Re: how

Am 22.04.2024 um 16:37 schrieb Moebius:

Am 22.04.2024 um 16:25 schrieb WM:

Le 20/04/2024 à 20:49, Richard Damon a écrit :

On 4/20/24 2:40 PM, WM wrote:

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Of course you can double all the elements, they just double into a subset of themselves.

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Impossible.
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But True.
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It may seem impossible to you,

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The original set is in (0, ω). The doubled set

 is in (0, ω) too (since it is in the original set).
 Hint: {2*n : n e IN} c IN.
 Alle geraden (natürlichen) Zahlen sind natürliche Zahlen. Erzählst Du Deinen Studenten an der THA etwas anderes?
 Proof: Let k in {2*n : n e IN}. Then there is an n in IN such that k = 2*n. Since IN is closed unter multiplication and 2 is in IN too, 2*n in IN and hence k in IN. Hence {2*n : n e IN} c IN. qed
 See: https://www.cuemath.com/questions/which-of-the-following-sets-are-closed-under-multiplication-select-all-that-apply/

Hint: "Es ist nicht möglich, zwei natürliche Zahlen zu addieren oder zu multiplizieren und dabei eine "nicht-natürliche" Zahl zu erhalten."
Quelle: https://3.vobs.at/maturawiki/index.php/Zahlenmengen