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 mathematics

elsewhere. Denied.

In spite of his dedication to the meaning of words,

there are NONE which apply.

But, of course, everything is TRUE when arguing

from inconsistency.