From: MoeBlee on
Virgil wrote:
> In article <45119c60$1(a)news2.lightlink.com>,
> Tony Orlow <tony(a)lightlink.com> wrote:
>
> > MoeBlee wrote:
> > > Tony Orlow wrote:
> > >>> It isn't. What does "successor to N" even mean?
> > >> Ask von Neumann. It is the set of all naturals,
> > >
> > > What are you talking about? The successor of w is not w. The successor
> > > of w is wu{w}.
> >
> > The size of the set x is the value
> What "value"
>
>
> > and it contains every natural less
> > than x.
> Cardinalities, as cardianlities, do not contain anything.

The cardinality of a set is a set, so except for 0, the cardinality of
a set has members.

MoeBlee

From: MoeBlee on
Tony Orlow wrote:
> Because N is defined as including all finite naturals, it is potentially
> infinite, each element having a finite index in the set.

I suppose you mean T-potentially infinite. But do you mean set
theoretic N or T-N?

MoeBlee

From: MoeBlee on
MoeBlee wrote:
> Tony Orlow wrote:
> > Because N is defined as including all finite naturals, it is potentially
> > infinite, each element having a finite index in the set.
>
> I suppose you mean T-potentially infinite. But do you mean set
> theoretic N or T-N?

P.S. If you mean set theoretic N, then it depends on which treatment we
are using whether N is defined as you described or whether instead it
is a theorem that N is as you described.

MoeBlee

From: MoeBlee on
MoeBlee wrote:
> Tony Orlow wrote:
> > Because N is defined as including all finite naturals, it is potentially
> > infinite, each element having a finite index in the set.
>
> I suppose you mean T-potentially infinite. But do you mean set
> theoretic N or T-N?

P.S. If you mean set theoretic N, then it depends on which treatment we
are using whether N is defined as you described or whether instead it
is a theorem that N is as you described.

MoeBlee

From: Virgil on
In article <73452$45123e3f$82a1e228$7325(a)news2.tudelft.nl>,
Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote:

> Virgil wrote:
>
> > In article <3a6c6$4510f00a$82a1e228$27505(a)news2.tudelft.nl>,
> > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote:
> >
> >>David R Tribble wrote:
> >>
> >>>mueckenh wrote:
> >>>
> >>>>>Nothing has changed. There is no complete set of natural numbers. Any
> >>>>>set that can be established is a finite set. Hence, the probability to
> >>>>>select a number divisible by 3 is 1/3 or very very close to 1/3.
> >>>
> >>>Virgil wrote:
> >>>
> >>>>That presumes that the allegedly finite set of naturals that can be
> >>>>constructed is nearly uniform with respect to divisibility by 3 at
> >>>>least, and probably by other numbers as well. What is the justification
> >>>>for this assumption?
> >>
> >>Wolfgang says litteraly: "_or_ very very close to 1/3".
> >
> > Which requires "_nearly uniform_ with respect to divisibility by 3".
>
> Sorry, Virgil. I don't get it.

As usual.