Re: Matching infinite sets

2016-08-21 Thread Martin Gregorie
On Sun, 2016-08-21 at 16:56 -0400, Dianne Skoll wrote: > On Sun, 21 Aug 2016 21:22:38 +0200 > Damian wrote: > > > > > > > > > So we define set B as everything in the universe that is not in > > > set > > > A. So set B is an infinite set, everything in the universe EXCEPT > > > apples and orange

Re: Matching infinite sets

2016-08-21 Thread Sidney Markowitz
Dianne Skoll wrote on 22/08/16 8:56 AM: > And... why can't a set contain itself? > It can't in standard modern set theory (ZFC), through the foundation axioms, also known as the axiom of regularity https://en.wikipedia.org/wiki/Axiom_of_regularity which is a formulation that allows set theory t

Re: Matching infinite sets

2016-08-21 Thread Dianne Skoll
On Sun, 21 Aug 2016 21:22:38 +0200 Damian wrote: > > So we define set B as everything in the universe that is not in set > > A. So set B is an infinite set, everything in the universe EXCEPT > > apples and oranges. > There is no such set B, as it would contain itself. And... why can't a set con

Re: Matching infinite sets

2016-08-21 Thread Dianne Skoll
On Sun, 21 Aug 2016 09:47:45 -0700 Marc Perkel wrote: > So we define set B as everything in the universe that is not in set A. That's a very specific kind of infinite set. It's the complement of a finite set. Try this one on for size: Consider the set A of all positive integral powers of pi

Re: Matching infinite sets

2016-08-21 Thread Antony Stone
On Sunday 21 August 2016 at 21:22:38, Damian wrote: > Am 21.08.2016 um 18:47 schrieb Marc Perkel: > > Actually - you can match an infinite set. And maybe this is what it's > > hard for some people to wrap their head around. > > > > Suppose set A contains 2 items, apples and oranges. > > So we def

Re: Matching infinite sets

2016-08-21 Thread Damian
Am 21.08.2016 um 18:47 schrieb Marc Perkel: > Actually - you can match an infinite set. And maybe this is what it's > hard for some people to wrap their head around. > > Suppose set A contains 2 items, apples and oranges. > So we define set B as everything in the universe that is not in set A. >

Matching infinite sets

2016-08-21 Thread Marc Perkel
Actually - you can match an infinite set. And maybe this is what it's hard for some people to wrap their head around. Suppose set A contains 2 items, apples and oranges. So we define set B as everything in the universe that is not in set A. So set B is an infinite set, everything in the universe