Re: Is {{}} a valid construct?

> > 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. Received on Fri Feb 02 2007 - 19:11:35 CET