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 the

lines satisfy the criterion. When all the

lines are removed, he perceives a contradiction

because the union over the empty set is not

the initial union over all of the monotonic

inclusive constructive sets of marks.

The problem with this reasoning is that a

contradiction is defined in terms of truth

and falsity of statements. The "property"

one would use for this induction, however,

does not change its truth value because

the empty set cannot be diminished by

removing lines. The inductive property

becomes vacuously satisfied at the "completion"

of the induction to the extent that one

may extend mathematics to WMytheology

to make such a statement.