Let X be an infinite set. Let X be endowed with discrete metric. Give an open cover of X which does not admit a finite subcover.  The open sets in X are singletone sets I know that and X=$\cup_x$ {x} where x$\in$X. But now i dont know how to solve this problem.
I am new to compact sets, and I had some hard time trying to solve this:  Let $X$ be an infinite set; $T$ the discrete topology on $X$ .Prove that $(X,T)$ is not compact.  I know that I may consider the open cover $\{\{x\},x \in X\}$ and prove that it doesn't have a finite subcover,but I don't know how to write it exactly.  Moreover, I seriously can't understant why $X$ itself cannot be considered as a finite subcover?  Any help is appreciated.
Can I find the connected components of a graph using matrix operations on the graph's adjacency matrix? If I have an adjacency matrix for a graph, can I do a series of matrix operations on the adjacency matrix to find the connected components of the graph? I am performing a meta-analysis with 137 study arms. From each arm I have extracted a proportion of a disease. Here are my proportions:  [1] 0.002710027 0.000000000 0.000000000 0.000000000 0.017857143 0.000000000 0.010269576 0.000000000 0.000000000 0.000000000 0.000000000  [12] 0.010000000 0.053691275 0.052631579 0.070351759 0.000000000 0.108333333 0.262626263 0.013043478 0.000000000 0.007000000 0.000000000  [23] 0.000000000 0.000000000 0.240000000 0.000000000 0.033333333 0.000000000 0.000000000 0.000000000 0.000000000 0.013201320 0.000000000  [34] 0.005361930 0.002308403 0.000000000 0.000000000 0.000000000 0.030000000 0.046296296 0.000000000 0.020000000 0.045454545 0.161073826  [45] 0.000000000 0.000000000 0.000000000 0.095238095 0.007194245 0.001472754 0.000000000 0.000000000 0.000000000 0.000000000 0.012048193  [56] 0.000000000 0.048780488 0.000000000 0.086253369 0.033898305 0.011966701 0.004162331 0.062790698 0.005555556 0.004451039 0.287356322  [67] 0.083333333 0.000000000 0.000000000 0.014666667 0.006160164 0.023809524 0.000000000 0.000000000 0.000000000 0.001552795 0.102564103  [78] 0.030555556 0.000000000 0.000000000 0.000000000 0.000000000 0.029411765 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000  [89] 0.003231018 0.000000000 0.037500000 0.040247678 0.000000000 0.000000000 0.007299270 0.014598540 0.000000000 0.015118790 0.000000000 [100] 0.000000000 0.005555556 0.000000000 0.000000000 0.000000000 0.003039514 0.042145594 0.250000000 0.307692308 0.324444444 0.002057613 [111] 0.008333333 0.000000000 0.027522936 0.022598870 0.000000000 0.000000000 0.000000000 0.135278515 0.033333333 0.000000000 0.000000000 [122] 0.003690037 0.003412969 0.000000000 0.017391304 0.004237288 0.033210332 0.000000000 0.008928571 0.038834951 0.030303030 0.142857143 [133] 0.170000000 0.000000000 0.112903226 0.000000000 0.007299270   A majority of the proportions has zero value. I am struggling with whether I should go for logit or arcsine transformation. One source says that arcsine transformation should not be used . On the other hand, I several zero counts. With logit transformation values 0 and 1 are mapped to infinity, and according to another source I should go with arcsine transformation . Furthermore, I found another study close to my topic in which they used arcsine transformation. The default in R with metaprop function is logit.   Which one I should go with my data? Inexact measurement and wavefunction collapse I have a COM dll written in vb6. When I try to create a new object of a class module from this dll I get a Run timer error 430: Class does not support automation or does not support expected interface. The interesting thing is that this happens only from outside the IDE, when I am debugging from within the IDE there is no error thrown and the new object of the class is created successfully. What can be the cause?  In general I occasionally get these kind of errors in COM dlls. What is the best way to debug COM issues? How can I know the path of the dll that is being used when a program is running? Why do some people answer in comments? Why do some people post comments that are actually answers to the question? Wouldn't posting an answer be better? Is there a package to secure rendered pdf with a password? Is there a package and command that can secure rendered pdf with a password? Why don't the Google Docs CTRL + ALT shortcuts work? I'm currently using Google Docs, but when I try to use the keyboard shortcuts like Ctrl+Alt+M it gives µ instead.    Is Chrome (9) overruling Google Docs in some way?  How can I get these shortcuts working?  I'm using Chrome dev 9 on a Dutch Windows 7 with a US-layout keyboard I have this HW where I have to calculate the $74$th derivative of $f(x)=\ln(1+x)\arctan(x)$ at $x=0$. And it made me think, maybe I can say (about $\arctan(x)$ at $x=0$) that there is no limit for the second derivative, therefore, there are no derivatives of degree grater then $2$. Am I right? Photo Map tip in QGIS 3 on windows How does atan2 work when getting angle of a vector? I know that atan2 gives me the absolute angle of any vector. But it doesn't give a value from 0 to 360 degrees. Instead, it gives a value (if I'm not mistaken), between 0 and 180, or between 0 and -180. For example, instead of giving angle 270, it will say -90.  This is a little confusing for me. Let me try to describe how I think this works, and please tell me if I'm correct. Actually, I'll draw it.    Is this correct? I'm having a little trouble understanding this. Thanks Please don't throw this one out as a duplicate of  I'm not asking about the plurality of the noun immediately following those two words - I'm interested in exactly why the example below is problematic (context: I have several children, one named John)...     1: One of my children's name is John.   I can't see any obvious reason why singular name there is completely unacceptable, but it certainly doesn't sit well with me. It seems to turn on whether one of my children can be treated collectively as the "subject" of the Saxon genitive 's, but I don't see a problem with...     2: It's actually one of my children's, but you can sleep in this bed.   I realise that in practice we'd normally pluralise names in the first example. But of course, this implies that one of attaches to my children's names, which isn't really the same construction.  So - is there some kind of "rule, principle" debarring #1 above? Or is it just "one of those things"?    (Apologies if my later switch from brothers to children invalidates any comments or answers.) How to change LCD brightness from command line (or via script)? Does a Rogue using Use Magic Device for a scroll or wand also need to emulate a class feature? I'm confused about Rogues and Use Magic Device. I've searched the core book and the Internet for the past 4 hours and can't find the answer to my simple question.   Since a Rogue doesn't have any spells, a spell list or caster level, do you have to emulate a class feature in addition to all other necessary checks to use items like scrolls and wands? How to remove the left part of a string? This is something that I always find a bit hard to explain to others:  Why do XML namespaces exist?  When should we use them and when should we not? What are the common pitfalls when working with namespaces in XML?   Also, how do they relate to XML schemas? Should XSD schemas always be associated with a namespace? Refused UK Visit visa for lack of sufficient funds - What more can I do? How to detect if a mob has been hit in minecraft with command blocks? i am making a boss battle for my minecraft adventure map, and using a mob spawned with commands as the boss. When the mob gets hit, some command blocks will give the player a potion effect, but I can't figure out how to activate the command block when the mob gets hit. I am in the latest snapshot (16w03a). please help me (the person who answers my question will be given credit for it in my map) Find $\lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right]$ (a question asked at trivia) How to extend USB beyond the recommended maximum cable length of 5m? I'm planning to use USB port for an application(from a device to a PC) but the distance between the device and the PC will be around 15m. The recommended maximum USB cable length is 5m.  How can I buffer the data without loosing any information, safely? Would a USB hub work? What is a NumberFormatException and how can I fix it?