Date: Apr 5, 2013 4:54 AM
Author: fom
Subject: Re: Matheology § 224

On 4/5/2013 3:43 AM, WM wrote:
> On 4 Apr., 21:01, William Hughes <wpihug...@gmail.com> wrote:
>> On Apr 4, 8:22 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>>
>>
>>
>>
>>

>>> On 4 Apr., 19:40, William Hughes <wpihug...@gmail.com> wrote:
>>
>>>> On Apr 4, 6:43 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>>
>>>>> On 4 Apr., 18:21, William Hughes <wpihug...@gmail.com> wrote:
>>
>>>>>> On Apr 4, 5:19 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>>
>>>>>>> On 4 Apr., 16:08, William Hughes <wpihug...@gmail.com> wrote:
>>>>>>> There is no need to say what numbers belong to mathematics - in
>>>>>>> mathematics. There is no need to say what paths belong to the Binary
>>>>>>> Tree

>>
>>>>>> However, you keep talking about two types of paths,
>>
>>>>> Not at all. I talk about sets of nodes that are in the Binary Tree.
>>
>>>> Indeed, and some of these subsets of nodes are paths and
>>>> some are not.

>>
>>> In the Binary Tree there is no stop at any path.
>>
>>>> You talk about subsets of nodes with a last node
>>>> and subsets of nodes without a last node. However,
>>>> you refuse outright to indicate what makes a subset of nodes
>>>> a path (certainly not all subsets of nodes are paths).

>>
>>> All nodes that belong to a finite path, belong to an infinite path
>>> too.

>>
>> Since you refuse to say what makes a subset of nodes a path
>> you cannot claim that a path without a last node exists.-

>
> I do not claim it. The infinite path, claimed or not, is simply
> existing as the union of all its FISONs. There is no rule that
> prevents unioning FISONs and there is no last node. (It is not
> necessary to *define* that there is no last node.)


Then it ought not be necessary to *define* choice functions.

Oh wait! It isn't. The existence of choice functions
is assumed through the axiom of choice.

However, in mathematics one has assumptions, definitions,
and theorems obtained using standard, accepted forms of proof.

One does not have "simply is" through "proof by reality".

Virgil has stated standard definitions with which WM refuses
to adhere.

WH has shown WM that he can formulate specific definitions
which he refuses to do.

WM simply claims and then simply claims to not simply claim.