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From: Tom Bola <Tom@bolamail.etc>
Newsgroups: sci.math
Subject: Re: how
Date: Fri, 19 Apr 2024 22:57:07 +0200
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Chris M. Thomasson schrieb:

> On 4/19/2024 8:37 AM, WM wrote:
>> Le 19/04/2024 à 00:42, Richard Damon a écrit :
>>> On 4/18/24 10:59 AM, WM wrote:
>> 
>>>>
>>>> ω follows upon all natural numbers. There is nothing between them and ω.
>> 
>>> Right, and any Natural Number * 2 is a Natural Number, so less than ω.
>> 
>> If all elements of the set {1, 2, 3, ...} are doubled and nevertheless 
>> remain below ω, then you have created new natural numbers which have not 
>> been doubled. Hence you have not doubled all natural numbers. But that 
>> is what has to be done and, according to actual infinity, can be done.
>>>
>>> Your logic can't handle the fact that the set of Natural  Numbers is 
>>> unbounded on the high side, so it doesn't understand that.
>> 
>> Your logic can't double all natural numbers such that none below ω is 
>> missing. You create always new natural numbers. They have  not been 
>> doubled.
> 
> Multiplying any natural number by two gives a natural number that is 
> already in the set of all natural numbers.

WM knows that definition but he doesn't ACCEPT it in his own math 
since 30++ years (which he doesn't mention this difference) because 
he feels that the used logic in today's mathematics is very wrong.