> Yes. Let me add another example to make things clearer (using > new syntax for categories with no export): > > A : Category == with () > > B : Category == with () > > If program has _only_ the two deffinitions above, then there > are no defined domains which belong to category A and no > defined domains which belong to category B. In other words > sets of defined domains which belong to A is the same as > set of defined domains which belong to B. Naive set > theoretic interpretation would say that A = B, but clearly > the language definition says that A is different than B.
Exactly. > So, something is needed to rescue set theoretic interpretation. > My solution is to consider all domains which may be potentially > defined -- once you add them all nonempty categories are > infinite, but equality of categores is just set theoretic > equality. That leaves me with the question what a "empty category" is. (Empty in the sense of "there is no domain that belongs to that category".) Theoretically, that would be the category with *all possible* exports. Such a category can never be written down and thus cannot be in any program. That in turn means that there all categories have infinitely many domains (and it is probably the same Aleph for any category). Or one accepts Join() to be the "empty category". Ralf --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
