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From: Keith Thompson <Keith.S.Thompson+u@gmail.com>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Thu, 10 Apr 2025 17:23:58 -0700
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wij <wyniijj5@gmail.com> writes:
[...]
> "lim(x->c) f(x)=L" means the limit of f approaching c is L, not f(c)=L 'eventually'.
> f at c is not defined (handled) in limit.

Correct.

> lim 0.333...=1/3    ... The *limit* is 1/3, not 0.333...=1/3
> 0.3+0.33+0.333+...  ... The sequence converges to 1/3
> Σ(n=1,∞) 3/10^n     ... The sum converges to 1/3 (or you can use lim)

The limit as the number of 3s increases without bound *is exactly what
we mean* by the notation "0.333...".  Once you understand that, it's
obvious that 0.333... is exactly equal to 1/3, and that 0.333... is a
rational number.

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
void Void(void) { Void(); } /* The recursive call of the void */