In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> potentially infinite list does not contain every whatever in the > sense of all. Because a list that in contains all whatevers is actual > with respect to these whatevers.
Potential infiniteness does not occur in the world of TERTIUM NON DATUR.
In such a world, a set either does or does not have an injection to a proper subset. as in such TERTIUM NON DATUR worlds as ZF, > > But of course the list contains every sequence that is a line between > 1 and n (including the limits) and therefore contains all these > sequences.
In SF and similarly "saner than WMytheology" set theories > > These two meanings have to be distuingusihed carefully. Example: A > potentially infinite set of natural numbers does not contain all > natural numbers.
Then it is not a set at all, at least unless one can tell which naturals are members and which are not.
> Otherwise it would be an actually infinite set, named |N.
The name |N can refer to an actual set because the membership is determinate rather than indeterminate. --