Re: Is {{}} a valid construct?

On Feb 3, 9:32 am, "-CELKO-" <jcelko..._at_earthlink.net> wrote:
> >> Can an empty set contain an empty set? Is it valid according to set theory? If so, what does it correlate to in the real world? (when last explained to me, I was left holding two empty bags of potatoes but no clear understanding :) <<
>
> Look up "ordinal numbers" in a book on set theory. This is how they
> are defined and the work on this was due to John von Neumann -- the
> same guy that invented Game Theory and the basic architecture for
> stored programs in computers. The idea is that 0 = {} and then a +
> 1 = a U {a} to build integers with a version of Peano's system.

Suppose the universal set is {0, apple}. If according to Neumann 0 equals {}, I should be able to restate the universal set as {{}, apple}. Now what is NOT {}? Is it {{}, apple} or {apple}? Received on Mon Feb 05 2007 - 05:27:54 CET