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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 11 Apr 2025 19:52:20 +0800
Organization: A noiseless patient Spider
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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, not 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, 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
> > 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
> Keep the insults to yourself.=C2=A0 Last warning.

I still think 'nut' is a common word, at least a terse word for people sayi=
ng
one thing and doing the other (or a liar more appropriate?)

> 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.)

Increases without bound -> yes
is exactly 1/3 -> no such logic

> 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 exactly
> 1/3.=C2=A0=C2=A0

Is this a lie? I have always consistently claiming "repeating decimals are =
irrational".

> Why do you object to the use of that particular notation for that
> particular concept?
>=20

Illogic

> Do you have any mathematical argument that isn't purely about notation
> that you dislike?

???

> Would, say "0.333<=E2=88=9E>" be clearer?=C2=A0 Could you agree that that=
 refers to
> the limit and gives a result that's exactly 1/3?=C2=A0=C2=A0

0.333... approaches 1/3 --> no problem.
0.333... equals exactly to 1/3 --> no way (I have provided proofs and you d=
on't).

> If so, why do you
> object to "..." but not to "<=E2=88=9E>" as a symbol for the limit?=C2=A0=
 (Note that
> "..." is easier to type, unless you happen to have an =E2=88=9E key your
> keyboard.)

Who say I object the use of "..."?
As said, it is 'the limit', not exactly equal (as explained)

As usual, you still only have irrelevant garbage talk, no valid logic proof=
..
If so, I can choose to stop responding.