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Subject: Re: how
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Date: Fri, 12 Apr 24 16:40:33 +0000
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From: WM <wolfgang.mueckenheim@tha.de>
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Le 12/04/2024 à 17:51, Tom Bola a écrit :
> 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

I wanted the image of 1, 2, 3, ..., ω under multiplication by 2.
> 
> The image of IN under f(n)=2n and w is still {0, 2, 4, 6, ..., w*2}

Yes, but where is ω in this sequence?

Regards, WM