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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Fri, 15 Nov 2024 22:53:36 +0100
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On 15.11.2024 18:54, Jim Burns wrote:
 > On 11/15/2024 5:04 AM, WM wrote:

 >> For infinite figures
 >> we use the analytical limit
 >> as is normal in mathematics.
 >
 > The reason you (WM) give is that
 > ☠⎛ whatever is true of all finite
 > ☠⎝ is also true of the infinite.

Not "whatever" but well-established rules.
 >
 > You (WM) are misinterpreting the infinite as
 > ☠( just like the finite, but bigger.

You are believing that the infinite can do magic. I believe that limits 
of simple sequences can be calculated. The sequence 1/5, 1/5, 1/5, ... 
has the limit 1/5 after all terms. It does never deviate.
 >
 > The finite are the countable.to from.nothing.
 > Anything countable.to from.nothing is finite.
 > It's what.we.mean.

Either we can calculate the infinite by means of the finite relations, 
or this will forever remain impossible. Only in the latter case your 
argument is acceptable. But why do you believe in Cantor's bijections if 
the infinite can disobey all logic?

If it is possible that the set {10^10^10^n, 10^10^10^m, n, m ∈ ℕ} has 
precisely as many elements as the set of algebraic numbers (i.e., if 
there can exist a bijection), then there is no trust in bijections.

If the intervals [n - 1/10, n + 1/10] can infinitely often cover the 
real line, then there is no trust in geometry.

 > And our sets do not change.

Then the density 1/5 will never change. Then never a new guest can be 
accomodated in the fully occupied Hilbert's hotel.

Regards, WM