Date: Feb 26, 2014 5:41 PM
Author: Dan Christensen
Subject: Re: Infinity: The Story So Far
On Wednesday, February 26, 2014 4:19:35 PM UTC-5, Virgil wrote:

> In article <d8f3388b-775f-441c-9324-df43a3179e73@googlegroups.com>,

>

> Dan Christensen <Dan_Christensen@sympatico.ca> wrote:

>

>

>

> > Assuming the implicit successor functions in each case, these sets are all

>

> > isomorphic to one another, i.e. you are simply using different symbols for

>

> > the various elements, but the successor relation is preserved, as is the

>

> > induction principle. As I said, such structures is embedded in EVERY infinite

>

> > set. So, you are on fairly safe ground to assume the existence of one such

>

> > structure at the beginning of a proof.

>

>

>

> If one does not have something like an axiom of choice, there is no

>

> guarantee that any infinite set need have any well-orderable subsets.

>

>

>

> So in ZFC you are correct but not necessarily so in ZF.

>

Whew!

Dan

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