Why don't "identical" index entries using math mode join?
Duplicate typeset index entries
Prove there is an increasing sequence ($s_n$) of points in $S$ such that $\lim s_n = \sup S$. Let $S$ be a bounded set. Prove there is an increasing sequence ($s_n$) of points in $S$ such that $\lim s_n = \sup S$. Note: If $\sup S$ is in $S$, it’s sufficient to define $s_n = \sup S$ for all $n$.  What I have tried so far:  Let $M=\sup S, L = \lim\, s_n,\,|s_n-L|&lt;\epsilon/2$, then $M-\epsilon &lt; L- \epsilon/2 &lt; s_n &lt; M &lt; M+\epsilon$. But I get this based on $M &lt;= \epsilon+L$, because $\epsilon+L$ is an upper bound for $s_n$.   However, as $s_n$ are just points in $S$, so I don't know if it's sufficient to say $M$, which is the $\sup$ of $S$, is smaller than $L+\epsilon$. Can I stop 100% Width Text Boxes from extending beyond their containers? Lets say I have a text box that I want to fill a whole line. I would give it a style like this:  input.wide {display:block; width: 100%}   This causes problems because the width is based on the content of the text box. Text boxes have margin, borders, &amp; padding by default, which makes a 100% width text box larger than its container.  For example, here on the right:    Is there any way to make a text box fill the width of its container without expanding beyond it?  Here is some example HTML to show what I mean:  &lt;!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"&gt; &lt;html xmlns="http://www.w3.org/1999/xhtml" &gt; &lt;head&gt;     &lt;title&gt;Untitled Page&lt;/title&gt;     &lt;style type="text/css"&gt;         #outer{border: 1px solid #000; width: 320px; margin: 0px;padding:0px}         #inner{margin: 20px; padding: 20px; background: #999;border: 1px solid #000;}         input.wide {display:block; margin: 0px}         input.normal {display:block; float: right}     &lt;/style&gt; &lt;/head&gt; &lt;body&gt;     &lt;div id="outer"&gt;         &lt;div id="inner"&gt;             &lt;input type="text" class="wide" /&gt;             &lt;input type="text" class="normal" /&gt;             &lt;div style="clear:both;"&gt;&lt;/div&gt;         &lt;/div&gt;     &lt;/div&gt; &lt;/body&gt; &lt;/html&gt;   If this is run, you can see by looking at the "normal" text box that the "wide" text box is sticking out beyond the container. The "normal" text box floats to the actual edge of the container. I'm trying to make the "wide" text box fill its container, without expanding beyond edge like the "normal" text box is. Every Finite Group is Isomorphic to a Subgroup of $A_n$ There are a couple of different ways to remove HTML tags from an NSString in Cocoa.   is to render the string into an NSAttributedString and then grab the rendered text.   is to use NSXMLDocument's -objectByApplyingXSLTString method to apply an XSLT transform that does it.  Unfortunately, the iPhone doesn't support NSAttributedString or NSXMLDocument. There are too many edge cases and malformed HTML documents for me to feel comfortable using regex or NSScanner. Does anyone have a solution to this?  One suggestion has been to simply look for opening and closing tag characters, this method won't work except for very trivial cases.   For example these cases (from the Perl Cookbook chapter on the same subject) would break this method:  &lt;IMG SRC = "foo.gif" ALT = "A &gt; B"&gt;  &lt;!-- &lt;A comment&gt; --&gt;  &lt;script&gt;if (a&lt;b &amp;&amp; a&gt;c)&lt;/script&gt;  &lt;![INCLUDE CDATA [ &gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt; ]]&gt; "This site is all about getting answers. It's not a discussion forum. There's no chit-chat." The  has this text:     This site is all about getting answers. It's not a discussion forum. There's no chit-chat.   It's probably an oversight and copied from the regular site tours. Can it be reworded/removed?  Right above that text, there's this:      So each community has a meta to discuss site-specific issues, and Meta Stack Exchange is for conversations about problems and ideas that affect the whole network.   Don't they contradict eachother? I remember reading a sci-fi story where astronauts visit a planet, which is covered in stationary aliens with mile long necks that filter feed from the atmosphere.  It was published between 1960 and 2000.    It was in English and involved a pair of astronauts that went from planet to planet on a tour or something, though I don't know details of any other planets they visited. show that the solution is a local martingale iff it has zero drift Proof that the real numbers are countable: Help with why this is wrong How to send and receive data from Salesforce to a FTP server My question is how I can intergrate Salesforce with different FTP servers in real time. I have read some articles about it, but to be absolutely sure I thought it would be a good idea to post a question here.  I want to be able to send and receive data from Salesforce as a csv file to a ftp server. How I'm thinking about doing this is listed below.  Send the data:  Create a apex class which query the necessary data in Salesforce and create a csv file. I guess this is trivial? Then send the file to a web service created in Salesforce, just by calling it in the apex code. Create a web service in Salesforce which receives the data from the apex code. This web service should in some way send the data to the appropriate ftp server. I guess I can simply modify some of the code provided by Salesforce to make this work? The file is sent. Receive the data  This one is a bit trickier. I guess I have to pull the data from the FTP server by using my web service, which then send the file collected to the appropriate apex class. Or, the FTP server could send the data to the SFDC web service, I don't know if this is possible? The web services on the other side that sends the data to the ftp server, could send it directly to the SFDC web service, which then again forward it to the apex class. I guess the web service will use the remote site url to connect to the SFDC web service? If I've decided to update my SE avatar (in any of the various ways well described in the answer to this ), am I able to return to either the original stock image or previous avatar images I have used? Cyclic vector implies commuting linear operator is a polynomial Let $T$ be a linear operator on the finite dimensional vector space $V$. Suppose $T$ has a cyclic vector. Prove that if $U$ is any linear operator which commutes with $T$, then $U$ is a polynomial in $T$. Resize Move Partitions on Dual Boot System How do I download torrents? How can I publish my game (*.aab file) on google play? Pick random row from a file What is the dimension of $R[[X]]$ where $R$ is a Noetherian ring? If $R$ is a Noetherian ring then we know that the Krull dimension of the polynomial ring $R[X]$ is $\rm dim(R)+1.$ Is there any formula for the Krull dimension of the power series ring $R[[X]] $ When $R$ is a Noetherian ring ? How to forbid a specific package to be installed? How is the equation of motion on an ellipse derived? I would like to show that a particle orbiting another will follow the trajectory   \begin{equation} r = \frac{a(1-e^2)}{1 + e \cos(\theta)}. \end{equation}  I would like to do this with minimal assumptions. Any pointers? I've read that this is nothing but the equation for an ellipse, as defined from the focus of the ellipse. But I'm not satisfied in just taking the result, I mean why should I assume that orbits are elliptical? I guess it should be derivable from energy and angular momentum considerations... What is the correct way of installing BOINC software? Compactness of  Multiplication Operator on $L^2$ Suppose we have an bounded linear operator A that operates from $L^2([a,b]) \mapsto L^2([a,b])$.  Now suppose that $A(f)(t) = tf(t)$.    Is A compact?  Edit: I know $A = A^*$ but I'm not really sure how to start on this.  It's not homework, just summer fun :D