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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: wij Newsgroups: comp.theory Subject: Re: Cantor Diagonal Proof Date: Fri, 11 Apr 2025 20:11:03 +0800 Organization: A noiseless patient Spider Lines: 71 Message-ID: References: <1ab7fe6b234496769adde06995790eebb827756e.camel@gmail.com> <60cbb326c7d65b1bbd9451319bd07721c76d307f.camel@gmail.com> <3e5a55b834962635ca7ecf428d074fba771a07f8.camel@gmail.com> <878qo74kbl.fsf@nosuchdomain.example.com> <875xjbt041.fsf@nosuchdomain.example.com> MIME-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Injection-Date: Fri, 11 Apr 2025 14:11:04 +0200 (CEST) Injection-Info: dont-email.me; posting-host="05950bb31754b8261a44aa641f85531a"; logging-data="1475815"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/pBxLeksuoAblcCL7w7i3N" User-Agent: Evolution 3.54.3 (3.54.3-1.fc41) Cancel-Lock: sha1:ccmCFYXlIXyQJbl2SKXRF0zE+ts= In-Reply-To: Bytes: 4439 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 writes: > > > > On Thu, 2025-04-10 at 17:23 -0700, Keith Thompson wrote: > > > > > wij 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