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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Fri, 15 Nov 2024 13:58:06 -0800
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On 11/15/2024 1:53 PM, WM wrote:
> 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.

Ugg, an infinite set is never exhausted. Taking a gallon of water out of 
an infinite pool of water means you are holding a gallon water, but the 
infinite pool is still infinite. The same. Taking an infinite amount of 
water means the pool is still full of water.