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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sat, 14 Sep 2024 18:24:21 +0200
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On 13.09.2024 23:13, Jim Burns wrote:
> On 9/13/2024 1:20 PM, WM wrote:

>> Fact is that the real axis is nothing but its points.
> 
> Yes.
> ℝ[ℚ[ℤ[ℕ[⟨0,…,n⟩]]]] holds
> points.between ratios of countable.to numbers.

>> There is no gap.
> 
> Yes.
>
>> Every point has a next point but
>> next to defined points are dark points.
> 
> No.
> Next.to.defined points are not.in ℝ[ℚ[ℤ[ℕ[⟨0,…,n⟩]]]]

Not in what you know about these sets, but existing, because:
WM: There is no gap.
JB: Yes
> 
>> Next to every defined points there are ℵo dark points.
>> This configuration cannot be changed.
> 
> Whatever it is you are talking about,
> we are talking about ℝ[ℚ[ℤ[ℕ[⟨0,…,n⟩]]]]

That's not enough.

Regards, WM