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

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On Mon, 2024-04-29 at 11:57 +0100, Ben Bacarisse wrote:
> wij <wyniijj5@gmail.com> writes:
> 
> > The purpose this text is for establishing the bases for computational algorithm.
> > This file https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber-en.txt/download
> > may be updated anytime.
> > 
> > +-------------+
> > > Real Number | ('computational' may be added to modify terms used in this file
> > +-------------+   if needed)
> > 
> > n-ary Fixed-Point Number::= Number represented by a string of digits, the
> >    string may contain a minus sign or a point:
> > 
> >      <fixed_point_number>::= [-] <wnum> [ . <frac> ]
> >      <wnum>::= 0 | <nzd> { 0, <nzd> }
> 
> Some readers will be confused by this.  When {}s are used for "zero or
> more repetitions" what goes inside is the same kind of thing that goes
> on the RHS of ::= and there (in production rules) you use | for
> alternation.  Hence
> 
>   <wnum> ::= 0 | { 0 | <nzd> }
> 
> would be clearer.  Of course, if you want "," to denote alternation, you
> could write
> 
>   <wnum> ::= 0, { 0, <nzd> }
> 
> instead.  It's the mixing up of the notation that's pointless and
> potentially confusing.
> 
> >      <frac>::= { 0, <nzd> } <nzd>
> >      <nzd> ::= (1, 2, 3, 4, 5, 6, 7, 8, 9)  // 'digit' varys depending on n-ary
> 
> Since you already have a notation for alternatives, it would be clearer
> to write
> 
>   <nzd> ::= 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
> 
> otherwise, you need to say what that the brackets with commas mean.
> 
> >      Ex: 78, -12.345, 3.1414159...(π)
> 
> The third example does not match the grammar.  Also, I would guess you
> intended to use the digits of pi.
> 
> >    Addition/subtraction of n-ary fixed-point numbers are the same as what is 
> >    taught in elementary schools (or on abacus). Any two n-ary fixed-point 
> >    number (same n-ary) a,b are equal iff their <fixed_point_number> 
> >    representation are identical. Otherwise, a>b or a<b, exactly one of these
> >    two holds (Law of trichotomy).
> 
> So which of -0>0 and -0<0 holds?  I'll take what you write about limits
> with a pinch of salt until the basics are clear.
> 

Got your idea. I'll try use '|' exclusively. Thanks for the suggestions:

     <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

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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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