
From:  Ralf Hemmecke 
Subject:  [Axiomdeveloper] Re: FW: data structure vs. mathematical structure 
Date:  Tue, 14 Nov 2006 23:03:26 +0100 
Useragent:  Thunderbird 1.5.0.8 (X11/20061025) 
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 Twould 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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