May 2nd, 2019, 07:35 PM  #11 
Senior Member Joined: Jun 2014 From: USA Posts: 525 Thanks: 40  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 
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?

May 2nd, 2019, 08:33 PM  #13 
Senior Member Joined: Aug 2012 Posts: 2,306 Thanks: 706  
May 2nd, 2019, 08:38 PM  #14  
Senior Member Joined: Sep 2016 From: USA Posts: 609 Thanks: 378 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
Last edited by skipjack; May 2nd, 2019 at 08:58 PM.  
May 2nd, 2019, 11:09 PM  #15 
Senior Member Joined: Aug 2012 Posts: 2,306 Thanks: 706  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.

May 8th, 2019, 06:11 PM  #16 
Senior Member Joined: Jun 2014 From: USA Posts: 525 Thanks: 40  

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