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Subject: Re: how
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Date: Thu, 25 Apr 24 20:20:19 +0000
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From: WM <wolfgang.mueckenheim@tha.de>
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Le 25/04/2024 à 01:13, Richard Damon a écrit :
> On 4/24/24 1:16 PM, WM wrote:
>> Le 24/04/2024 à 04:01, Richard Damon a écrit :
>>> On 4/23/24 3:34 PM, WM wrote:
>>>> 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].
>>>> If [0, ω) --> [0, ω) and ω*2 --> ω*2, then ω*2 is the only image 
>>>> point in (ω, ω*2]. Infinitely many points remain empty. Crippled 
>>>> mathematics. Ugly. Inacceptable.
>> 
>>> Why?
>> 
>> Continuity.
> 
> Who says we have that sort of "Continuity"?

I.

If the preimage has intervals of 1, then the image has intervals of 2.

ω+n is existing. How is it approached if not from the finite domain?

Regards, WM