Date: Feb 3, 2013 5:04 PM
Author: fom
Subject: Re: Matheology § 203
On 2/3/2013 3:58 PM, WM wrote:

> On 3 Feb., 22:29, William Hughes <wpihug...@gmail.com> wrote:

>>>> We can say "every line has the property that it

>>>> does not contain every initial segment of s"

>>>> There is no need to use the concept "all".

>>

>>> Yes, and this is the only sensible way to treat infinity.

>>

>> So now we have a way of saying

>>

>> s is not a line of L

>>

>> e.g. 0.111... is not a line of

>>

>> 0.1000...

>> 0.11000...

>> 0.111000....

>> ...

>>

>> because every line, l(n), has the property that

>> l(n) does not contain every initial

>> segment of 0.111...

>

> But that does not exclude s from being in the list. What finite

> initial segment (FIS) of 0.111... is missing? Up to every line there

> is some FIS missing, but every FIS is with certainty in some trailing

> line. And with FIS(n) all smaller FISs are present.

>

>> Is there a sensible way of saying

>> s is a line of L ?

>

> There is no sensible way of saying that 0.111... is more than every

> FIS. And every FIS is in a line.

Do you mean "is in some line"?

As in "there exists a line containing a given FIS"