Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how

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