Date: Mar 17, 2013 8:20 PM
Author: fom
Subject: Re: Matheology § 224

On 3/17/2013 2:57 PM, Virgil wrote:
> In article
> <f3530023-6c75-428c-b15d-0d7eced6aee4@a14g2000vbm.googlegroups.com>,
> WM <mueckenh@rz.fh-augsburg.de> wrote:
>

>> On 17 Mrz., 00:25, Virgil <vir...@ligriv.com> wrote:
>>

>>>>> Can WM provide any definition for natural numberss which doe not state,
>>>>> or at least imply, that every natural must have a successor natural?

>>>
>>>> Numbers are creations of the mind. Without minds there are no numbers.
>>>
>>> Which is not a relevant answer.

>>
>> By definition of a matheologian.

>
> Which is a non-response to my original question:
> Can WM provide any definition for natural numberss which doe not state,
> or at least imply, that every natural must have a successor natural?
>
> WM's failure to respond positively I take as a "no" answer.

>>>
>>>
>>> Can WM provide an definition for natural numbers which doe not state,
>>> or at least imply, that every natural must have a successor natural?

>>
>> It is always stated or at least implicitly assumed in classical
>> mathematics that we are able to add 1. In reality this is an erroneous
>> assumption as has been shown in MatheRealism.

>
> Unless you can produce such a natural, which even in your alleged
> "mathrealism" you have not done, your claim is, as always, unfounded.

>>>
>>>> you are not able to write aleph_0 digits of a real numbers like 1/9.
>>>
>>> So what? There are lot of things in mathematics one cannot do, but that
>>> should not keep us from doing what we can do, the way you would limit us.

>>
>> But the claim of matheology is that all digits exist and can be
>> determined - for instance all digits of pi.

>
> I do not make the claim that all the digits of the number pi can be
> found, but I do claim that the number pi has a definition, as do
> infinitely many other reals whose exact decimal representations cannot
> be found.
>
> E. g., the square roots of each of the infinitely many primes are all
> defined, though none can be given exactly as decimals.
>


And, necessary to the proof of an algebraically closed field.

But when one 'knows' such things 'by reality' there is
no need of definition or proof.