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Re: Real Number --- Merely numbers whose digits can be infinitely long

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wij <wyniijj5@gmail.com> writes:
> On Wed, 2024-05-01 at 18:38 -0700, Keith Thompson wrote:
>> wij <wyniijj5@gmail.com> writes:
>> > On Wed, 2024-05-01 at 22:58 +0100, Ben Bacarisse wrote:
>> > > wij <wyniijj5@gmail.com> writes:
>> [...]
>> > > >      <fixed_point_number>::= [-] <wnum> [ . <frac> ]  // excluding "-0" case
>> > > >      <wnum>::= 0
>> > > >      <wnum>::= <nzd> { 0 | <nzd> }
>> > > >      <frac>::= { 0 | <nzd> } <nzd>
>> > > >      <nzd> ::= 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 // 'digit' varys depending on n-ary
>> > > > 
>> > > >     Ex: 78, -12.345, 3.1414159
>> > > 
>> > > So what's the point of defining these strings that represent a subset of
>> > > the rationals?
>> > 
>> > <fixed_point_number> is a super set of rationals.
>> [...]
>> 
>> An extraordinary claim.
>> 
>> Do you agree that 1/3 is a rational number?  How is 1/3 represented in
>> your <fixed_point_number> notation?
>> 
>
> I already told you: 1/3= 0.1 (3-ary <fixed_point_number>)
> Substitute the n in n-ary with the q in p/q, every p/q is representable 
> by <fixed_point_number>.
> And, the rule of <frac> can generate infinitely long fractions, read it carefully!

That kind of notation almost universally refers to *finite* sequences of
symbols.

If you intend it to be able to specify infinite sequences, that's fine,
but it's not inherent in the notation you've presented.  I also wonder
how an infinitely long <frac> can have <nzx> as its last element.

So <frac> can be infinitely long.  Can <wnum> be infinitely long?

I presume that the "n-ary" base can be any integer greater than or equal
to 2, and that the digits can range from 0 to n-1.  That means you'll
need arbitrarily many distinct symbols for the digits in large bases.
That's all fine, but it would be good to state all this explicitly.

There are already perfectly good mathematical methods for constructing
the integers, the rationals, and the reals.  Your method of using base-n
notation to *define* the reals and/or rationals seems superfluous.  It
can probably be done consistently, but I fail to see how it's useful.

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Medtronic
void Void(void) { Void(); } /* The recursive call of the void */

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Real Number --- Merely numbers whose digits can be infinitely long wij <wyniijj5@gmail.com> - 2024-04-29 04:42 +0800
  Re: Real Number --- Merely numbers whose digits can be infinitely long Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-04-29 11:57 +0100
    Re: Real Number --- Merely numbers whose digits can be infinitely long Andy Walker <anw@cuboid.co.uk> - 2024-04-29 13:35 +0100
    Re: Real Number --- Merely numbers whose digits can be infinitely long wij <wyniijj5@gmail.com> - 2024-04-30 11:03 +0800
      Re: Real Number --- Merely numbers whose digits can be infinitely long Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-04-29 22:02 -0700
      Re: Real Number --- Merely numbers whose digits can be infinitely long Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-05-01 22:58 +0100
        Re: Real Number --- Merely numbers whose digits can be infinitely long wij <wyniijj5@gmail.com> - 2024-05-02 09:33 +0800
          Re: Real Number --- Merely numbers whose digits can be infinitely long Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-05-01 18:38 -0700
            Re: Real Number --- Merely numbers whose digits can be infinitely long wij <wyniijj5@gmail.com> - 2024-05-02 10:03 +0800
              Re: Real Number --- Merely numbers whose digits can be infinitely long Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-05-01 20:38 -0700
                Re: Real Number --- Merely numbers whose digits can be infinitely long Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-05-01 20:46 -0700
                Re: Real Number --- Merely numbers whose digits can be infinitely long Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-01 21:52 -0700
                Re: Real Number --- Merely numbers whose digits can be infinitely long Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-01 22:40 -0700
                Re: Real Number --- Merely numbers whose digits can be infinitely long Andy Walker <anw@cuboid.co.uk> - 2024-05-02 09:36 +0100
                Re: Real Number --- Merely numbers whose digits can be infinitely long Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-02 13:22 -0700
                Re: Real Number --- Merely numbers whose digits can be infinitely long wij <wyniijj5@gmail.com> - 2024-05-02 12:46 +0800
                Re: Real Number --- Merely numbers whose digits can be infinitely long Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-05-02 13:51 -0700
                Re: Real Number --- Merely numbers whose digits can be infinitely long wij <wyniijj5@gmail.com> - 2024-05-03 08:43 +0800
                Re: Real Number --- Merely numbers whose digits can be infinitely long Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-05-02 18:02 -0700
                Re: Real Number --- Merely numbers whose digits can be infinitely long wij <wyniijj5@gmail.com> - 2024-05-03 09:44 +0800
                Re: Real Number --- Merely numbers whose digits can be infinitely long Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-05-02 19:58 -0700
                Re: Real Number --- Merely numbers whose digits can be infinitely long Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-02 20:23 -0700
                Re: Real Number --- Merely numbers whose digits can be infinitely long Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-04 10:36 -0700
          Re: Real Number --- Merely numbers whose digits can be infinitely long Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-05-02 23:03 +0100
            Re: Real Number --- Merely numbers whose digits can be infinitely long wij <wyniijj5@gmail.com> - 2024-05-03 08:41 +0800
              Re: Real Number --- Merely numbers whose digits can be infinitely long Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-05-04 00:02 +0100
                Re: Real Number --- Merely numbers whose digits can be infinitely long wij <wyniijj5@gmail.com> - 2024-05-04 08:28 +0800
                Re: Real Number --- Merely numbers whose digits can be infinitely long Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-05-05 10:14 +0100

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