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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Wed, 09 Apr 2025 20:25:50 +0800
Organization: A noiseless patient Spider
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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.
>=20
> 	I don't think that's quite what Wij is claiming.=C2=A0 He thinks,
> rather, that 0.333... is different from 1/3.=C2=A0 No matter how far you
> pursue that sequence, you have a number that is slightly less than
> 1/3.=C2=A0 In real analysis, the limit is 1/3 exactly.=C2=A0 In Wij-analy=
sis,
> limits don't exist [as I understand it], because he doesn't accept
> that there are no infinitesimals.=C2=A0 It's like those who dispute that
> 0.999... =3D=3D 1 [exactly], and when challenged to produce a number
> between 0.999... and 1, produce 0.999...5.=C2=A0 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.=C2=A0 But we have no goo=
d
> and widely-known notation for what can follow a "...", so the Wijs of
> this world get mocked.=C2=A0 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.