```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 theexpress purpose of obtaining "support" forcontrary opinions from some of my statementswhich are non-standard.I expect that my response had put that torest quickly, but, it makes plain that WM'spolitical approach to these matters hasinfluence where beliefs are in play.I will not fault anyone for their beliefsabout infinity.  It is just that there isgood mathematics they could look atinstead of the pretend mathematics of"monotonic-inclusive" crayon marks.
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