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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: 2N=E
Date: Fri, 1 Nov 2024 20:55:21 -0400
Organization: i2pn2 (i2pn.org)
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On 11/1/24 6:28 AM, WM wrote:
> On 01.11.2024 00:44, Richard Damon wrote:
>> On 10/31/24 1:36 PM, WM wrote:
>>> On 31.10.2024 12:36, Richard Damon wrote:
>>>> On 10/30/24 3:52 PM, WM wrote:
>>>
>>>>> Do all numbers between 0 and ω exist such that they can be doubled?
>>>
>>>> All Natural Numbers can be doubled and get a number that is in that 
>>>> set.
>>>
>>> But some of them were not doubled.
> 
>> Nope, they all were.
> 
> If numbers are doubled, then greater numbers are produced.
> That is simple mathematics. There is no doubt about it.
> If all natural numbers are doubled, then not only natural numbers are 
> produced.

No;e, becuase those greater numbers were already there.

> 
>> Which one wasn't?
> 
> Natural numbers greater than ω/2.
> Note that in actual infinity all natural numbers including ω-1 are 
> existing.

ω/2 isn't a number, as ω is DEFINED as the beginning of a new category 
of ordinals, that follows a SET of numbers (not any number in 
particular), thus, you can not "back down" from ω by any means.

> 
> Regards, WM
> 
> 
>