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

On 08.11.2024 18:05, Richard Damon wrote:
 > On 11/8/24 11:43 AM, WM wrote:
 >> The infinite of the real axis is a big supply but an as big drain.
 >
 > What "drain", the numbers exist.
But their density is everywhere the same.
 >
 >> 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.
 > Since 1/5 of infinity isn't a finite measure, you can't use finite logic
 > to handle them.
Since 1/5 is a finite number and for every finite set the covering is 1/5, the limit is 1/5 too.
 >
 > You are just proving your use of broken logic.
Chuckle. Everybody who believes that the intervals
I(n) = [n - 1/10, n + 1/10]
0--------_1_--------_2_--------_3_--------_4_--------_5_--------_...
could grow in length or number to cover the whole real axis is a fool or worse.
Regards, WM