In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 23 Mrz., 23:58, William Hughes <wpihug...@gmail.com> wrote: > > On Mar 23, 10:56 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 23 Mrz., 21:54, William Hughes <wpihug...@gmail.com> wrote: > > > > <snip> > > > > > > You have agreed that, "under the assumption that actual > > > > infinity is a meaningful notion" > > > > you have not shown that we could remove all finite lines > > > > without changing the union in any way. > > > > > You reverse the facts. > > Under the assumption that actual infinity is a meaningful notion, I > have shown that one can remove all finite lines without changing the > union.
WM has 'shown' nothing, at least nothing to the satisfaction of anyone but WM. > > > > WH: this does not mean that one can do something > > WH: that does not leave any of the lines of K > > WH: and does not change the union of all lines. > > This does not mean that one can really do so > > > > WM: That is clear because my proof rests > > WM: upon the premise that actual infinity is a meaningful notion.
WM has yet to produce anything that qualifies as a proof outside his WMytheological dreamworld. > > because actual infinity is not a meaningful notion.
That WM is incapable of thinking of it does not equally cripple the rest of us.
> And I have set out to prove precisely that. Perhaps you have not yet > fully understood the structure of my proof.
We have yet to see anything of yours with enough structure to be a proof. > > Act. inf. is meaningful ==> Removal of all lines without change is > possible
That may hold in WM's Wolkenmuekenheim, but not elsewhere.
In a saner world than WM inhabits, a set of FISONs has the infinite set of all naturals, |N, as its union if and only if that set of FISONs is itself an infinite set. --