In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 11 Jun., 13:25, William Hughes <wpihug...@hotmail.com> wrote: > > On Jun 11, 6:16 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > WM: The idea that the infinite union of finite segments > > WM: results in an infinite segment is false. > > > > WM now gives a "counterexample", finding an infinte union > > of finite segments that does not result in > > an infinite segment. > > Nobody has any evidence of an example supporting the idea that the > infinite union of finite segments > results in an infinite segment.
We have plenty of examples showing that the infinite union of a sequence of sets each a proper subset of the next, cannot be a finite set.
And there is no consistent set theory extant in which there is any such thing as a potentially infinite set.
> No form of logic does support it. > I gave a counter example.
Which has itself been countered, so is invalid. > > The only pro-argument is that set theorists feel obliged to believe in > that idea. But that is not enough.
They feel obliged to follow the logic which says that if there can be an infinite sequence of finite sets, each a proper subset of its successor, which existence WM accepts, then there must be a union of all those sets, i.e., a set of which all those nested sets are proper subsets, and any such a union must be itself infinite.