Date: Jan 30, 2013 4:37 AM
Subject: Re: Matheology § 203
On 30 Jan., 10:13, Virgil <vir...@ligriv.com> wrote:
> In article
> 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.