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

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.
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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.
Regards, WM