Date: Mar 13, 2013 5:41 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Mar 13, 6:33 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 13 Mrz., 17:59, William Hughes <wpihug...@gmail.com> wrote:
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> > On Mar 13, 5:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > On 13 Mrz., 13:19, William Hughes <wpihug...@gmail.com> wrote:
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> > <snip>
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> > > > If you wish to contest this, use my words not
> > > > yours  (e.g.  I have never said "The list contains more
> > > > numbers than fit into a single line",  I have said
> > > > "There is no line in the list which contains every
> > > > number in the list".)

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> > > Correct. The list has more numbers than a single line has. Since every
> > > number that is in the list, must be in at least one line, this implies
> > > that the numbers are in more than one line.

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> > To be precise, a set of lines, say K, that contains all the numbers
> > contains at least two lines.

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> In actual infinity, this is not avoidable.
> We note: At least two lines belong to the set that contains all
> numbers. We call these lines necessary lines.


Why, when they are clearly not necessary?

Let J be a set of the lines of L with no
findable last line. At least two lines
belong to J. Are any lines of J necessary?