Re: Incompleteness of Cantor's enumeration of the rational numbers (doubling-spaces)

On 11/11/2024 2:04 PM, Ross Finlayson wrote:

On 11/11/2024 11:00 AM, Ross Finlayson wrote:

On 11/11/2024 10:38 AM, Jim Burns wrote:

Our sets do not change.
Everybody who believes that
  intervals could grow in length or number
is deeply mistaken about
  what our whole project is.

>
How about Banach-Tarski equi-decomposability?

The parts do not change.

(We had a great long thread over on sci.logic
about Banach-Tarski and Vitali-Hausdorff, there's
quite a bit about the historical and technical arrival,
including references and links to Hausdorff's original.
>
Vitali's doubling-space reflects on "Zeno's graduation
course", where Zeno also has a doubling-space or
doubling-measure argument, since about 2300 years ago.
>
These are considered part of "mathematics", if
your project is wider than "bumbing- or dumbing-down W.M.".)

My project is potentially (dare I say it?) much wider
than explanations that sets do not change.
But what do I accomplish by talking about more,
if I say one thing, and a different thing is heard?