Re: Collatz Conjecture proved.

From	wij <wyniijj5@gmail.com>
Newsgroups	comp.lang.c
Subject	Re: Collatz Conjecture proved.
Date	2026-01-26 01:20 +0800
Organization	A noiseless patient Spider
Message-ID	<9dca223cfefd1e3e79492484e04d9ca343637fa2.camel@gmail.com> (permalink)
References	<96ed450bdb96454829f94b79519afa93595b27c1.camel@gmail.com> <5dbb5d96b3bb34ac21754a4f59617b572059e857.camel@gmail.com> <10l44rd$u7or$1@dont-email.me> <975e829c29ff11e83681aa87e347c7ef1ffe43dc.camel@gmail.com> <10l5g5u$1pdvi$1@dont-email.me>

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On Sun, 2026-01-25 at 11:25 -0500, James Kuyper wrote:
> On Sun, 25 Jan 2026 13:28:31 +0800, wij wrote:
> 
> > On Sat, 2026-01-24 at 23:06 -0500, James Kuyper wrote:
> > > 
> > > This generalizes to work with any recurring decimal. When the
> > > recurrence is n digits long (in the above example, n=2), just
> > > multiply by 10^n.
> > 
> > Such arithmetic is called approximation ...
> 
> So what is, in your opinion, the exact representation of 4/33 as a
> decimal fraction? Marking it as infinitely repeating means that it is
> not in any sense an approximation - it is exact.

You need to prove 4/33 exactly equal to 0.1212..., not approximation.
But,...

>  If it were an
> approximation, there would be a finite difference between 4/33 and
> 0.1212.... How big is that difference? No matter how small of a finite
> difference you might think it has, going to infinitely many decimal
> digits makes the actual difference smaller than that.

Yes, the same as infinity/infinitesimal.

> Keep in mind that, in the absence of specification to the contrary,
> we're talking about the standard real number system, not one of those
> alternatives that extends the real number system by adding
> infinitesimals, such as the surreals or the hyperreals.

True if you are not referring to the current 'standard real number system'.
What else? (doesn't sound to contain much information)

The standard real number system is not a constant thing, it will correct
itself. Not even religion is constant.

To be explicitly 'C' related, I remember people talking about what INF 
should mean (an option may be merely for signifying overflow), I would
suggest reserve the bit, not mixing with other meaning.

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Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2025-12-24 20:05 +0800
  Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-25 00:37 +0800
    Re: Collatz Conjecture proved. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-01-25 00:23 +0000
    Re: Collatz Conjecture proved. James Kuyper <jameskuyper@alumni.caltech.edu> - 2026-01-24 23:06 -0500
      Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-25 13:28 +0800
        Re: Collatz Conjecture proved. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-01-25 08:15 +0000
          Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-25 16:46 +0800
            Re: Collatz Conjecture proved. David Brown <david.brown@hesbynett.no> - 2026-01-25 10:38 +0100
              Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-25 18:55 +0800
              Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-25 19:06 +0800
                Re: Collatz Conjecture proved. David Brown <david.brown@hesbynett.no> - 2026-01-25 12:47 +0100
                Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-25 23:44 +0800
                Re: Collatz Conjecture proved. James Kuyper <jameskuyper@alumni.caltech.edu> - 2026-01-25 12:22 -0500
            [OT] Proofs.  Was: Collatz Conjecture proved. Ben Bacarisse <ben@bsb.me.uk> - 2026-01-25 11:33 +0000
              Re: [OT] Proofs.  Was: Collatz Conjecture proved. richard@cogsci.ed.ac.uk (Richard Tobin) - 2026-01-25 13:11 +0000
            Re: Collatz Conjecture proved. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-01-25 18:52 +0000
              Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-26 03:58 +0800
        Re: Collatz Conjecture proved. James Kuyper <jameskuyper@alumni.caltech.edu> - 2026-01-25 11:25 -0500
          Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-26 01:20 +0800
            Re: Collatz Conjecture proved. Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-01-26 01:25 +0100
              Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-26 23:51 +0800
                Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-27 00:07 +0800
                Re: Collatz Conjecture proved. David Brown <david.brown@hesbynett.no> - 2026-01-26 21:05 +0100
                Re: Collatz Conjecture proved. David Brown <david.brown@hesbynett.no> - 2026-01-26 21:07 +0100
                Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-27 04:34 +0800
                Re: Collatz Conjecture proved. David Brown <david.brown@hesbynett.no> - 2026-01-27 09:21 +0100
                Re: Collatz Conjecture proved. antispam@fricas.org (Waldek Hebisch) - 2026-01-27 16:31 +0000
                Re: Collatz Conjecture proved. Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-01-27 18:24 +0100
                Re: Collatz Conjecture proved. antispam@fricas.org (Waldek Hebisch) - 2026-01-28 15:17 +0000
                Re: Collatz Conjecture proved. David Brown <david.brown@hesbynett.no> - 2026-01-27 18:44 +0100
                Re: Collatz Conjecture proved. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-01-27 22:52 +0000
                Re: Collatz Conjecture proved. David Brown <david.brown@hesbynett.no> - 2026-01-28 08:29 +0100
                Re: Collatz Conjecture proved. Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-01-28 10:27 +0100
                Re: Collatz Conjecture proved. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-28 12:59 -0800
                Re: Collatz Conjecture proved. Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-01-30 06:33 +0100
                Re: Collatz Conjecture proved. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-30 11:59 -0800
                Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-28 04:08 +0800
                Re: Collatz Conjecture proved. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-01-27 15:11 -0800
                Re: Collatz Conjecture proved. Ben Bacarisse <ben@bsb.me.uk> - 2026-01-28 17:34 +0000
                Re: Collatz Conjecture proved. richard@cogsci.ed.ac.uk (Richard Tobin) - 2026-01-28 18:23 +0000
                Re: Collatz Conjecture proved. David Brown <david.brown@hesbynett.no> - 2026-01-29 08:39 +0100
                Re: Collatz Conjecture proved. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-28 13:02 -0800
                Re: Collatz Conjecture proved. James Kuyper <jameskuyper@alumni.caltech.edu> - 2026-01-26 21:18 -0500
                Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-28 04:01 +0800
            Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-30 08:29 +0800
        Re: Collatz Conjecture proved. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-01-27 19:46 -0800
          Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-28 12:34 +0800
            Re: Collatz Conjecture proved. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-02-03 04:16 -0800
          Re: Collatz Conjecture proved. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-28 13:04 -0800
    Re: Collatz Conjecture proved. Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-01-29 16:50 +0000
      Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-30 05:40 +0800
        Re: Collatz Conjecture proved. Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-01-30 02:20 +0000
          Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-30 11:03 +0800
            Re: Collatz Conjecture proved. Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-01-30 04:22 +0000
            Re: Collatz Conjecture proved. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-01-29 20:38 -0800
              Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-31 05:30 +0800
                Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-02-06 14:16 +0800
          Re: Collatz Conjecture proved. wij <wyniijj5@gmail.com> - 2026-01-30 11:52 +0800
  Re: Collatz Conjecture proved. Jan van den Broek <fortytwo@xs4all.nl> - 2026-01-31 14:11 +0100
    Re: Collatz Conjecture proved. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-02-03 03:58 -0800
      Re: Collatz Conjecture proved. Jan van den Broek <balglaas@dds.nl> - 2026-02-03 21:27 +0000

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