Date: Jan 30, 2013 4:53 PM
Author: Virgil
Subject: Re: Matheology � 203

In article 
WM <> wrote:

> On 30 Jan., 10:13, Virgil <> wrote:
> > In article
> > <>,
> >
> >  WM <> wrote:

> > > You can prove something for all natural numbers, but not for a larger
> > > set.

> >
> > You can prove that the set of naturals can be injected into a proper
> > subset of itself. n --> n+1 is such an injection.

> In fact this property only shows potential infinity. You prove
> something for every n but not for all elements of the set.

In my world proving something "for all naturals numbers" proves it for
all elements of the set of natural numbers.
> > Any set of objects
> > with this property (of being injectable to a proper subset of itself) is
> > by definition actually infinite.

> So what? Similarly we can define: Every set of more than ten natural
> numbers and sum less than 5 is by definition actually finite.

Since everywhere but inside Wolkenmuekenheim there is already a
perfectly adequate defnition of a set being finite, your attempt revise
that definition is irrelevant outside of Wolkenmuekenheim.

> Nevertheless there is no actually finite set of natural numbers.

Actually, every FISON is an actually finite set of natural numbers, it
is just that none of those FISONs is a set of ALL natural numbers the
way their union is.