Date: Jan 24, 2013 7:23 PM
Author: Virgil
Subject: Re: ZFC and God
In article

<1bff3260-2afe-4cb5-b296-cbfcd931316d@x3g2000yqo.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 24 Jan., 21:43, Virgil <vir...@ligriv.com> wrote:

>

> > > > U_n {1,...,n} is not infinite. (*)

> >

> > > It is not actually infinite. The cardinality is not larger than every

> > > n.

> >

> > Then there must be some n that it is not larger than.

> >

> > Either

>

> There can be every n. Because no n is infinite!

If there can be "every n", then there can be set containing "every n".

>

> What is actually infinite is something that has *no* last n, if I

> remember correctly what you have said.

You have not!

That only would apply to ordered sets, like |N.

A set S is infinite whenever there is an injection from |N to S,

regardless of whether S is ordered.

The sets of al elements in |N that are less than some element of |N are

all finite sets and every finite set is, at least in theory, bijectable

with one of them.

Unordered sets can also be either finite or infinite.

The set of points on the surface of a 3D sphere is not ordered but is

infinite.

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