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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Wed, 9 Apr 2025 13:48:12 +0100
Organization: Fix this later
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On 09/04/2025 13:25, wij wrote:
> On Tue, 2025-04-08 at 19:44 +0100, Andy Walker wrote:
>> On 08/04/2025 16:17, Richard Heathfield wrote:
>>> It will, however, take me some extraordinarily convincing
>>> mathematics before I'll be ready to accept that 1/3 is irrational.
>>
>> 	I don't think that's quite what Wij is claiming.  He thinks,
>> rather, that 0.333... is different from 1/3.  No matter how far you
>> pursue that sequence, you have a number that is slightly less than
>> 1/3.  In real analysis, the limit is 1/3 exactly.  In Wij-analysis,
>> limits don't exist [as I understand it], because he doesn't accept
>> that there are no infinitesimals.  It's like those who dispute that
>> 0.999... == 1 [exactly], and when challenged to produce a number
>> between 0.999... and 1, produce 0.999...5.  They have a point, as
>> the Archimedean axiom is not one of the things that gets mentioned
>> much at school or in many undergrad courses, and it seems like an
>> arbitrary and unnecessary addition to the rules.  But we have no good
>> and widely-known notation for what can follow a "...", so the Wijs of
>> this world get mocked.  He doesn't help himself by refusing to learn
>> about the existing non-standard systems.
> 
> Lots of excuses like POOH. You cannot hide the fact that you don't have a
> valid proof in those kinds of argument.
> If you propose a proof, be sure you checked against the file I provided.
> I have no no time for garbage talk.

I have read that document, about which I have a simple question.

 From Theorem 2 and Axiom 2, if x can be expressed in the form of 
p/q, then p and q will be infinite numbers (non-natural numbers). 
Therefore, x is not a rational number. And since a non-rational
number is an irrational number, the proposition is proved.

Let p = 1
Let q = 3

Is it or is it not your contention that p and q are "infinite" 
(non-natural) numbers?

Prediction: you will evade the question. Why not surprise me?

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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