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From: Tom Bola <Tom@bolamail.etc>
Newsgroups: sci.math
Subject: Re: how
Date: Fri, 12 Apr 2024 17:51:31 +0200
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WM schrieb:

> Le 12/04/2024 à 17:00, Tom Bola a écrit :
>> WM schrieb:
>> 
>>> Le 12/04/2024 à 16:40, Tom Bola a écrit :
>>>> 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 
>>> 
>>> I am meaning the distance between N*2 and ω*2 after multiplication. 
>> 
>> Yes, that is the set after multiplication: 
>> {0, 2, 4, 6, ..., w, w+1, w+2, w+3, ..., w*2} 
> 
> Why are the distances below ω 2 but beyond ω 1?

This is the union of the image from IN under f(n)=2n and 
the "elements fall between ω and ω*2" that you wanted above
WM = {0, 2, 4, 6, ...} u {w, w+1, w+2, w+3, ..., w*2}

The image of IN under f(n)=2n and w is still {0, 2, 4, 6, ..., w*2}