Re: Proposal: 6NF

JOG wrote:
> Thanks for the clarification guys. My confusion in this discussion
> stems from this quote on set closure from the same site:
>
> "Set Closure:
>
> A set S and a binary operator * are said to exhibit closure if applying
> the binary operator to two elements S returns a value which is itself
> a member of S.
>

That's the closure under discussion.

> The closure of a set A is the smallest closed set containing A. Closed
> sets are closed under arbitrary intersection, so it is also the
> intersection of all closed sets containing A."

That's the topological closure.

>
> The first statement, from my reading, support's vc's argument
> wholeheartedly - a binary operator returns a value from the same set if
> it is to exhibit closure.However the second statement indicates that
> the closure of a set is the smallest closed set /containing A/ - i.e.
> the closure can be a superset of A. This seems to support Jan's point
> of view.

The closure of any finite set is the set itself if one talks about topolgical spaces.

>
> In relation to the example under discussion I read it as:
> * A = {0, 1, 2, 3, 4} and 'plusMod4' exhibit closure.
> * But the closure of B = {2,3} under 'plusMod4' , is the smallest
> /closed/ set containing B - which would be A.

It would be B in the context of topolgical spaces which is irrelevant here.

>
> There seems a very subtle point here which I am currently missing. Or
> perhaps the terminology is being used in two subtly different ways?

See above.

> Either way I am vexed, as from a certain angle you both appear to be
> right.
>
[...] Received on Fri Oct 20 2006 - 04:59:14 CEST