Date: Mar 23, 2013 6:23 PM
Author: fom
Subject: Re: Matheology § 224

On 3/23/2013 4:56 PM, WM wrote:
> On 23 Mrz., 21:54, William Hughes <wpihug...@gmail.com> wrote:
>> On Mar 23, 4:15 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>>
>>
>>
>>
>>

>>> On 23 Mrz., 15:01, William Hughes <wpihug...@gmail.com> wrote:
>>
>>>> On Mar 23, 2:43 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>>
>>>>> On 23 Mrz., 10:31, William Hughes <wpihug...@gmail.com> wrote:
>>>>>> We both agree that you have not shown that we can
>>>>>> do something which leaves no lines and does not
>>>>>> change the union.

>>
>>>>> No, of course we do not.
>>
>>>> WH: this does not mean that one can do something
>>>> WH: that does not leave any of the lines of K
>>>> WH: and does not change the union of all lines.

>>
>>>> WM: That is clear
>>
>>> Please complete this sentence: "That is clear because my proof rests
>>> upon the premise that actual infinity is a meaningful notion."

>>
>>> If actual infinity was existing as a meaningful notion, then we could
>>> remove all finite lines without changin the union in any way.

>>
>> nope
>> actual infinity existing as a meaningful notion, does not mean
>> we could remove all finite lines without changing the union
>> in any way.

>
> Do you think it is not a contradiction, to have the statements:
> 1) 0.111... has more 1's than any finite sequence of 1's.
> 2) But if we remove all finite sequences of 1's, then nothing remains.

how you define

0.111...

as an abbreviation.

For example, if it is the limit
of partial sums,

x_n = Sum(1 to n)(1/10^n)

lim(n=>oo) x_n = 0.111...

which, without the 'oo' is

for each epsilon>0 there exists
an integer k>0 such that if n>=k
then |x_n - 0.111...|<epsilon

Then, it is clear that 0.111...
has nothing to do with the finite
sequences you wish to "remove".

On the other hand, what is implicit
in this approach to what Cantor
referred to as "potential infinity"
is the arbitrariness of choice from
some domain.

You deceive people when they naturally
assume your use of mathematical jargon
implies a mathematical literacy.

Crayon marks are not definitions.