Sets, Subsets, and the Null Set

Date: 06/22/2004 at 21:31:23
From: Jon
Subject: Sets

Can the null set be an element of any set?  I know that the null set 
is a subset of any set.

Date: 06/23/2004 at 11:00:12
From: Doctor Ian
Subject: Re: Sets

Hi Jon,

Note that the null _set_ is just that, a set.  So it can only be an
_element_ of a set that contains sets, such as the set of subsets of a 
set. 

If 

  A = {1, 2, 3}

then the set of subsets of A is 

  S = { {},
        {1}, {2}, {3},
        {1, 2}, {1, 3}, {2, 3},
        {1, 2, 3} }

and the null set is an _element_ of S, and a _subset_ of A.  But it's
not an _element_ of A. 

Does this help?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 06/24/2004 at 20:02:01
From: Jon
Subject: Thank you (Sets)

Dr. Ian,

Yeah, it cleared up my confusion.  Thanks a lot!

                                         Jon