Proof of compact sets
Generalized Tube Lemma
Chrome asks for password to unlock keyring on startup In Google Chrome, when I go to a login page, a window pops up asking to "Enter password for keyring 'default' to unlock". In most cases, whether I click Cancel or enter my password, the login form gets auto filled anyway.  How do I get rid of the popup? I want it to auto login each time, not ask for my system password. The dialog box never appears for any other apps. Using Drupal 7.14 with the PHP filter on I have the following in a Basic Page content type:  &lt;?php if ($is_mobile == TRUE):?&gt; &lt;div class="fb-like-box" data-href="http://www.facebook.com/a page" data-width="710" data-height="600" data-show-faces="false" data-border-color="#73AA4B" data-stream="true" data-header="false"&gt;&lt;/div&gt; &lt;?php else: ?&gt; &lt;div class="fb-like-box" data-href="http://www.facebook.com/a page" data-width="900" data-height="600" data-show-faces="false" data-border-color="#73AA4B" data-stream="true" data-header="false"&gt;&lt;/div&gt; &lt;?php endif; ?&gt;   I get the error message:  Notice: Undefined variable: is_mobile in eval() (line 1 of D:\websites\modules\php\php.module(80) : eval()'d code).  I sort of understand - I'm trying to grab a variable from the Drupal system but is there any way to do this? Maybe using Tokens? Statistics module doesn't show the "Enable access log" checkbox I dont know what to do to show "Enable access log" option.  I activated logging all messages and checked all statistics permissions.  Thanks. Gollum had his life largely extended because he possessed the One Ring. He appeared to be an old, deformed, and twisted creature.  According to , he had the Ring for 478 years. His loss of the Ring and the events of The Lord of the Rings are separated by around 77 years.  Did the Ring continue to extend his life after he lost it? "Accountsd wants to use the 'iCloud' keychain" I, too, am suddenly getting this message.  I don't see a Keychain First Aid option in Keychain, and the two Login Keychain Settings were already unlocked.  Any other ideas for what the error message is all about, and what I should do about it? I have a midterm coming up and on the past exams the hard question(s) usually involve some form of $\lim_{x\to0^{+}} x \ln x$. However, we're not allowed to use l'Hopital's rule, on this year's exam anyways.  So how can I evaluate said limit without l'Hopital's rule? I got somewhere with another approach, don't know if it's useful:   $\lim_{x\to0^{+}} x \ln x = \lim_{x\to0^{+}} x^2 \ln (x^2) = L$ $= (\lim_{x\to0^{+}} 2x)(\lim_{x\to0^{+}} x \ln x)$ $= 0 * L$   Then I just need to prove that L is finite/exists (which means it must be 0) Today, comparing processors is obviously not just looking at the frequency and the number of cores.  When choosing a new PC, how do you compare processors? Is there some resource, like a site or something that does (not necessarily super-precise) processor comparisons?  Thanks. Can't boot into Ubuntu in Windows 10 / Ubuntu dual boot Can a hotel kick you out if you let an unregistered guest share a room with you? Why can't the Polynomial Ring be a Field? I'm currently studying Polynomial Rings, but I can't figure out why they are Rings, not Fields. In the definition of a Field, a Set builds a Commutative Group with Addition and Multiplication. This implies an inverse multiple for every Element in the Set.   The book doesn't elaborate on this, however. I don't understand why a Polynomial Ring couldn't have an inverse multiplicative for every element (at least in the Whole numbers, and it's already given that it has a neutral element). Could somebody please explain why this can't be so? How can you turn on or off the cheats after you make an offline server?My brother did something in settings but I can't find it. How to use an ESC I'm new to RC related modules. Today I got my 's Skywalker 20A brushless esc. Manual is .    I also have a brushless outrunner motor (HL3512)    I don't have any device to program the esc's (even the seller hasn't mentioned about such requirement).   The  talks about programming by listening to the beep patterns. But for that it seems that the esc should be connected to a flight controller (it talks about throttle positions etc...). But I don't have any flight controller.  Can some one tell me how to use the esc with what I have? (I have 2200mAh LiPo and  too) Speed $v$ of a wave on a tightrope Is is true &lt;h1&gt; tag should not have more than 1 on every page for SEO?   Every pages on the header, it includes and &lt;h1&gt; tag. Website Name which show an image from logo class, like this:  &lt;div id="header"&gt;   &lt;h1 class="logo"&gt;      &lt;a href="#"&gt;Website Name&lt;/a&gt;   &lt;/h1&gt; &lt;/div&gt;   and I also include &lt;h1&gt; on the contact page, help, etc and article page for example:  &lt;h1&gt;Contact Us&lt;/h1&gt; &lt;h1&gt;Name of the Article Title here&lt;/h1&gt;   On the homepage, it just has one &lt;h1&gt; for the logo Site Name... other pages have 2 &lt;h1&gt; tags "1 out of 100 chickens is" or "1 out of 100 chickens are"? Multiplicative inverse questions This is my first time posting on Math exchange. I have been self-teaching myself Mathematics and recently started learning some Algebra. I was posed the following questions, in which I would like to answer before I proceed, but having some trouble finding proper solutions. So the format will be question, and my answer.      What name do we give an element $a \in \mathbb{Z}_n$ that has a multiplicative inverse?   A modular multiplicative inverse of an integer $a$ is an integer $x$ such that $ax \cong 1 (\mod m)$. This means that the remainder after dividing $ax$ by integer $m$ is equal to $1$.      Give an example, for some $n \in \mathbb{N}$, of an element of $\mathbb{Z}_n$, that does not have a multiplicative inverse?   This question is throwing me off because - does the $n$ we speak of matter for both $n \in \mathbb{N}$ and $\mathbb{Z}_n$ ot solely $n$? My guess here would be $0$ because we cannot have an inverse of $0$.      Prove that multiplicative inverse are unique; an element $a \in \mathbb{Z}_n$ cannot have two multiplicative inverses.    Suppose that an element $a\in\mathbb{Z}_n$ has an inverse $a'$. Next, suppose that $a^*$ is also an inverse of $a$. Then, $a'$ is a solution to $a \cdot_n x=1$, and similarly $a^*$ has a solution to $a \cdot_n x=1$.   Lemma: Suppose $a'$ is multiplicative inverse of $a$ in $\mathbb{Z}_n$, then for any $b \in \mathbb{Z}_n$ the equation $a \cdot_n x=b$ has a unique solution, such that $x = a' \cdot_n b$.   By Lemma, equation $a \cdot_n x = 1$ has a unique solution, namely $x=a'=a^*$. Therefore, an element $a\in \mathbb{Z}_n$ cannot have two multiplicative inverses.    Thank you for the help. I would love any constructive feedback for these. If you can help me elaborate on some ideas, that would be really helpful also.  Thank you very much! Summary table with a field that shows components of each summarized record I have a table with 2 fields the first is for community and the second for the main community that it belongs to, as in the image  I want to summarize the second field (Belongs_to) but with an extra field (multiple value field) that shows components of each main community, as in the image  Could anyone help me please? Is there any way to deserialize JSON into an object using JSON.deserialize if some of the property names in the JSON are reserved words in apex? I want to do something like this:  string jsonString = '{"currency" : "ABC"}'; public class JSONResult {     public string currency; } JSONResult res = (JSONResult) JSON.deserialize(jsonString, JSONResult.class); system.debug(res);   but of course I get an error that the identifier name is reserved. Is it possible to interrupt spellcasting? As  suggests, there seems to be a hole in the D&amp;D Basic rules.  Maybe.  The rules for readying an action state:     When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger.   This seems to imply that it is impossible to interrupt a spell in 5e.  If you set your trigger to be "I attack the Wizard when he casts a spell", then you make the attack after the spell has been cast.  Does this mean that spells can no longer be interrupted in combat like they could be in previous editions? In Windows XP we can search for files that contain a defined keyword (inside all files types).  Windows 7 can look inside files for a keyword, but only for text files. (*.doc, *.txt, *.inf, ...), not (*.conf, *.dat, *.*, ...).   don't contain any filter I can use for this.  How is this possible?