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

On Thu, 2024-05-02 at 23:03 +0100, Ben Bacarisse wrote:

wij <wyniijj5@gmail.com> writes:
 

On Wed, 2024-05-01 at 22:58 +0100, Ben Bacarisse wrote:

wij <wyniijj5@gmail.com> writes:
 

Got your idea.

 
It's not my idea.  It's a standard notation.
 

 
There is no standard notation for formal grammar. I adopt the idea using either
',' or '|'. <fixed_point_number> is simple, average readers know what it should be.
 
 

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

 
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.

 
Give an example <fixed_point_number> that is not rational.
 
If you can it should be one of the examples you give since you are
obviously using the EBNF notation is a new, non-standard way.  Giving
three examples that at conventional rational numbers is a huge missed
opportunity to show what you really mean.
 

If you don't like it, you can read it as anything.
Read it as a joke and keep believing 0.333...∉ [0,1/3) and
 1/3 ≠ 0.333... + nonzero_remainder

I mean strongly hold that believe, don't change in your life-time.