```Date: Jan 30, 2013 4:03 AM
Author: Virgil
Subject: Re: WMytheology � 203

In article <e289d619-2f59-4f4d-82d9-0e81428830da@m12g2000yqp.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 30 Jan., 00:16, William Hughes <wpihug...@gmail.com> wrote:> > On Jan 29, 10:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> >> > > On 29 Jan., 21:28, William Hughes <wpihug...@gmail.com> wrote:> >> > <snip>> >> > > > It does, however, imply that d in not one> > > > of the lines of the list L> >> > > For that sake you must check all lines. Can you check what is not> > > existing?> >> > So now your claim is> >> > We can know> >> >   There does not exist a natural number n> >   such that d is equal to the nth line> >   of L> >> > but we cannot know> >> >   d is not one of the lines of L> > You are trying hard to misunderstand!He is not trying not to understand anywhere as strongly as you are.> > For a potentially infinite setOutside of WMytheology sets are either finite or not finite (infinite) with no middle ground.> But a potentially infinite setNo such things exist in standard set theories. > But "actually> infinite" means a number larger than every n.Not at all. Actually infinite means  set that is bigger than any single FISON, such as the union of all FISIONS.Note that if one can discriminate a FISON from a non_FISON, then one can have a set of all FISONS, which is easily provable not to be the surjective image of any FISON, and thus must be infinite.> It is easy to understand> that this number can never be exhausted by finite numbers n. Infiniteness of a set is not a number at all but a property possessed by  some sets, the property of being injectable to a proper subset of itself, which property |N enjoys.Does WM declare there is any natural number, n, such that n+1 is not also a natural number? Unless WM can find some such natural number, the the set of naturals injects into a proper subset of itself, and is thus infinite.--
```