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

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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