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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: Sun, 20 Oct 2024 19:04:20 -0700
Organization: A noiseless patient Spider
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On 10/14/2024 9:20 AM, Moebius wrote:
> Am 14.10.2024 um 18:15 schrieb Moebius:
>> Am 14.10.2024 um 18:04 schrieb joes:
>>> Am Mon, 14 Oct 2024 15:40:01 +0200 schrieb WM:
>>>> On 14.10.2024 14:15, joes wrote:
>>>>
>>>>> No, we are taking the complete, actually infinite set [of ordinal 
>>>>> numbers which lie] "before" ω.
>>
>>>> and fills the space between 0 and ω evenly. Same happens with the
>>>> doubled set between 0 and ω2.
>>
>>> No, there is no consequent infinity. The even numbers do not go
>>> 0, 2, 4, ..., ω, ω+2, ω+4, ..., ω*2
>>
>> Just let Mückenhirn know:
>>
>>      An e IN: n*2 < ω .
>>
>> Proof: An e IN: n*2 e IN (easy) and An e IN: n < ω. qed
> 
> Hint@Mückenhirn:
> 
>      0 < 1 < 2 < 3 < 4 < 5 < 6 < ... < ω ,
> 
> "hence":
> 
>      0 < 2 < 4 < 6 < ... < ω .
> 

With a view to a kill:

https://youtu.be/gkuUnnlAPZk