On 09 May 2012, at 13:19, R AM wrote:
On Wed, May 9, 2012 at 12:48 PM, Bruno Marchal <[email protected]>
wrote:
The empty set is the absence of elements (nothing) in that set. It
is the set { }.
The empty set is not nothing. For example, the set is { { } } is not
empty. It contains as element the empty set.
Just to be precise.
Well, I guess that the empty set is more like an empty box.
Yes.
"Nothing", in set theory, would be more like an empty *collection* of
sets, or an empty "universe" (a model of set theory), except that in
first order logic we forbid empty models (so that AxP(x) -> ExP(x)
remains valid, to simplify life (proofs)).
Bruno
http://iridia.ulb.ac.be/~marchal/
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