Re: how

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:

>

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ω follows upon all natural numbers. There is nothing between them and ω.

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Right, and any Natural Number * 2 is a Natural Number, so less than ω.

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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.