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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: 2N=E
Date: Fri, 1 Nov 2024 18:08:45 +0100
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On 01.11.2024 13:37, FromTheRafters wrote:
> WM laid this down on his screen :
>> On 01.11.2024 11:59, FromTheRafters wrote:
>>> WM used his keyboard to write :
>>>> On 31.10.2024 22:53, FromTheRafters wrote:
>>>>> WM pretended :
>>>>
>>>>>>> Our sets do not change.
>>>>>>
>>>>>> Then:
>>>>>> Multiplication of all infinitely many fractions of the open 
>>>>>> interval (0, 1) results in some fractions in (1, 2).
>>>>>> Multiplication of all infinitely many numbers of the open interval 
>>>>>> (0, ω) result in some numbers in (ω, ω*2).
>>>>>
>>>>> No, there are no finite numbers in the transfinites.
>>>>
>>>> Numbers like ω + 4 are in the infinite. But if all natural numbers 
>>>> are doubled, then numbers in the infinite are produced.
>>>
>>> What makes you think so?
>>
>> Simplest mathematics. Doubling increases the value. If all natnumbers 
>> are existing, then the greatest existing natnumber is existing too,
> 
> That is not the nature of the set of natural numbers. There is no last, 
> that is for finite sets only.

But there are all. No point can escape doubling.
> 
>> then doubling it does not produce a natural number.
> 
> Stemming from a bad assumption, any garbage can be claimed.

Yes, Cantor's theory is the best example.
> 
>> Actual infinity is not about variable sets!
> 
> Sets don't change!

Therefore not all doubled elements can be absorbed by the set.

Regards, WM