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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 11 Apr 2025 19:32:32 +0800
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On Fri, 2025-04-11 at 09:50 +0000, Alan Mackenzie wrote:
> wij <wyniijj5@gmail.com> wrote:
> > On Thu, 2025-04-10 at 17:23 -0700, Keith Thompson wrote:
> > > wij <wyniijj5@gmail.com> writes:
> > > [...]
> > > > "lim(x->c) f(x)=3DL" means the limit of f approaching c is L, not
> > > > f(c)=3DL 'eventually'.=C2=A0 f at c is not defined (handled) in lim=
it.
>=20
> > > Correct.
>=20
> > > > lim 0.333...=3D1/3=C2=A0=C2=A0=C2=A0 ... The *limit* is 1/3, not 0.=
333...=3D1/3
> > > > 0.3+0.33+0.333+...=C2=A0 ... The sequence converges to 1/3
> > > > =CE=A3(n=3D1,=E2=88=9E) 3/10^n=C2=A0=C2=A0=C2=A0=C2=A0 ... The sum =
converges to 1/3 (or you can use lim)
>=20
> > > The limit as the number of 3s increases without bound *is exactly wha=
t
> > > we mean* by the notation "0.333...".=C2=A0 Once you understand that, =
it's
> > > obvious that 0.333... is exactly equal to 1/3, and that 0.333... is a
> > > rational number.
>=20
> > You agree "f at c is not defined (handled) in limit", yet, on the other=
 hand
> > ASSERTING 0.333... is 'exactly' 1/3 from limit? Are you nut?
>=20
> No, Keith Thompson is simply correct, here.=C2=A0 It is you who are nuts,
> making unfounded claims about mathematics without having studied it.
>=20
> The sentence ....
> > > The limit as the number of 3s increases without bound *is exactly wha=
t
> > > we mean* by the notation "0.333...".
> .... is entirely correct.
>=20
> > As usual, you need to prove what you say. Or you are just showing yours=
elf=20
> > another olcott, just blink belief, nothing else.
>=20
> No, one doesn't need continually to prove standard mathematical
> definitions and results.=C2=A0 One could spend the whole day, every day, =
doing
> nothing else.
>=20
> It is _you_ who needs to prove your remarkable assertions.=C2=A0 You can'=
t, of
> course, because they're false.=C2=A0 What you could do, of course, is to =
show
> a bit of respect for those who have studied and learnt mathematics.

I am not interesting to blind beliefs.
As I may guess from your posts, your knowledge is essentially 'what people =
say'
without knowing the meaning of words.
You may say it is 'standard', 'mainstream'...,etc. But whatever it is, simp=
ly=20
no logical proof.

Remind you, the so called 'standard', 'mainstream'=C2=A0is on the side of l=
ogical proof.
They may evolve/change from errors. It is not a static thing and not the so=
urce of fact.

To save garbage talks, provide your logical proof (as usual, I believe NONE=
).