Date: Mar 18, 2013 1:09 PM
Author: fom
Subject: Re: Matheology § 224

On 3/18/2013 7:29 AM, WM wrote:
>
> Every list yields another diagonal.
> And every diagonal can be included in another list.
>
> Both these facts are the two sides of infinity.


What these facts correspond with is the
structure of a directed set.

Directed sets are, indeed, infinite.

Absolute infinity cannot be treated as
a number.

That does not mean one cannot have a
transfinite arithmetic.

<snip>

> With same right he could have argued that there are more even than odd
> non-negative integers, because 0 is even and after every odd integer
> there follwos an even one, just overlooking that after every even
> integer there follows an odd one.


But, Cantor understood the strict reasoning inherent
to the nature of class-based logical construction.

What he could have done if he were of lesser skill
is not what he did do -- because he knew better.