In article <email@example.com>, firstname.lastname@example.org wrote:
> On Thursday, 27 June 2013 02:37:17 UTC+2, Zeit Geist wrote: > > > You can't build the infinite from a finite set of finite things. > > Of course I can, and many have done it before. The sequence 1, 2, 3, ... is > infinite by induction.
But that ",,," makes it not a finite set of finite things. > > > AoI accomplishes the construction of an Infinite set. And yes, "Oh, oh, > > it's magic" > > No. The magic only came into play when a "cardinal number" was attached to > that set. aleph_0 is not derived from any axiom.
Without an axiom of infinity in ZF, there is no provable |N or provable aleph_0, but with that axiom, in ZF one gets both. > > Here an unreasonable limit