On 13/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote: > Question to David, and others who could be interested: is the notion > of enumerable and non enumerable set clear? Can you explain why the set > of functions from N to N is not enumerable?
Do please remind us. "Off the top of my head", do you mean, by non-enumerable, arbitrary extensibility by the generation of new members via diagonalisation? > Do you people know the difference between ordinal and cardinal (I know > some knows 'course). Yes > I don't think Church thesis can be grasped > conceptually without the understanding that the class of programmable > functions is closed for the diagonalization procedure. Please explain 'programmable functions' and 'closed for the diagonalisation procedure'. > Do everyone > (interested) know how to prove the non enumerability of the subset of N > by diagonalization? Which subset do you mean? I've encountered the diagonalisation/enumerability argument, assuming it's the one I referred to above. > Let us go slow and deep so that everybody can understand, once and for > all. OK? Definitely OK. David > > > Le 13-août-07, à 13:29, Kim Jones a écrit : > > > where he appears to serve the option of being machine or some other > > order of being. I must confess that I still don't understand the > > ontology of angels as opposed to machines but I'm sure his reply > > contains the reason > > > Don't worry, I will try to explain. > > > Question to David, and others who could be interested: is the notion > of enumerable and non enumerable set clear? Can you explain why the set > of functions from N to N is not enumerable? > > Just say no, and I go back to Cantor, the one who discussed with the > pope about the question of naming infinities (!), and indeed the one > who will discover (or invent) the varieties of infinities. > > Do you people know the difference between ordinal and cardinal (I know > some knows 'course). I don't think Church thesis can be grasped > conceptually without the understanding that the class of programmable > functions is closed for the diagonalization procedure. Do everyone > (interested) know how to prove the non enumerability of the subset of N > by diagonalization? > > Let us go slow and deep so that everybody can understand, once and for > all. OK? > > > Bruno > > > http://iridia.ulb.ac.be/~marchal/ > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" 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/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
