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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Thu, 10 Apr 2025 01:30:55 +0800
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On Wed, 2025-04-09 at 18:10 +0100, Richard Heathfield wrote:
> On 09/04/2025 17:45, wij wrote:
>=20
> <snip>
>=20
> > Stick to the problem. Such puzzle won't prove the "0.999... problem".
>=20
> You know what? You're right. 1/3 is irrational, 1 is infinite, 3=20
> is unnatural, and Achilles never did catch the tortoise. I don't=20
> know what I was thinking, claiming that rationals are rational!=20
> Clearly the arithmetic I learned at school was deeply flawed, and=20
> I was naif to think it could be trusted. How happy I am, now that=20
> I have learned the truth from some faceless bloke on the=20
> Internet. Well done you, eh? 1/3 is irrational; who knew?
>=20

1/3 is rational "by definition".

0.333... (repeating decimal) is irrational.

Achilles puzzle gives us two models. One can catch the tortoise, one
cannot. Since we believe Achilles can, so it make? people to believe
0.99.... will finish (false from the other model. Also the term=C2=A0
'repeating' implies (define) never terminate)