```Date: Apr 6, 2013 5:25 PM
Author: fom
Subject: Re: Matheology § 224

On 4/6/2013 3:51 PM, Virgil wrote:> In article> <f579d155-6b76-4b0f-a34d-7519fe5256d1@j9g2000vbz.googlegroups.com>,>   WM <mueckenh@rz.fh-augsburg.de> wrote:>>> On 5 Apr., 23:54, Virgil <vir...@ligriv.com> wrote:>>>>>> If not, how do you prove its finiteness?>>>>>> By finding its largest member.>>>> Find the largest line of the list>>>> 1>> 1, 2>> 1, 2, 3>> ...>>>> that cannot be removed without changing the union of the remaining>> lines.>>>> Regards, WM>> What makes you think that there is such a line?>> As far as I can see removing any one line alone from the union of all> lines has no effect on the union.>> So which lines does WM claim satisfy his criterion?>I did this analysis elsewhere.The sense of his question is that all thelines satisfy the criterion.  When all thelines are removed, he perceives a contradictionbecause the union over the empty set is notthe initial union over all of the monotonicinclusive constructive sets of marks.The problem with this reasoning is that acontradiction is defined in terms of truthand falsity of statements.  The "property"one would use for this induction, however,does not change its truth value becausethe empty set cannot be diminished byremoving lines.  The inductive propertybecomes vacuously satisfied at the "completion"of the induction to the extent that onemay extend mathematics to WMytheologyto make such a statement.
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