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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Real Number  & Restoring Interpretation of Calculus
Date: Sun, 24 Mar 2024 18:13:19 +0200
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On 2024-03-24 14:59:52 +0000, wij said:

>    Note: This definition implies that repeating decimals are irrational number.

This contradicts the definition that an irrationa number is not rational.

>          Let's list a common magic proof in the way as a brief explanation:
>            (1) x= 0.999...
>            (2) 10x= 9+x  // 10x= 9.999...
>            (3) 9x=9
>            (4) x=1
>          Ans: There is no axiom or theorem to prove (1) => (2).

A theory of numbers should have enough axioms to determine what
the sum or product of any two numbers is.

-- 
Mikko