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From: Keith Thompson <Keith.S.Thompson+u@gmail.com>
Newsgroups: comp.lang.c
Subject: Re: Modern Pythagorean
Followup-To: comp.theory
Date: Mon, 29 Aug 2022 02:18:03 -0700
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wij <wyniijj2@gmail.com> writes:
> Pythagorean: Any number can be infinitely approached by ratio p/q. There is
> no REAL number (e.g. the diagonal of a square) that cannot be approached by
> ratio number.
>
> The limit theory perfectly says THE LIMIT of lim(x->c) f(x) is L, and
> jumps to (logically invalid) conclusion f(c)=L (EQUAL).
> lim(x->1) x= 1 ... yes x can be 1
> lim(x->1) 1/(x-1)=? ... no x cannot be 1
> lim(x->∞) n/x=0 ... whatever, the magic of infinity emerges. (no x in
> ℝ can make 1/x=2/x=0, ∞ is also said not in ℝ)
>
> PS. I believe TM (program,algorithm) should/would be the foundation of math.
> These are for programmers.

I encourage anyone who wants to discuss this to do so in comp.theory,
where wij also posted.  (Note the complete lack of any content relevant
to C.)

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips
void Void(void) { Void(); } /* The recursive call of the void */