Date: Mar 23, 2013 9:34 PM
Author: fom
Subject: Re: Matheology § 224

On 3/23/2013 8:13 PM, Virgil wrote:
> In article
> <6d096d49-90e0-49ca-8821-3d885e2c0d80@l9g2000yqp.googlegroups.com>,
> WM <mueckenh@rz.fh-augsburg.de> wrote:
>

>> On 23 Mrz., 15:20, William Hughes <wpihug...@gmail.com> wrote:
>>> On Mar 23, 3:13 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
>>>

>>>>> WH: this does not mean that one can do something
>>>
>>>> Of course we cannot really do infinite things. This is only an
>>>> abbreviation.

>>>
>>>> I say that there is no finite line that changes the union.
>>>
>>> Correct
>>>

>>>> So the union would be the same if there was no finite line.
>>>
>>> Nope, does not follow.

>>
>> It follows in ordinary logic. The negation of "no finite line changes
>> the union"

>
> But changing finite lines may well change unions of sets of finite lines.
> The distinction is on whether the set of lines in question has a maximal
> member when ordered by inclusion.
>
> If it does then the removal of the maximal member changes the union, so
> that WM's claim is not true in general, but can only be true for the
> special case in which the set of sets does not have a maximal member by
> inclusion.
>
> And or a set sets of of naturals like WM's sets of lines not to have a
> maximal member requires that for every line in it there is a longer line
> in it which is a superset of that previous line.
>
> Thus it follows that theses things that WM claims for sets of lines can
> only hold when such sets have n maximum by inclusion member.
>
> Outside of Wolkenmuekenheim, such sets of sets are called infinite.
> Inside Wolkenmuekenheim, they cannot get visas to enter.
>
>
>
>
>

>> is "at least one finite line changes the union". But this
>> is excluded by my proof.

>
> WM's poofs convince no one.



That may be optimistic.

A thread on sci.math had been started for the
express purpose of obtaining "support" for
contrary opinions from some of my statements
which are non-standard.

I expect that my response had put that to
rest quickly, but, it makes plain that WM's
political approach to these matters has
influence where beliefs are in play.

I will not fault anyone for their beliefs
about infinity. It is just that there is
good mathematics they could look at
instead of the pretend mathematics of
"monotonic-inclusive" crayon marks.