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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 11 Apr 2025 20:11:03 +0800
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On Fri, 2025-04-11 at 12:04 +0000, Mr Flibble wrote:
> On Fri, 11 Apr 2025 19:52:20 +0800, wij wrote:
>=20
> > On Fri, 2025-04-11 at 04:21 -0700, Keith Thompson wrote:
> > > wij <wyniijj5@gmail.com> writes:
> > > > 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, n=
ot
> > > > > > f(c)=3DL 'eventually'.
> > > > > > f at c is not defined (handled) in limit.
> > > > >=20
> > > > > Correct.
> > > > >=20
> > > > > > lim 0.333...=3D1/3=C2=A0=C2=A0=C2=A0 ... The *limit* is 1/3, no=
t 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
> > > > > what we mean* by the notation "0.333...".=C2=A0 Once you understa=
nd
> > > > > that, it's obvious that 0.333... is exactly equal to 1/3, and tha=
t
> > > > > 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
> > > > As usual, you need to prove what you say. Or you are just showing
> > > > yourself another olcott, just blink belief, nothing else.
> > >=20
> > > Keep the insults to yourself.=C2=A0 Last warning.
> >=20
> > I still think 'nut' is a common word, at least a terse word for people
> > saying one thing and doing the other (or a liar more appropriate?)
> >=20
> > > My assertion is simply about what the "..." notation means.
> > >=20
> > > Do you agree that the limit of 0.3, 0.33, 0.333, as the number of 3s
> > > increases without bound, is exactly 1/3?=C2=A0 (You said so above.)
> >=20
> > Increases without bound -> yes is exactly 1/3 -> no such logic
> >=20
> > > What exactly do you think the notation "0.333..." means?=C2=A0 I and =
many
> > > others use that notation to mean the limit, which you agree is exactl=
y
> > > 1/3.
> >=20
> > Is this a lie? I have always consistently claiming "repeating decimals
> > are irrational".
>=20
> The decimals only repeat in certain bases:=C2=A0

Agree

> it is wrong to think that any=20
> part of mathematics relies on a specific base such as base 10.

Did I claimed what you said "any part of mathematics relies on a specific b=
ase"?

>=20
> /Flibble