Date: Feb 4, 2013 5:02 PM
Author: fom
Subject: Re: Matheology § 203
On 2/4/2013 3:48 PM, Virgil wrote:

> In article

> <52da52b8-a093-4a27-8b52-8cee878dc323@r3g2000yqd.googlegroups.com>,

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

>

>> On 4 Feb., 13:19, William Hughes <wpihug...@gmail.com> wrote:

>>> On Feb 4, 1:05 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>>>

>>> So we have according to WM

>>>

>>> 0.111...

>>>

>>> is not a single line of

>>>

>>> 0.1

>>> 0.11

>>> 0.111

>>> ...

>>>

>>> and

>>>

>>> there is no list of every 0/1 sequence.

>>

>> You have to distinguish more carefully: There is nothing of such a 0/1-

>> sequence that you can name and that was missing from every line of an

>> appropriate list.

> Ever such FIS corresponds to a member of |N, and every list of FIS's

> that is not infinite has a last one, which has a successor.

> So WM cannot produce a list which is complete.

>>

>> And there is no list of every FISON in exaxtly the same sense. Thus it

>> is impossible to distinguish countability and uncountability in

>> potential infinity.

>

> But it is impossible to impose the nonsense of potential infiniteness on

> ZF or most other set theories.

>

Potential infinity need not be nonsense.

Your objection to mixed metaphors certainly applies.

From the beginning (I showed up when Zuhair was asking questions)

I have not understood terminology. A CIBT is the Cantor space.

It is a topological construct and the C refers to topological

completeness.

Of course, many logicians work primarily with logical

constructs involving discrete alphabets. So, I assume

that I am just misunderstanding the jargon of a

particular branch of mathematicians.

I do not include WM's uses in that remark. While I

understand his objections, I am still trying to understand

some of his statements.