On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:
> > Bruno Marchal skrev: >> 4) The set of all natural numbers. This set is hard to define, yet I >> hope you agree we can describe it by the infinite quasi exhaustion by >> {0, 1, 2, 3, ...}. >> > > Let N be the biggest number in the set {0, 1, 2, 3, ...}. > > Exercise: does the number N+1 belongs to the set of natural numbers, > that is does N+1 belongs to {0, 1, 2, 3, ...}? Yes. N+1 belongs to {0, 1, 2, 3, ...}. This follows from classical logic and the fact that the proposition "N be the biggest number in the set {0, 1, 2, 3, ...}" is always false. And false implies all propositions. But this is a bit advanced matter, Torgny. The math I am explaining to Kim and some others are typical classical mathematics. 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 everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---