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NNTP-Posting-Date: Tue, 15 Oct 2024 18:29:08 +0000
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Tue, 15 Oct 2024 11:29:25 -0700
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On 10/15/2024 08:51 AM, joes wrote:
> Am Mon, 14 Oct 2024 18:37:31 +0200 schrieb WM:
>> On 14.10.2024 18:04, joes wrote:
>>> 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 which reaches
>>>>> to "before" w.
>>>> 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, ..., w, w+2, w+4, ..., w*2
>> Either the doubled numbers are natural, then half of them have not been
>> among the original set, or all natural numbers have been doubled, then
>> the result contains infinite numbers.
> Which "half"?
>
>> That doubling _all_ natural numbers only yields _all_ natural numbers is
>> impossible.
> Of course. But all doubled naturals are themselves natural.
>

Aliquot parts, i.e. density where the "half of the integers are even",
and the equivalency of the countably infinite, where "integers are
1-1 squares" were around centuries and THOUSANDS of years before
Grosseteste and Galileo, and are such OLD HAT that this "old wrapped
as new" is long, long, long past its freshness dating.