Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Repeating decimals are irrational
Date: Wed, 27 Mar 2024 07:34:15 +0800
Organization: A noiseless patient Spider
Lines: 33
Message-ID: <c75f33b5df723f71bae7a7a1c125abba782bab85.camel@gmail.com>
References: <e9009d933dc0c3008201ba6cfced892d235192c8.camel@gmail.com>
	 <87wmppuhn8.fsf@nosuchdomain.example.com>
	 <fa1bc63730570ff93fb7b43f81e735453829bab3.camel@gmail.com>
	 <87sf0dueli.fsf@nosuchdomain.example.com>
	 <27544510d7559860979611a504b6ad0d9aebfd1c.camel@gmail.com>
	 <87o7b0vja4.fsf@nosuchdomain.example.com>
	 <1b980d564d961c4c290b5bf722835f2f2f284969.camel@gmail.com>
	 <87jzloveiw.fsf@nosuchdomain.example.com>
	 <ca4c6e9d56ec2929d0c4b1319627f0ae17c7cfc1.camel@gmail.com>
	 <87frwcvc19.fsf@nosuchdomain.example.com>
	 <02aa964280a00d97c3d3d23af84f5582d5497ff7.camel@gmail.com>
	 <87bk70varb.fsf@nosuchdomain.example.com>
MIME-Version: 1.0
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
Injection-Date: Tue, 26 Mar 2024 23:34:16 +0100 (CET)
Injection-Info: dont-email.me; posting-host="e58f2b2de37d2d0fd85c976e2be071c6";
	logging-data="2548231"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18NBxkTXZSoa7/T/n0yEeEc"
User-Agent: Evolution 3.50.2 (3.50.2-1.fc39)
Cancel-Lock: sha1:WjenI6GeP25kJv4Z1GMqdsInTa0=
In-Reply-To: <87bk70varb.fsf@nosuchdomain.example.com>
Bytes: 2651

On Tue, 2024-03-26 at 16:22 -0700, Keith Thompson wrote:
> wij <wyniijj5@gmail.com> writes:
> > On Tue, 2024-03-26 at 15:55 -0700, Keith Thompson wrote:
> [...]
> > > Do you understand what a mathematical limit is?=C2=A0 Can you explain=
 it?
> > >=20
> > > If you understand limits, you should be able to understand that
> > > 0.333..., where the "..." denotes the limit as the number of 3s excee=
ds
> > > without bound, is exactly equal to 1/3.
> > >=20
> > > [...]
> > >=20
> >=20
> > I already stated it the file:
> > https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber-en.tx=
t/download
>=20
> OK, in that file you wrote:
>=20
> =C2=A0=C2=A0=C2=A0 Ex1: A=3D lim(n->=E2=88=9E) 1-1/n=3D lim(n->0=E2=81=BA=
) 1-n=3D lim 0.999...=3D1
> =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 B=3D lim(n->=E2=88=9E) 1=
+1/n=3D lim(n->0=E2=81=BA) 1+n=3D lim 1.000..?=3D1
>=20
> What do you mean by that question mark?=C2=A0 Do you agree that both limi=
ts
> in your example (A and B) are equal to 1?
>=20

Agree.