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.