```Date: Feb 7, 2013 8:19 PM
Author: fom
Subject: Re: Matheology § 210

On 2/7/2013 6:38 PM, Virgil wrote:> In article> <c00c57de-f177-4019-b022-e7f76ae7acd4@fn10g2000vbb.googlegroups.com>,>   WM <mueckenh@rz.fh-augsburg.de> wrote:>>> On 7 Feb., 19:50, William Hughes <wpihug...@gmail.com> wrote:>>> On Feb 7, 7:28 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>>>>>>>>>>>>>>>>>>> On 7 Feb., 19:14, William Hughes <wpihug...@gmail.com> wrote:>>>>>>>> On Feb 7, 5:57 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>>>>>>>>> On 7 Feb., 15:56, William Hughes <wpihug...@gmail.com> wrote:>>>>>>>>>> On Feb 7, 3:25 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>>>>>>>>>> <snip>>>>>>>>>>>> ... a subset S of the countable set F of finite words bijects with>>>>>>>> the set D of definable numbers>>>>>>>>> by definition.>>>>>>>>>> Nope.   Every D corresponds to some finite word.>>>>>>>>> No, D is a set or at least a collection. A definable number is an>>>>>> element of D.>>>>>>>>>>    However, S,>>>>>>> the collection of all the correspondences, may not be a subset>>>>>>> of F  (subsets must be computable).>>>>>>>>> Need not be a subset. It is sufficient to know that there are not more>>>>>> than countably many correspondences,>>>>>>>> There is no set of correspondences thus there is no number>>>>> of correspondences.  You cannot know anything about>>>>> the number of correspondences.->>>>>>> You are in error again. There is the axiom of power set. For any F,>>>> there is P such that D e P if and only if D c F. According to it every>>>> subset of the countable set F exists. Will you dispute that the finite>>>> definitions of numbers are a subset of F?>>>>>> Yes.  A subset must be constructable.->>>> Sorry, we are in classical set theory. There nothing must be>> constructable.>>>>>> Perhaps you are interested in definition and domain of application of>> "subcountable"?>>>> In constructive mathematics>> But only WM claims t be constrained to constructable mathematics here,> and has not the power to constrain anyone else.> And even WM does not follow those constraints consistently.>Actually, I asked about constructive mathematicselsewhere.  Denied.In spite of his dedication to the meaning of words,there are NONE which apply.But, of course, everything is TRUE when arguingfrom inconsistency.
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