Re: Incompleteness of Cantor's enumeration of the rational numbers

Am Fri, 08 Nov 2024 17:43:15 +0100 schrieb WM:

On 08.11.2024 13:28, Richard Damon wrote:

On 11/8/24 5:18 AM, WM wrote:

>

My understanding of mathematics and geometry is that reordering cannot
increase the measure (only reduce it by overlapping). This is a basic
axiom which will certainly be agreed to by everybody not conditioned
by matheology. But there is also an analytical proof: Every reordering
of any finite set of intervals does not increase their measure. The
limit of a constant sequence is this constant however.
This geometrical consequence of Cantor's theory has, to my knowledge,
never been discussed. By the way I got the idea after a posting of
yours: Each of {...,-3,-2,-1,0,1,2,3,...} is the midpoint of an
interval.

which makes the error that the properties of finite objects apply to
the infinite objects, which isn't true, and what just breaks your
logic.

The infinite of the real axis is a big supply but an as big drain.

>
You take it as a given, but that just means that your logic is unable
to actually handle the infinite.

I take it as evident that intervals of the measure 1/5 of the positive
real axis will not, by any shuffling, cover the real axis completely,
let alone infinitely often. I think who believes this is a deplorable
fanatic if not a fool.

What is the measure you are using and what does it give for the real
axis?