Virgil
Posts:
4,483
Registered:
1/6/11
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Re: Matheology � 203
Posted:
Jan 30, 2013 4:53 PM
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In article
<a7b295fd-a628-46ef-aae1-5b847cee357e@f6g2000yqm.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 30 Jan., 10:13, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <b79952f1-a65c-4b62-9cb4-5a358b78b...@4g2000yqv.googlegroups.com>,
> >
> > WM <mueck...@rz.fh-augsburg.de> 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.
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