On 3/26/2013 3:36 AM, WM wrote: > On 26 Mrz., 00:28, Virgil <vir...@ligriv.com> wrote: > >>> But in effect every FISON fails to empty |N. >> >> No one FISON does, >> nor do even finitely many of them, >> but all infinitely many of them, collectively, do. > > Amen. >
So, WM thinks he wins one?
Nonsense. It should amaze anyone that Virgil and WH can make any sense of this load of crap in order to "debate" it.
|N is not the union of its finite initial segments.
It is a system described by axioms.
WM confuses these facts as well as the general rules involving set inclusions and unions.
This is precisely what occurs in the snipped segment. It is what was being addressed.
>>>> Why should any FISON be left? >>> >>> Every natural is in at least one FISON, so without at least one FISON >>> in that set of only FISONs there is nothing to contain ANY natuals. >> >> That is so in potential infinity. > > I neither know nor care what WM claims goes on in his Wolkenmuekenheim. > > But in standard mathematics, what I said above is true, a set of FISONs > containing no FISONs means a union of no naturals. > > > >> There is no sequence that is larger >> than every FISON, but only for every FISON, there is a larger one. >> But in actual infinity, there is a sequence that is larger than every >> FISON. > > True, but it is not a FISON. > > >> But in effect every FISON fails to empty |N. > > No one FISON does, > nor do even finitely many of them, > but all infinitely many of them, collectively, do. > > At least everywhere outside Wolkenmuekenheim. >