On 11/14/2006 10:17 PM, Page, Bill wrote:
On November 14, 2006 12:01 AM Gaby wrote:
|
| > From constructive mathematics point of view, the only things
| > that are required for a set are:
| >
| > (1) say how to build element of a set
| > (2) equality test.
| >
Bill Page wrote:
| No, there is a lot more to the mathematics of set than that.
| It would mean that all sets are finite and that is quite far
| from the case.
On Tuesday, November 14, 2006 1:20 PM Gaby wrote:
How do you arrive to that conclusion?
I thought I was stating something obvious.
I remember I said that "Set" is somehow a bad name for a domain in Axiom
that only implements "(the collection of) finite sets of elements of a
given type T".
Or (from sets.spad):
++ A set over a domain D models the usual mathematical notion of a
++ finite set of elements from D.
Although
i: Integer
and
s: FinitePowerSet T
would be in perfect analogy if one read ":" as "element of", then to go
on "l: List T" would mean "List" is the container of all finite
sequences (with some information about their representation (linked
list)). It's soon getting confusing. So I would rather choose
"FiniteSet". But then (except proper classes) everything is a set. Why
would one need a domain of sets? "SetCategory" is more important.
And in Axiom it is an approximation anyway, since it is Set(T), ie a
collection of things of a common type T. The name "Set" is probably an
exception one could accept.
Ralf
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