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From: Tom Bola <Tom@bolamail.etc>
Newsgroups: sci.math
Subject: Re: how
Date: Fri, 12 Apr 2024 15:56:42 +0200
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WM schrieb:

> Le 11/04/2024 à 19:36, Jim Burns a écrit :
>> On 4/11/2024 8:07 AM, WM wrote:
> 
>>>> Which ones were unused by e = 2*n?
>>>
>>> Those of {1, 2, 3, ...} with less than ℵo successors.
>> 
>> {1,2,3,…} is
>> the least.upper.bound of all finiteⁿᵒᵗᐧᵂᴹ.{1,2,3,…,k}
> 
> Yes, but many natnumbers will never be used.
> 
>> For each m ∈ {1,2,3,…}:
>> ( for each k ∈ {1,2,3,…}
>> m+k is a successor of m in {1,2,3,…} )
> 
> Consider the set {1, 2, 3, ..., ω} and multiply every element by 2 with 
> the result {2, 4, 6, ..., ω*2}. What elements fall between ω and ω*2? 

{w+1, w+2, w+3, ...,} 

> What size has the interval between N*2 and ω*2? 

N*2 is not a number, so there is no interval between it and w*2