"Bill Page" <[EMAIL PROTECTED]> writes:
| > Bill Page writes:
| > | > | All domains that have SetCategory are required to have a
| > | > | hash| into SmallInteger.
| > | >
| > | Gaby wrote:
| > | > That is not a mathematical requirement.
| > |
| > Bill Page wrote;
| > | I would tend to agree but perhaps Kurt Gödel would not have...
| > | ;-)
| >
|
| 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.
| >
|
| 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.
How do you arrive to that conclusion?
| Rather, sets should be strongly related to types.
|
| I think the "constructive mathematics" that is most suitable
| to Axiom is probably is probably Intuitionist type theory
| (Martin-Löf). See:
In fact, I prefer the definition given by Erret Bishop. See chapters 1
and 2 "his" book
"Constructive Analysis",
Erret Bishop
Douglas Bridges
>From my perspective, it shows a much deeper impact.
-- Gaby
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