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

On 3/23/2013 8:13 PM, Virgil wrote:
> In article
> <>,
> WM <> wrote:

>> On 23 Mrz., 15:20, William Hughes <> wrote:
>>> On Mar 23, 3:13 pm, WM <> wrote:

>>>> On 23 Mrz., 15:01, William Hughes <> wrote:
>>>>> On Mar 23, 2:43 pm, WM <> wrote:
>>>>>> On 23 Mrz., 10:31, William Hughes <> 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.