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From: Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups: comp.theory
Subject: Re: Real Number --- Merely numbers whose digits can be infinitely long
Date: Sun, 05 May 2024 10:14:39 +0100
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wij <wyniijj5@gmail.com> writes:

> On Sat, 2024-05-04 at 00:02 +0100, Ben Bacarisse wrote:
>> 3.1414159
>
> 3.1414159... (infinitely long)

That's not a string produced by your grammar for <fixed_point_number>.
(Also, your quoting and attributions are incorrect.)

You've cut all the context, presumably because you don't want people to
see the question you can't answer.  Here's the context with the question
you are not able to answer restored:

You: <fixed_point_number> is a super set of rationals.

Me: Give an example <fixed_point_number> that is not rational.

Me again (because you didn't answer): Can you give an example
<fixed_point_number> that is not rational?  If not, why not?

Your eventual reply is not a string produced by your grammar.  Here is
the grammar again since you cut it from your reply.

  <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

"3.1414159" is a string produced by this grammar (but, anyway, it's
rational).  None of the other characters ("... (infinitely long)") can
form part of a <fixed_point_number>.

-- 
Ben.