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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: 2N=E
Date: Thu, 31 Oct 2024 07:36:48 -0400
Organization: i2pn2 (i2pn.org)
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On 10/30/24 3:52 PM, WM wrote:
> On 30.10.2024 17:52, Jim Burns wrote:
>> On 10/30/2024 11:27 AM, WM wrote:
> 
>>> If infinity is complete,
>>> the we can double all natural numbers with the result
>>> (0, ω)*2 = (0, ω*2).
>>> Then some products are in the interval (ω, ω*2).
>>
>> ω is infinite.
> 
> Do all numbers between 0 and ω exist such that they can be doubled?
> 
> Regards, WM
> 

Between as in exclusive, YES, as that is just the set of the Natural 
Numbers (since that is the domain that defines omega).

All Natural Numbers can be doubled and get a number that is in that set.

If you include omega, then no, omega doubled is two omega, but the rest 
of the set doubles and stays in the set.