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Date: Thu, 25 Apr 24 20:03:50 +0000
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From: WM <wolfgang.mueckenheim@tha.de>
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Le 24/04/2024 à 21:42, Jim Burns a écrit :
> On 4/24/2024 12:57 PM, WM wrote:
>> Le 23/04/2024 à 21:55, Jim Burns a écrit :
>
>>> Arithmetic of the familiar.
>>
>> Nevertheless it is wrong because
>> for every set {1, 2, 3, ..., n}
>> doubling extends the set.
>
> Doubling doesn't extend it to or beyond ω
If all smaller numbers are doubled, then there is no place for the doubled
numbers below ω.
> The arithmetic of ω is not the familiar arithmetic.
The arithmetic of doubling produces other numbers than the doubled ones.
>
> It would also raise the question of
> who is responsible for putting you (WM)
> in front of a classroom of students.
Those are experts which a disappearing Bob cannot estimate.
Look, here you can find the fourth edition of a known best seller with
thousands of sold copies: W. Mückenheim: "Mathematik für die ersten
Semester", A4, DeGruyter, Berlin 2015. ISBN 978-3-11-037733-0.
And here you can find the seventh edition of another book of mine with
almost 1000 sold copies: W. Mückenheim: "Die Geschichte des Unendlichen",
A7, Maro-Verlag, Augsburg 2011. ISBN: 978-3-87512-156-8
Regards, WM