C grammar compound statement
Why was mixing declarations and code forbidden up until C99?
Is it possible to do The Pitt without a slave outfit? Equation mode, labelling equations I have the following   \[K^{-1}\left\|\sum\limits_{n=1}^N a_ny_n\right\|    \leq \left\|\sum\limits_{n=1}^N a_nx_n\right\|    \leq K\left\|\sum\limits_{n=1}^N a_ny_n\right\| (\dagger)\]   But the dagger doesn't appear at the right hand end of the page. How can I Get it so that it does appear on the end of the page? the \hfill command doesn't seem to work. Thank you. Blank image when I render Device that makes metal malleable I am a student who has taken the basic calculus courses but I am working through Calculus (the fourth edition) by Spivak in my spare time in order to both review the material and to gain a more rigorous understanding of the concepts. I am currently in Chapter 8 where he supplies a proof of the basis of the Intermediate Value Theorem, Theorem 7-1 (pp. 135-136 of the fourth edition). It seems mostly straightforward but I think there is some nuance of it that I don't grasp.  I am including in this post the statement Theorem 6-3 since he references it in the proof of Theorem 7-1 as well as part of Theorem 7-1 itself.     Theorem 6-3 Suppose $f$ is continuous at $a$, and $f(a) &gt; 0$. Then $f(x) &gt; 0$ for all $x$ in some interval containing $a$; more precisely, there is a number $\delta &gt; 0$ such that $f(x) &gt; 0$ for all $x$ satisfying $|x-a| &lt; \delta$. Similarly, if $f(a) &lt; 0$, then there is a number $\delta &gt; 0$ such that $f(x) &lt; 0$ for all $x$ satisfying $|x-a| &lt; \delta$.     Problem 6-16 is also referenced. However,it is the same thing as Theorem 6-3 for one-sided limits. The following proof is the Theorem 7-1 up through the paragraph which I don't fully understand.     Theorem 7-1: If $f$ is continuous on $[a,b]$ and $f(a) &lt; 0 &lt; f(b)$, then there is some number $z$ in $[a,b]$ such that $f(x) = 0$.  Proof: Define the set $A$ as follows:  $$A = \{x : a \le x\le b, \mbox{ and } f \mbox{ is negative on the interval } [a,x] \}.$$  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Clearly $A \ne \emptyset$, since $a$ is in $A$; in fact, there is some $\delta &gt; 0$ such that $A$ contains all points $x$ satisfying $a \le x &lt; a + \delta$; this follows from Problem 6-16, since $f$ is continuous on $[a,b]$ and $f(a)&lt;0$. Similarly, $b$ is an upper bound for $A$ and, in fact, there is a $\delta &gt; 0$ such that all points $x$ satisfying $b-\delta &lt; x \le b$ are upper bounds for $A$; this also follows from Problem 6-16, since $f(b) &gt; 0$. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; From these remarks it follows that $A$ has a least upper bound $\alpha$ and that $a &lt; \alpha &lt; b$. We now wish to show that $f(\alpha) = 0$, by eliminating the possibilities $f(\alpha) &lt; 0$ and $f(\alpha) &gt; 0$. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Suppose first that $f(\alpha) &lt; 0$. By Theorem 6-3, there is a $\delta &gt; 0$ such that $f(x) &lt; 0$ for $\alpha - \delta &lt; x &lt; \alpha + \delta$. Now there is some number $x_0$ in $A$ which satisfies $\alpha - \delta &lt; x_0 &lt; \alpha$ (because otherwise $\alpha$ would not be the least upper bound of $A$). This means that $f$ is negative on the whole interval $[a,x_0]$. But if $x_1$ is a number between $\alpha$ and $\alpha+\delta$, then $f$ is also negative on the whole interval $[x_0,x_1]$. Therefore $f$ is negative on the interval $[a,x_1]$, so $x_1$ is in $A$. But this contradicts the fact that $\alpha$ is an upper bound for $A$; our original assumption that $f(\alpha) &lt; 0$ must be false.    The point I don't understand is in the final paragraph of the excerpt. Why does Spivak split the interval $[a,b]$ up into the subintervals $\lbrack a,x_0 \rbrack$ and $[x_0,x_1]$? Isn't it true that, because $\alpha$ is a least upper bound of $A$ and $f$ is continuous on $[a,b]$, it must be true that if $a \le x &lt; \alpha$ then $f(x)&lt;0$? I understand the need to pick out the $x_1$ but not the $x_0$. Especially perplexing is the statement "there is some number $x_0$ in $A$ which satisfies $\alpha - \delta &lt; x_0 &lt; \alpha$ (because otherwise $\alpha$ would not be the least upper bound of $A$." Wouldn't it be true that if there were some $x_0$ such that $a \le x_0 &lt; \alpha$ and $f(x_0) \ge 0$ that $x_0$ would be an upper bound for $A$, contradicting that $\alpha$ is the least upper bound of $A$?  Thanks for any help. Compare two dates with JavaScript Can someone suggest a way to compare the values of two dates greater than, less than, and not in the past using JavaScript? The values will be coming from text boxes. Convert list of ints to one number? This question might be wrong, I am not sure about it. Because I am not clear on this.  I know add_action it is used to to hook our function to the specified function. For example add_action('wp_head'.'myfunc'); now what ever code in myfunc will be executed in the wp_head(). This is clear but i am having doubt in do_action what it does?  I think it is used to create our own hook like already available hooks(wp_head,wp_footer,..etc) If i am correct can anyone show me a simple understandable answer with simple example.  I have tried the difference in internet but all are pointing to difference between add_action and add_filter. I don't want to go there because first i want to clarify this and then I’ll move there.  Can anybody help me?  EDIT after Question POST  function custom_register() {     echo '&lt;script&gt;jQuery(document).ready(function(){alert("Learning Hooks");});&lt;/script&gt;';  } do_action('custom');  add_action('custom','custom_register');   I tried this in plugin but i didn't get the alert message.  But when i hook the same function with wp_head then it is working fine  /******************working****************/ add_action('wp_head','custom_register'); Plotting a 3d surface in tikz, with a limit to the infinity I'm a citizen of an EU member state traveling to a small city in Vermont. Looking at flight data, it seems that it would be quite a bit quicker to fly into Montreal (Canada) and then drive a rental car to my final destination in Vermont (and back), rather than getting a connecting flight into a small local US airport. I am slightly worried about the trouble I might get myself into by crossing a land border twice, though.  Can anyone give me an idea of what I'd be getting into in terms of:   Crossing time Discomfort Additional paperwork required   For both the outbound (Canada/US) and the return leg (US/Canada) of my journey, when compared to crossing the border at an international airport?  Also, do I need to take any special actions when I'm arranging a rental car if I intend to drive it over to the US and back? Broken screen while debug mode was disabled. How can I re-enable adb? The screen of my phone is physically broken, so it doesn't display anything, but the touch aspect does seem to be working, as I can unlock my phone, and get haptic feedback.  Before I go to get it replaced, I'd like to back up some personal data from the built-in memory to the SD card. I'm fairly certain that if I can get adb to recognize the device, then I can use  to see where I am touching the screen and do what I need to do. Problem is, when I plug it in, it's not recognized, while my emulator is.  I suspect that I might not have USB debugging enabled, which I think is necessary for adb to work. If this is the case, can someone give me screenshots of their Droid X (running 2.3.X) going from the home screen, through all the menus, to activating debug mode? Hopefully I can do it by dead reckoning and adb from there.  Edit: I haven't changed anything about the ROM or launcher; it's all stock. 80/90s UK children's drama series about an "alien" boy with radio weapon I've been trying to track down a live-action children's TV series (or short story perhaps) from the 1980s or 1990s, probably on CBBC or CITV.  A few people I've spoken to IRL have suggested The Boy from Space or Sky, but I'm pretty sure it's neither as a lot of the details don't seem to match.  The story was set on Earth (possibly England or Wales) and was about an "alien" boy who was being pursued by a group of people, though I don't remember who they were.  Somehow he encountered siblings, a girl and a boy, and made friends with them. I think they lived on a farm with their parents, as I remember quite a large barn or other building, and they hid(?) the boy in a car which was inside or next to this building. He also slept in this car with a dog (which might have been a German shepherd).  The "alien" boy had a portable "radio" (all silver, very 1980s) that repelled his pursuers by emitting a high-pitched sound when he turned a dial on it, and he used it when out and about with the other children whenever they encountered a pursuer. I seem to remember lots of hills and valleys, lots of green.  In the end it turned out he wasn’t really an alien, but a human from the far future. He was pretending to be an alien as he was from 20000 years into the future and humans' appearance had changed by then, but he had the ability to make himself look like current-day humans. When he was in his car/bed he reverted to his normal appearance, so he would hide under the blankets until he was able to assume current-day human appearance.  In the finale, it was revealed that he was never in any danger – the pursuers were testing him as part of a kind of coming-of-age thing. I remember a scene on a spaceship or something where his elders/parents where shown telling him that he was safe all along and that he "passed".  I also seem to remember them referring to "ancestors" and making sure they didn't find out, so the either the girl or boy could well have been a direct ancestor. Does this parallel structure need coordinated prepositions to avoid being a faulty parallelism? Is Site Traffic Data Gone for Good After Fixing Previous Bug? There was a previous bug affecting site traffic statistics showing -zero- for months (). This has been fixed in that it is now graphing the data.  It appears that previous data may be lost? The graphs below are from . I don't have access to any other sites' graphs to see if they are showing similar results. One of my columns is called from. I can't change the name because I didn't make it. Am I allowed to do something like SELECT from FROM TableName or is there a special syntax to avoid the SQL Server being confused? Updating global js variable within function and sending updated to HTML document How to dynamically change a web page's title? I have a webpage that implements a set of tabs each showing different content. The tab clicks do not refresh the page but hide/unhide contents at the client side.  Now there is a requirement to change the page title according to the tab selected on the page ( for SEO reasons ). Is this possible? Can someone suggest a solution to dynamically alter the page title via javascript without reloading the page? Are there 'stack' sites for Mac or Windows? Prove that if $0\le p_n&lt; 1$ and $S=\sum p_n&lt; \infty$ then  $\prod (1-p_n)&gt;0$. Hint given: First show that if $S&lt;1$, then $\prod (1-p_n)\ge 1-S$.   Attempt: I was able to show the hint by using recursion setting $A_n=\prod_{i=1}^{n}(1-p_i)$ re expression the $\prod (1-p_n)$ as $1-S+\sum_{n_1, n_2=1,n_1&lt;n_2 }^{\infty} p_{n_1}p_{n_2}-..... $ and observed that every subsequent term is less than the previous term hence  $\prod (1-p_n)\ge 1-S$ which is $&gt;0$ if $S&lt;1$ but am unsure about how to extend it to $S\ge1$. Is there a Ubuntu sanity check? Is there a standard procedure to 'unit test' an Ubuntu system against the deb packages?  Assume, a system has ubuntu-desktop installed according to the package manager. Can I find out, whether the file system has all the files in ubuntu-desktop and dependencies?   related question: