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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: how
Date: Fri, 19 Apr 2024 13:06:13 -0700
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On 4/19/2024 8:20 AM, WM wrote:
> Le 19/04/2024 à 00:35, Richard Damon a écrit :
>> On 4/18/24 11:05 AM, WM wrote:
>>> ω is amidst the interval (0, ω2) because in the image there are as 
>>> many ordinals in (ω, ω2) as in (0, ω).
>>
>> But all those ordinals are transfinite ordinals, and none are the 
>> value of double a finite Natural Number.
> 
> You are in error. Counting goes like this: 1, 2, 3, ..., ω, ω+1, ω+2, .. 
> You simply pass ω although no known natural number k+1 will reach ω. But 
> by multiplication, which goes faster, you cannot pass ω?

Huh?

any_natural_number * 2 = another_natural_number

These natural numbers are already in the set of all natural numbers.