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From: WM <wolfgang.mueckenheim@tha.de>
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Le 23/04/2024 à 22:03, Tom Bola a écrit :
> WM schrieb:
> 
>> Le 23/04/2024 à 21:45, Tom Bola a écrit :
>>> WM schrieb:
>>> 
>>>> Le 23/04/2024 à 01:01, Richard Damon a écrit :
>>>>> On 4/22/24 10:15 AM, WM wrote:
>>>> 
>>>>>> The results cannot be compressed to the interval (0, ω) of the set { 1, 
>>>>>> 2, 3, ...}. This shows that new numbers are generated by multiplication.
>>>>>> 
>>>>> Of course they can be compressed into the interval (0, ω), as every 
>>>>> finite number n < ω, when doubled results in a finite number 2n which is 
>>>>> also < ω.
>>>> 
>>>> Try to map the closed interval [0, ω]*2 = [0, ω*2].
>>> 
>>> f = 
>>> (0, 0),
>>> (1, 2),
>>> (2, 4),
>>> (3, 6),
>>> (..., ...),
>>> (w, w*2)
>> 
>> Indeed. When n reaches ω, 2n reaches ω2.
> 
> I forgot the surrounding brackets {}... 
> 
> f = {
>  (0, 0),
>  (1, 2),
>  (2, 4),
>  (3, 6),
>  (..., ...),
>  (w, w*2) }
> 
> If you want something else *you* are (the one) to define it. 

What is between ω and ω*2?

Regards, WM