In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 10 Dez., 21:34, Virgil <vir...@ligriv.com> wrote: > > > > Irrelevant. The necessary FISON is always only one. > > > > But every "necessary" fison must have a successor. > > then that is the necessary one. The former is no longer necessary.
But the instant that any fison becomes "necessary", it has a successor and is then, by your own definition, no longer necessary. > > > > > > > > > But all that is completely irrelevant, as I do not claim that my model > > > is correct and as I do not base my reasoning upon that basis. > > > > You then confess that your model is incorrect, at jast! > > I do not pretend to have a model. All I know is that Cantor's actual > infinity is disproved.
"It ain't what you don't know that hurts you most, its what you know for sure that jest ain't so." Mark Twain! > > > > > > > > > My reasoning > > > > Your what? > > > > > shows that, according to mathematics, all natural numbers > > > fit into one (potentially in-) finite set. > > > > mathematics shows no such thing. WM's matheology pretendes to show it > > but even there WM has no logically sound arguments. > > The sequence of FISONs is finite.
In the JvN model of ZFC, EACH fison has a successor fison since each fison is a natural and each natural has a successor natural.
>It contains not more natural numbers > than fit into one FISON.
The sequence of all fisons contains AT LEAST one more natural than any fison, since for every fison there is a successor fison which contains one more natural.
> It is the most obvious nonsense to claim that > there are mot natural numbers than do fit into one FISON.
It is even more nonsensical to deny it, since there is no fison capable of containing its successor fison as a subset.
Wm keeps claiming the existence of a fison containing all naturals, but for each fison, WM must admit that there is a natural not in it.
In fact for each fison, it is easily shown that there are more naturals not in it than in it:
Every non-empty fison has a maximum member, and for every natural there is a fison of which it is the maximum member. Note that one might properly consider the empty set a fison with no members.
So for every fison not having a member as large as a natural number n there is a fison having maximum member 2*n, which has at least twice as many natural number members as the original fison. --