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

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!