My Math Forum Null set paradox

 Number Theory Number Theory Math Forum

 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:
 The empty set is the unique set having no elements

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:
 Originally Posted by Loren 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.
You are mixing several different mathematical notions and pretending they are somehow related. To see why this is absurd, consider the related "theorem" you could prove using the exact same argument.

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 timey-wimey stuff.
Quote:
 Originally Posted by Loren 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.
Think of 0 as the additive identity. That means it is something, not nothing.

-Dan

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:
 The empty set is the unique set having no elements
I was trying to grasp (the count of) how many elements the null (empty) set has, and whether the null set could exist without a concept of zero.

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

Quote:
 Originally Posted by Loren whether the null set could exist without a concept of zero.
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 timey-wimey stuff.
Quote:
 Originally Posted by Maschke It's also the set of all purple flying elephants. No numbers needed to make that definition either.
Now wait a minute! I know three of them and they like the same brand of whiskey I do!

-Dan

June 7th, 2019, 11:11 PM   #9
Senior Member

Joined: May 2015
From: Arlington, VA

Posts: 457
Thanks: 29

Math Focus: Number theory
Quote:
 Given any set X, the empty set is the set of all x∈X such that x≠x
Simple yet profound, Maschke.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post zylo Topology 9 February 15th, 2016 03:21 PM Kinroh Linear Algebra 3 October 25th, 2014 03:59 AM Kinroh Linear Algebra 0 October 1st, 2014 07:00 PM tinynerdi Linear Algebra 4 May 16th, 2010 02:57 PM tinynerdi Linear Algebra 4 May 10th, 2010 02:39 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top