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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Sun, 20 Oct 2024 17:00:54 -0400
Organization: Peripheral Visions
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References: <vb4rde$22fb4$2@solani.org>   <b0fa9a1c-8375-4523-a15e-65789688660e@tha.de> <3f63bc22-83b2-4d56-9837-849551170c77@att.net> <50ac7044-f8c1-47d9-947f-9fa6044e1848@tha.de> <68b8be64-7fe8-47e7-a991-7adf14713af5@att.net> <vejmkm$e069$1@solani.org> <eb21591a-a60a-4baf-bdbd-afef2a69c230@att.net> <vejte9$e3ds$1@solani.org> <53460f91-4542-4a92-bc4b-833c2ad61e52@att.net> <ventec$255vi$2@dont-email.me> <venunr$2533b$4@dont-email.me> <29ce40e9-f18a-44d4-84d9-23e587cf9dea@att.net> <veor6u$2asus$1@dont-email.me> <2b6f9104-a927-49ee-9cf0-6ee3f82edc23@att.net> <verkkk$2r6kk$1@dont-email.me> <22f95ff7-c361-4d8a-943c-1df76abb98cc@att.net> <vevpsl$3pi3s$2@dont-email.me> <ed1862ff-3679-4175-bb25-c317be9713b2@att.net> <vf0t7i$3v3cv$5@dont-email.me> <9c55eda1-bb24-44ae-9158-2a3b354170cd@att.net> <vf2ck9$amc3$1@dont-email.me> <4ce512c0-8196-4923-9a6b-359c25fdfa3a@att.net> <vf3ldc$hgts$2@dont-email.me> <8418a2e3-bba2-43b4-8c77-3e947a270476@att.net> <vf3n5v$i1ai$2@dont-email.me>
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WM formulated the question :
> On 20.10.2024 21:42, Jim Burns wrote:
>> On 10/20/2024 3:24 PM, WM wrote:
>>> On 20.10.2024 20:20, Jim Burns wrote:
>>>> On 10/20/2024 3:48 AM, WM wrote:
>>>>> On 20.10.2024 00:54, Jim Burns wrote:
>>>>>> On 10/19/2024 2:19 PM, WM wrote:
>> 
>>>>>> A doubled finite is finite.
>>>>>
>>>>> If all finites are doubled,
>>>>> then not all results can be in that set.
>>>>
>>>> If all finites are doubled,
>>>> then all results are in the set of finites.
>>>
>>> But not in the mapped or multiplied range.
>> 
>> If n is countable.to from 0
>> then ⟨0,1,...,n-1,n⟩ exists
>> 
>> If ⟨0,1,...,n-1,n⟩ exists
>> then ⟨n,n+1,...,2⋅n-1,2⋅n⟩ exists
>> 
>> If ⟨0,1,...,n-1,n⟩ and ⟨n,n+1,...,2⋅n-1,2⋅n⟩ exist
>> then ⟨0,1,...,n-1,n,n+1,...,2⋅n-1,2⋅n⟩ exists
>> 
>> If ⟨0,1,...,n-1,n,n+1,...,2⋅n-1,2⋅n⟩ exists
>> then 2⋅n is countable.to from 0
>> 
>> ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
>> If n is countable.to from 0
>> then 2⋅n is countable.to from 0
>> 
>>>> If all finites are doubled,
>>>> then all results are in the set of finites.
>>>
>>> But not in the mapped or multiplied range.
>> 
>> If n is countable.to from 0
>> then 2⋅n is countable.to from 0
>
> Nevertheless 2n is not in the set {1, ..., n}.

Neither is n+1, what's your point?