My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Thanks Tree1Thanks
Reply
 
LinkBack Thread Tools Display Modes
May 2nd, 2019, 07:35 PM   #11
Senior Member
 
Joined: Jun 2014
From: USA

Posts: 525
Thanks: 40

Quote:
Originally Posted by Maschke View Post
Didn't you say it was 1?
I said the intersection between a Vitali set and the rationals would have a cardinality of 1. You said it had a measure of 0 and I'm fine with that too, but that's wholly irrelevant. Here I thought maybe you were just alluding to the fact that you thought the measure of the relevant intersection would be 0 since the measure of $\mathcal{C}$ is zero, but now I realize you really didn't have a clue what this thread was about. double
AplanisTophet is offline  
 
May 2nd, 2019, 07:39 PM   #12
Senior Member
 
Joined: Jun 2014
From: USA

Posts: 525
Thanks: 40

Let's pose a more generalized version of the question for you then. Are there sets A and B where A $\cap$ B = A, the measure of A is undefined, and the measure of B is 0?
AplanisTophet is offline  
May 2nd, 2019, 08:33 PM   #13
Senior Member
 
Joined: Aug 2012

Posts: 2,306
Thanks: 706

Quote:
Originally Posted by AplanisTophet View Post
now I realize you really didn't have a clue what this thread was about.
I'm truly sorry I wasted my time on you tonight.
Maschke is offline  
May 2nd, 2019, 08:38 PM   #14
SDK
Senior Member
 
Joined: Sep 2016
From: USA

Posts: 609
Thanks: 378

Math Focus: Dynamical systems, analytic function theory, numerics
Quote:
Originally Posted by AplanisTophet View Post
I get it now, you were neglecting the possibility that the measure of the intersection between $V$ and $\mathcal{C}$ could be undefined, especially if the intersection were to equal $V$. You can't just assume that the intersection would have a measure of $0$ simply because $\mathcal{C}$ does as this says nothing of whether or not the measure of the intersection may be undefined.
He is neglecting that possibility because it isn't a possibility. It's a fundamental fact that if $A$ has (Lebesgue) measure zero, then every subset of $A$ is measurable and also has measure 0. In fact, this is true of any complete measure which follows as an easy consequence of the Carathéodory (sp?) completion procedure.
Thanks from AplanisTophet

Last edited by skipjack; May 2nd, 2019 at 08:58 PM.
SDK is offline  
May 2nd, 2019, 11:09 PM   #15
Senior Member
 
Joined: Aug 2012

Posts: 2,306
Thanks: 706

Quote:
Originally Posted by AplanisTophet View Post
Let's pose a more generalized version of the question for you then. Are there sets A and B where A $\cap$ B = A, the measure of A is undefined, and the measure of B is 0?
Hey man I'm sorry I overreacted. That silly goose remark got to me for some reason. You're right, you said cardinality and I misread it. All the best.
Maschke is offline  
May 8th, 2019, 06:11 PM   #16
Senior Member
 
Joined: Jun 2014
From: USA

Posts: 525
Thanks: 40

Quote:
Originally Posted by Maschke View Post
Hey man I'm sorry I overreacted. That silly goose remark got to me for some reason. You're right, you said cardinality and I misread it. All the best.
No worries. You told me what a Vitali set was in the first place.
AplanisTophet is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
intersection, question, sets



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Curve Intersection Question jonnegetier Algebra 4 August 16th, 2014 07:56 PM
Ortogonality and intersection of sets Deiota Real Analysis 4 April 1st, 2013 10:08 AM
Intersection of an infinite number of open sets (induction) mAraujo Real Analysis 2 July 26th, 2009 12:56 PM
Intersection of sets Carl Applied Math 7 October 20th, 2008 08:11 AM
intersection of two sets boxerdog246 Real Analysis 3 October 6th, 2008 10:33 AM





Copyright © 2019 My Math Forum. All rights reserved.