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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.
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