Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.theory > #104056

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

Show all headers | View raw

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.

-- 
Ben.

Back to comp.theory | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

Thread

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

csiph-web