June 6th, 2019, 11:00 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 457 Thanks: 29 Math Focus: Number theory  Null set paradox
Paradox: if any member, or lack thereof, in the null (i.e., empty) set is countable, it requires the concept of zero, so it is not truly empty.

June 6th, 2019, 11:20 PM  #2 
Senior Member Joined: Oct 2009 Posts: 863 Thanks: 328 
???

June 6th, 2019, 11:46 PM  #3  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 Math Focus: Yet to find out. 
Empty set: Quote:
 
June 7th, 2019, 04:58 AM  #4  
Senior Member Joined: Sep 2016 From: USA Posts: 642 Thanks: 406 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
Theorem: All sets containing a 1984 Honda Accord, must contain at least 1983 other elements. The proof is obvious. Since any such set requires the concept of 1984, it can't truly have fewer than 1984 elements.  
June 7th, 2019, 05:05 AM  #5 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,266 Thanks: 934 Math Focus: Wibbly wobbly timeywimey stuff.  
June 7th, 2019, 11:01 AM  #6  
Senior Member Joined: May 2015 From: Arlington, VA Posts: 457 Thanks: 29 Math Focus: Number theory 
I wish you all success in a field I know much less about. Quote:
For instance, could any set exist without the concept of numbers? No wonder why zero was so late on the number scene!  
June 7th, 2019, 11:27 AM  #7 
Senior Member Joined: Aug 2012 Posts: 2,386 Thanks: 746  Given any set $X$, the empty set is the set of all $x \in X$ such that $x \neq x$. No numbers are required to make that definition. It's also the set of all purple flying elephants. No numbers needed to make that definition either. Sets precede numbers in the modern formalism. Although of course numbers preceded sets historically. 
June 7th, 2019, 02:08 PM  #8 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,266 Thanks: 934 Math Focus: Wibbly wobbly timeywimey stuff.  
June 7th, 2019, 11:11 PM  #9  
Senior Member Joined: May 2015 From: Arlington, VA Posts: 457 Thanks: 29 Math Focus: Number theory  Quote:
 

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