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From: Tom Bola <Tom@bolamail.etc>
Newsgroups: sci.math
Subject: Re: how
Date: Fri, 12 Apr 2024 16:38:20 +0200
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WM schrieb:

> Le 12/04/2024 à 15:56, Tom Bola a écrit :
>> WM schrieb:
> 
>>> 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, ...,} 
> 
> No, all elements emergeing from doubling have larger distances than 1.
>> 
>>> 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
> 
> N*2 is a set having elements but not including w*2. So there is a 
> distance.

This is wrong because there is a distance to any element of that set. 
But you probably are meaning the distance between the set limit of IN which 
is w and w*2 which I wrote down above already: {w+1, w+2, w+3, ...,}.