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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 12:50:23 -0700
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On 10/20/2024 11:51 AM, Chris M. Thomasson wrote:
> On 10/20/2024 12:48 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.
> 
> Sigh.

{ 1, 2, 3, 4, 5, 6, ... }

{ 1*2, 2*2, 3*2, ... }

All the doubled numbers are already in the set of naturals:

{ 2, 4, 6, ... }

{ 1, (2), 3, (4), 5, (6), ... }

See?




> 
> 
>> Either more finites appear, or the results are infinite.
>>>
>>> No k exists such that
>>> 2⋅k is a finite and 2⋅k+2 > 2⋅k is not a finite.
>>
>> All doubled numbers result in larger numbers. That cannot be avoided.
>>
>> Regards, WM
>