fom
Posts:
1,037
Registered:
12/4/12
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Re: Matheology § 203
Posted:
Feb 4, 2013 5:02 PM
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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.
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