Constructing perfect set without rationals by removing open neighborhood around rationals
Perfect set without rationals
Abelian quotient group I'm stuck on the following practice problem.   Any hints would be appreciated.  Suppose $N$ is a normal subgroup of  $G$ such that every subgroup of $N$ is normal in $G$ and $C_{G}(N) \subset N$. Prove that $G/N$ is abelian.  I'm not sure how to use the fact that $C_{G}(N) \subset N$.  Thanks How can I delete my printer from Ubuntu? Using 12.04 my printer a canon ip2600 will not print.   SystemSettings/printers shows it as installed, connected to local host, enabled, accepting jobs, shared and allowing printing for everyone. Yet it does not print.   I have tried to remove it but get a request for user name and password which I enter (I only have one password) but the password is listed as incorrect.   I need a sudo command which I can use to delete the printer so I can attempt to re-install it. As it is the printer is useless and I can not even uninstall it. Though I never quite understood what those numbers were and they were quite ugly, they were the only reason I ever visited the reviews page.   Can we have similar functionality back on the top bar please? Word or phrase for mere coincidence that brings happiness I added a new field on Opportunity table to keep a count of records, as well as track the updates made on that record.  This is needed for an external system we use. Opportinity table already has around 5000 records now. I would like to update the new field that I added with some sequence order initially. Say each record to have a unique sequence number like 1,2,3 etc(can't use the Id field for unique). The field "Identifier__c" was added for this purpose with data type number and unique contraint. For that I created a temporary class and trigger. But it is throwing the error.     Review all error messages below to correct your data. Apex trigger OpportunitySAPIdentifierHandler caused an unexpected exception,   contact your administrator: OpportunitySAPIdentifierHandler: execution   of BeforeUpdate caused by: System.DmlException: Update failed. First   exception on row 0 with id 006E00000038FPSIA2; first error:   CANNOT_INSERT_UPDATE_ACTIVATE_ENTITY, OpportunitySAPIdentifierHandler:   execution of BeforeUpdate caused by: System.DmlException: Update   failed. First exception on row 0 with id 006E00000038FPTIA2; first   error: CANNOT_INSERT_UPDATE_ACTIVATE_ENTITY,   OpportunitySAPIdentifierHandler: execution of BeforeUpdate caused by:   System.DmlException: Update failed. First exception on row 0 with id   006E00000038FPSIA2; first error: SELF_REFERENCE_FROM_TRIGGER, Object   (id = 006E00000038FPS) is currently in trigger   OpportunitySAPIdentifierHandler, therefore it cannot recursively   update itself: [] Class.AutoNumber.OpportunityAutoNumber: line 76,   column 1 Trigger.OpportunitySAPIdentifierHandler: line 4, column 1: []   Class.AutoNumber.OpportunityAutoNumber: line 76, column 1   Trigger.OpportunitySAPIdentifierHandler: line 4, column 1: []:   Class.AutoNumber.OpportunityAutoNumber: line 76, column 1   Below is the trigger and class used.  trigger Opportuniwith sIdentifierHandler on Opportunity (before insert,before update) {          If(Trigger.isInsert || Trigger.isUpdate){             AutoNumber.OpportunityAutoNumber(Trigger.new);         }   }   The class is   public with sharing class AutoNumber {       public static void OpportunityAutoNumber (List&lt;Opportunity&gt; Opp) {          if(Trigger.isUpdate || Trigger.isInsert) {              for(Opportunity p: Opp) {                  List&lt;Opportunity&gt; oppList = new List&lt;Opportunity&gt;();                 oppList = [SELECT Id, createdDate, Identifier__c FROM Opportunity where Identifier__c = null and Id != :p.Id limit 100 FOR update];                 for (Opportunity oppL: oppList) {                      if(oppL.Identifier__c == null) {                          List&lt;Opportunity&gt; OpportunityList = new List&lt;Opportunity&gt;([select Identifier__c from Opportunity where Identifier__c != null order by Identifier__c desc limit 1]);                          if (!OpportunityList.isEmpty()) {                               Decimal maxval = OpportunityList.get(0).Identifier__c;                             oppL.Identifier__c = maxval + 1;                             update oppL;                         }                      }                     // integer currentCounter = Integer.valueOf(opp.Identifier__c);                     // oppr.Identifier__c = currentCounter + 1;                     // update oppr;                 }             }         }        }  } List the files accessed by a program time is a brilliant command if you want to figure out how much CPU time a given command takes.  I am looking for something similar that can list the files being accessed by a program and its children. Either in real time or as a report afterwards.  Currently I use:  #!/bin/bash  strace -ff -e trace=file "$@" 2&gt;&amp;1 | perl -ne 's/^[^"]+"(([^\\"]|\\[\\"nt])*)".*/$1/ &amp;&amp; print'   but its fails if the command to run involves sudo. It is not very intelligent (it would be nice if it could only list files existing or that had permission problems or group them into files that are read and files that are written). Also strace is slow, so it would be good with a faster choice. If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism. Let $X$ and $Y$ be metric spaces, $X$ compact, and $T:X \to Y$ bijective and continuous. Show that $T$ is a homeomorphism.   My attempt:  We need only show that $T^{-1}$ is continuous.  Let $M \subset Y$ be closed. Then, from the surjectiveness of $T$, there exists a $A \subset X$ such that $T(A)=M$. Since $M$ is closed, by the continuity of $T$, we must have that $A$ is closed.  Now $$T^{-1}(T(A))=T^{-1}(M)$$ i.e, $A=T^{-1}(M)$. Since $A$ and $M$ are closed, we must have that $T^{-1}$ is continuous.  My problem with this, however, is that I am not using the fact that $X$ is compact anywhere in the proof. Is there perhaps another way that I can show this, using the compactness of $X$?   Any hints will be appreciated. Ubuntu boots from USB but get GRUB rescue after installation I can boot Ubuntu from USB, but when I took the USB stick out of the laptop and booted again, I got an error saying   Error: unknown filesystem. grub rescue&gt;   What can I do to fix this? Let $t∈\Bbb N$ and let $x=6t+1, \:y=12t+1$ and $z=18t+1$. $x, y$ and $z$ are all primes and let $n=xyz$. Prove that  $a ^{n-1} \equiv 1 \pmod  n\;$ whenever $ a∈\Bbb Z$ and $\gcd(a,n) = 1$.  I have started using the Euler-Fermat Theorem since $\gcd(a,n)=1$. Giving $\phi (n)=(1296t^3) $ But unsure how to proceed? This is a question that's been nagging me for some time. I always thought that C++ should have been designed so that the delete operator (without brackets) works even with the new[] operator.  In my opinion, writing this:  int* p = new int;   should be equivalent to allocating an array of 1 element:  int* p = new int[1];   If this was true, the delete operator could always be deleting arrays, and we wouldn't need the delete[] operator.  Is there any reason why the delete[] operator was introduced in C++?  The only reason I can think of is that allocating arrays has a small memory footprint (you have to store the array size somewhere), so that distinguishing delete vs delete[] was a small memory optimization. Bash script to remove the oldest file from from a folder I want to make a bash script to delete the older file form a folder. Every time when I run the script will be deleted only one file, the older one. Can you help me with this? Thanks How to change the voltage polarity in an inverting amplifier? I want to implement a simple circuit which can map -10V  +10V voltage range to 0V 5V voltage range. Thus I'm planning to use two op-Amps, one for the slope and the other for the offset. So basically I'm planning to use an inverting amplifier and a summing amplifier consecutively.  But Inverting amplifiers multiplies the input voltage with a minus sign. I need a positive slope. How can I overcome this?  Also Could you gibe me any ideas for a cheap op-Amp models for this purpose? Remove HTML Tags from an NSString on the iPhone What is the black thing on the circuit What is the black thing on the below circuit?   Is it used to hide the IC (or other components) that is used on the circuit?   What material is it? Is an expanding map on a compact metric space continuous? I got inspired by this question  to think about the following problem: Suppose you have a compact metric space $(X,d)$ and an expanding map $T:X\rightarrow X$, i.e. $d(Tx,Ty)\geq d(x,y)$ for every $x,y\in X$. Is the map $T$ then continuous? Without assuming continuity we already know that $T^n(X)$ must be dense in $X$ for any $n\geq 1$, since given $z\in X$ the orbit of $z$ must accumulate upon $z$. But showing continuity has escaped me so far. If there are counter-examples using the Axiom of Choice that also interests me. Let $n$ is a natural number. Prove that $$\left\lfloor\frac{n}{1}\right\rfloor+\left\lfloor\frac{n}{2}\right\rfloor+....+\left\lfloor\frac{n}{n}\right\rfloor+\left\lfloor{\sqrt{n}}\right\rfloor$$   is even.   I used induction and the inequality $$x-1&lt;\lfloor{x}\rfloor\le{x}$$ to prove it.  Is there any other, nicer way to do it? The RSA signature operation is basically the same as encrypting with the private key.  In particular, both operations use the same kind of keys.  Is it safe to use the same RSA keypair both for encryption / decryption and for signing / verification? How to completely remove Notepad++ in Ubuntu 18.04 terminal?  I can't find it in Synaptic package manager, and don't know where is on system, but I can see an icon in Activity. It is probably not completely installed, because I can't open it. Why don't we read ''k'' here?  Know → /nəʊ/   Knotty → /ˈnɒt.i/   Knockout → /ˈnɒk.aʊt/ How to match all occurrences of a regex