Prove that a complete metric space without isolated points is uncountable
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
QGIS 3.0 and Qt 5.7 time schedule When will QGIS 3.0 with QT5.7 (possibly) be released as a stable and long term support version? Generalized Tube Lemma Which statistics to use? What happens if I buy a game I already own through Steam a second time? I am debating whether or not to get the Potato Sack (yes, I realize I've been debating for several weeks now) bundle through steam.  I already own: Defense Grid: The Awakening, Super Meat Boy, and Audiosurf, all of which are part of the sack pack. What happens if I buy the Potato Sack?  Do I get 2nd copies of the three above mentioned games to gift elsewhere?  Is the price of the bundle reduced by the games I already have?  Do I get nothing special for already owning those 3 games? Google Chrome PPA upgrade invalid signature Making a string out of a string and an integer in Python Examples of a non-commutative division ring I have a very simple component:  PushTopicTest.cmp &lt;aura:component implements="flexipage:availableForAllPageTypes" access="global"&gt;     &lt;lightning:empApi aura:id="empApi"/&gt;     &lt;aura:handler name="init" value="{!this}" action="{!c.onInit}"/&gt; &lt;/aura:component&gt;    PushTopicTestController.js ({     onInit: function(component, event, helper) {         var empApi = component.find("empApi");         empApi.setDebugFlag(true);         empApi.subscribe("/topic/AccountChanges?Id=0011t0000033C9QAAU", -1, function(message) {             console.log("Event Received : " + JSON.stringify(message));         });     } })   I also have PushTopic created like this:   What I am trying to do, is to only receive events for specific record Id. Based on documentation this should work: "/topic/AccountChanges?Id=0011t0000033C9QAAU", but it doesn't.   "/topic/AccountChanges" works though.  I've tried Id='0011t0000033C9QAAU' aswell, but no luck.  Do you know if it is possible at all? How to secure recommendations and apply for PhD after having worked outside of academia for two years? The number of permutations of $\{1,2,\ldots,n\}$ that have exactly one ascent (rise). Sloane's  counts the number of $n$-permutations with exactly one ascent.  For example $a(3)=4$ because we have: $1\wedge32$, $21\wedge3$, $2\wedge31$, $31\wedge2$ where I have marked the unique ascent with $\wedge$.  The same sequence also counts the number of length $n$ binary words that contain at least two $1$'s. For example $a(3)=4$ because we have: $011, 101, 110, 111.$  Is there a simple bijection between these two classes?  The formula for the sequence is $a(n) = 2^n - n - 1$.  I see how this counts the number of such binary words.  Is there a combinatorial derivation of this formula demonstrating that it counts the number of such n-permutations?  Both the exponential and ordinary generating functions of the sequence are given.  Again, I understand their symbolic derivation for enumeration of such binary words but can these functions be derived symbolically by considering the structure of such n-permutations? How to Disable Copy Paste (Browser) Standardize Training and Validation Data Would spending one more year as an undergraduate adversely affect my chances of getting into a graduate program?   I wasn't really thinking about economics PhD until recently so my GPA is not too impressive and I lack in math courses so I've decided to spend one more year to boost my GPA taking upper level courses and get a math minor.  However, could the very fact of spending one more year to finish college be a disadvantage of getting into a graduate program? How to easily build your own Linux Distro? I wanted to have a go at creating my very own Linux Distribution. Could you suggest some nice and easy-to-follow tutorials (preferably text based and not videos). I have heard something about Arch Linux but I don't know how to go from there. What do I need? Any Set with Associativity, Left Identity, Left Inverse is a Group Suppose we are in $\mathbb R^n$. What can we say about the sign of $\Delta u(\vec x)$ if u($\vec x$) has a local max/min at $\vec x$? I've tried looking at the reverse of the second partial derivative test and it seems to suggest that $\Delta u(\vec x) \leq 0$ if $\vec x$ is a min and $\Delta u(\vec x) \geq 0$ if $\vec x$ is a max. However, I'm not convinced of this result. Can somebody point me towards a statement (theorem, etc.) involving the above. I appreciate the help. Aluminum foil is said to be not absorbing light at all. It reflects light. So, does it mean that a more shiny aluminum foil will reflect more light and thus make the room more cooler as compared to less shiny foil?  If yes, then where does unreflected light go in case of less shiny aluminum foil?  Does less shiny and more shiny actually make a difference? Why?  In order to keep whole room cool will it help if I stick the foil to the outside of wooden door (exposed to the sunlight) too? Is it possible to bring built-in lightning components into aura component? I have a form that needs to let the user select 3 out of 5 products, something similar to Order > Add Product (Modal). I was wondering if there was a way to bring that piece into my component (markup) and add some sort of filter that only shows the products I want to show.  What I found so far:  &lt;lightning:listView objectApiName="Products2" listName="productsView" showActionBar="true" enableInlineEdit="true" showRowLevelActions="true"/&gt;   But Product2 is not supported for that component.  also these from browser inspector:  forceMultiAddUsingLVM forceListViewManager   These are data-aura-class attributes when rendered.  I'm looking for directions here. Thanks in advance. I have unistalled and reinstalled the Ubuntu Software Center as per info I found in a similar thread and I got the same response about line 91 or something like that.  I just tried to upload a screen shot but since I'm new it won't allow me to.  I also can not figure out how to cut and paste anything so I have to hand type what the error screen says, both when I attempt to open the software center and nothing happens, when I try to enter commands into the terminal to uninstall, reinstall, whatever I get the same following:  COULD NOT INTITIALIZE THE PACKAGE INFORMATION An unresolvable problem occured while initializing the package information Please report t:his bug against the 'update-manager' package and include the following error message: 'E: Malformed line 91 in source list/etc/apt/sources.list (dist parse)  E: The list of sources could not be read.,  E: The package list of status file could not be parsed or opened.   How do I report bugs?  What can be done about this.  I have searched and everything everyone says to do leads me back to the same line error message.  So, I don't know how to get to line 91 in the source list; to tell you what it says. Sorry, I'm really new to this. That is what I need is to find out how to get there and fix what it says. I would really like to NOT have to re partition my hard drive and start from scratch, so I'm really looking forward to getting this problem solved. I need to be able to install new software. If all derivatives of $f$ are uniformly bounded by a common constant and $f(1/n) = 0$ for all $n$, is $f$ identically zero? $$ f: \Re \longrightarrow \Re \ \in C^{\infty} \\ \exists \ L&gt;0: \ \forall x \in \Re, \forall n\in N \\ |f^{(n)} (x)| \le L \\ f(\frac{1}{n})=0 \ \forall n\in N \\ f(x) \equiv 0  $$  Good morning,  Can you give me an help to make this proof?  This is my thought:   $\lim_{n \rightarrow +\infty } \dfrac{1}{n}=0=\theta$ $f(\theta)=0$ $f^{(n)} (\theta) =0\\f(x)=\sum_{k=0}^n \dfrac{f^{(k)}(x-\theta)^k}{k!}$  $f$ is analytic, the rest of Taylor's expansion is 0, because the derivatives are bounded, $f$ is null.   I have thought this reasoning, but I have difficulties to demonstrate part 3. Can you help me?  Is there any mistake?  Can I use an easier way to make the proof?  Thanks.