Date: Apr 12, 2013 2:34 AM
Author: William Hughes
Subject: Re: Matheology § 238

On Apr 12, 7:40 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 11 Apr., 23:52, William Hughes <wpihug...@gmail.com> wrote:
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> > On Apr 11, 9:51 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > On 11 Apr., 20:52, William Hughes <wpihug...@gmail.com> wrote:
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> > > > On Apr 11, 8:17 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > On 11 Apr., 19:19, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > So you agree that B implies A.
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> > > > > > yep, but A does not imply C:  P(d_1,d_2,d_3..)
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> > > > > That is your interpretation.
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> > > > One you agree with,
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> > > Not at all!
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> > Yep, you have agreed that saying something is true for
> > every element of a collection does not imply that it
> > is true for the collection.

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> It is true for all elements.


Correct every element has the property that it can be removed.

>No mentioning of collection.

Correct, the collection cannot be removed without changing
the union, and you cannot leave no lines without removing the
collection of lines.

> I am not at
> all interested whether these elements form something like a
> collection. Of course you cannot say that the collection of real
> numbers is a real number. But when all real numbers have been
> removed, the collection has gone too.


Correct. Removing all elements is the same as removing the
collection.

Now let P be (can remove the collection without changing
the union of the remaining lines).  We have there is no
contradiction in saying A: for all n, the nth line can be removed
because A does not imply C and only C is a contraction.