Date: Mar 13, 2013 2:19 PM
Author: fom
Subject: Re: Matheology § 222 Back to the root<br> s
On 3/13/2013 12:33 PM, WM wrote:

> On 13 Mrz., 17:59, William Hughes <wpihug...@gmail.com> wrote:

>> On Mar 13, 5:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>>

>>> On 13 Mrz., 13:19, William Hughes <wpihug...@gmail.com> wrote:

>>

>> <snip>

>>

>>>> 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".)

>>

>>> 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.

>>

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

>> contains at least two lines.

>

> 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.

> So the set of necessary lines is not empty.

>

>> However, this does *not* imply that

>> there are two numbers that are not in a single line.

>

> Why then should two lines be necessary?

> One being the substitute in case the other falls ill?

>

>> Nor does it imply that there is a necessary line in K.

>

> If there is not one necessary line, then there are two or more

> required.

> Proof: If you remove all lines from the list, then there remains no

> line and no number.

>

>> Note that a sufficient set does not imply a necessary line

>> even in potential infinity. There is no line that is needed

>> to make L have an unfindable last line.

>

> So you believe that there can remain all numbers in the list after

> removing all lines? That is a remarkable claim. I would not accept it

> in mathematics.

>

> Note in actual infinity it makes sense to talk about all lines and to

> remove all lines.

I think this is just a difference of interpretation

concerning "necessary".

To borrow from linear algebra, you are describing

something that might be more along the lines of

a "spanning set". Any particular lines are not

necessary, but whenever one speaks of the possibility

of given lines containing all the numbers, the

count of those lines would necessarily have a

non-zero value greater than one because of

partiality.