Date: Mar 13, 2013 6:05 PM
Subject: Re: Matheology § 222 Back to the roots

On 13 Mrz., 22:41, William Hughes <> wrote:

> 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?

Remove all lines.
Can any numbers remain in the list? No.
Therefore at least one line must remain in the list.

We do not know which it is, but it is more than no line.
In other words, it is necessary, that one line remains.

Now you say that not all numbers of the list can be in this one line.
This means that at least two lines are necessary.
We do not know which lines.
But if all numbers exist in the list, at least two lines must exist in
the list, containing these numbers.
In other words, two lines are necessary.

From the construction we know, that all numbers, that are in two
lines, are in one line. Therefore your claim, that more than two lines
must remain in the list, is contradicted.

Regards, WM