> On Monday, 18 August 2014 20:46:40 UTC+2, Virgil wrote: > >> For example. WM's argument saying for every n the set of naturals up to >> n does not ennumerate all of Q+, thus |N does not ennumerate Q+ or Q is >> based on the clearly false assumption that what is true for every FISON >> (Finite Initial Set Of Naturals up to some n in |N) must be true for the >> infinite set of naturals, |N. > > For indexing are only finite natural numbers available. What cannot be > indexed by them, cannot be indexed at all. Your mystical "set |N" is > nothing more than all n - in mathematics.
An excellent example of fine words with no mathematical significance. What are "available" numbers? Set theory has no such notion. And in set theory, "indexed" means being put into bijection with N -- something you've reluctantly agreed to for Q+. Un-indexed members of a set would not be in the image of the bijection -- again, you've agreed that no such positive rational exists. It's all just rhetoric based on, sadly, deliberately misleading use of terms.