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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Fri, 25 Oct 2024 11:50:49 -0700
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On 10/25/2024 9:57 AM, WM wrote:
> On 25.10.2024 16:53, Jim Burns wrote:
>> On 10/25/2024 7:42 AM, WM wrote:
> 
>>> The whole interval (0, ω) is not finite,
>>> let alone the doubled interval.
>>
>> ⟦0,ω⦆ is the set of finite ordinals.
>> That is the definition of finite ordinal.
>> That is the definition of ω,
>> the first ordinal after all finite ordinals.
> 
> Correct so far.
>>
>> γ before ω: γ is finite.
>> γ ∈ ⟦0,ω⦆ ⇒
>> ∀β ∈ ⦅0,γ⟧: ∃α: α+1=β
>>
>> ω before ξ: ξ is not finite.
>> ω ∈ ⦅0,ξ⟧ ⇒
>> ¬∀β ∈ ⦅0,ξ⟧: ∃α: α+1=β
>>
>> (Keep in mind that ¬∃α: α+1=ω )
> 
> That is wrong in complete infinity.

All the natural numbers, does NOT imply that there is a, largest one...!

Damn it.