Re: how

Liste des GroupesRevenir à s math 
Sujet : Re: how
De : moebius (at) *nospam* example.invalid (Moebius)
Groupes : sci.math
Date : 22. Apr 2024, 15:37:53
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v05so1$10fk3$2@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11
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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:
 
Of course you can double all the elements, they just double into a subset of themselves.
>
Impossible.
>
But True.
>
It may seem impossible to you,
 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/

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