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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Mon, 16 Dec 2024 12:14:20 +0200
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On 2024-12-15 11:25:26 +0000, WM said:

> On 15.12.2024 11:56, Mikko wrote:
>> On 2024-12-14 08:53:19 +0000, WM said:
> 
>>> Please refer to the simplest example I gave you on 2024-11-27:
>>> The possibility of a bijection between the sets ℕ = {1, 2, 3, ...} and 
>>> D = {10n | n ∈ ℕ} is contradicted because for every interval (0, n] the 
>>> relative covering is not more than 1/10, and there are no further 
>>> numbers 10n beyond all natural numbers n.
>> 
>> It is already proven that there is such bijection. What is proven cannot
>> be contradicted unless you can prove that 1 = 2.
> 
> What is proven under false (self-contradictory) premises can be shown 
> to be false.

If your premises are contradictory (as they seem to be) then everything
can be proven to be both true and false.

> Here we have a limit of 1/10 from analysis and a limit of 0 from set 
> theory. That shows that if set theory is right, we have
> 1/10 = 0 ==> 1 = 0 ==> 2 = 1.

That is the fallacy of equivocation. The limit of analysis is a different
concept from the limit of set theory.

-- 
Mikko