On Tue, Sep 16, 2008 at 3:21 AM, Ralf Hemmecke wrote: > >>> So "singleton" category can not be just one element set. >> >> ??? By *definition* it is a category that contains just one domain. >> Are saying that this definition is inconsistent? > > Sounds like both of you don't understand each other. >
Yes, perhaps that is true. I hope that by continuing this discussion we can reach an agreement. Thanks for your attempt to help. :-) > Let me use Aldor here... > > ---BEGIN aaa.as > #include "aldor" > C: Category == with; > D: C == add; > ---END aaa.as > > ---BEGIN bbb.as > C: Category == with; > D1: C == add; > D2: C == add; > ... > Dn: C == add; > ---END bbb.as > > In aaa.as C is a category that only has exactly one domain in it. But > this is only true if I consider one fixed program. C is not a "singleton" category. Something is not a singleton category just because it happens to be used in one domain in some program. > As bbb.as shows that "singleton" category definition depends on the > context. No, no, no. Currently there is no such thing as "singleton" category in either Aldor or Spad so it is not possible to give an example of it. The singleton category 'Cat(D)' is *defined* as the category containing just domain D. That is a definition - not something that can be shown by an example. > Thus, Waldek is right, that a category always contains (potentially) > infinitely many domains (or in other words, one can define > infinitely many domains to a given category). > Of course that is correct but it has nothing to do with what I meant by singleton category. > Did I understand you intentions correctly? I am sorry, but no I do not think so. :-( Ralf, did what I write about anonymous categories make sense to you? I.e. that anonymous categories are not reflexive? Regards, Bill Page. --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
