In article <email@example.com>, firstname.lastname@example.org wrote:
> On Friday, 12 July 2013 19:13:19 UTC+2, Zeit Geist wrote: > > It is rather silly to expect the process that creates each of the Naturals > > would produce the set of all Naturals, as that set is, itself, not a > > Natural. > > Each natural belongs to a finite initial segment. None of them requires a > number that is larger than every natural number.
Even the set of all natural numbers does not require a natual number larger than every natural number
> In fact the contrary. If you > do not talk about the set, then there is no reason to talk about alephs.
But for induction, one must have "for all natural numbers", so one might as well have the set of all of them. > > You seem to understand that each or every natural is quite different from the > set of all naturals?
Each member of ANY set is distinguishable from the set containing it, at least outside of WM's wild, weird world of WMytheology . --