. It is the case since one may write $$\left( H_\alpha^+\cup H_\alpha^- \right) \cap \left( H_\beta^+\cup H_\beta^- \right) =\left( H_\alpha^+\cap H_\beta^+ \right)  \cup\left( H_\alpha^+\cap H_\beta^- \right)  \cup \left( H_\alpha^-\cap H_\beta^+ \right)  \cup\left( H_\alpha^-\cap H_\beta^- \right).$$ Therefore openness and convexity of the Weyl chambers are straightforward since half-spaces are open and convex, so are their intersections. Moreover, we would replace $V$ by $\Bbb R^{\dim V}$ since they are isomorphic. Now we can prove that the Weyl chamber is connected by showing that every convex set in $\Bbb R^{\dim V}$ is connected. And I'm sure that proof of this statement existed. So am I done? Date Format In RUBY