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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: how
Date: Fri, 19 Apr 2024 21:31:51 -0700
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On 4/19/2024 1:57 PM, Tom Bola wrote:
> 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.

Yikes!