Re: Is {{}} a valid construct?

"Neo" <neo55592_at_hotmail.com> wrote in message quote:

news:1170439894.973627.309270_at_l53g2000cwa.googlegroups.com...
> > Can an empty set contain an empty set?
>
> If a set contains an element, bit it the empty set or not,
> its not the empty set.
>
> So put your one empty bag of potatoes into your other
> empty bag of potatoes. And wush your second bag is not
> empty anymore. You see, it contains the first empty bag.

Thanks, however I am still confused as Bod Badour in comp.database.theory has the following reply to your post:

Sigh, I know I waste my breath but here goes: The empty set is the canonical (and only) set of cardinality zero: {} The set containing only the empty set is the canonical (but not the only) set of cardinality one: {{}}
The set containing both the empty set and a set containing the empty set
is the canonical set of cardinality two: {{},{{}}} And so on.
One can research this further by searching 'formalism' in mathematics or
by searching 'foundations of mathematics'.

Neo needs to pay particularly close attention that the set {{}} is not
empty because it contains {}.
Another way of writing {} is ? ie. ? === {} Perhaps it would clarify if I rewrote the above sets as: ?, {?}, {?, {?}}

? is the empty set
{?} is not empty because it contains ?
{?,{?}} is not empty because it contains both ? and {?} etc.

end quote.

The real question is... what is NOT Neo? Received on Mon Feb 05 2007 - 17:30:03 CET