Date: Jan 30, 2013 4:37 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

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.

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

Regards, WM