On 2/4/2013 3:48 PM, Virgil wrote: > In article > <email@example.com>, > WM <firstname.lastname@example.org> 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.