Re: Does the number of nines increase?

Liste des GroupesRevenir à s math 
Sujet : Re: Does the number of nines increase?
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.math
Date : 04. Jul 2024, 16:08:24
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v66dt9$2pshb$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12
User-Agent : Mozilla Thunderbird
Am 04.07.2024 um 16:30 schrieb Moebius:
Am 04.07.2024 um 15:59 schrieb WM:
Le 04/07/2024 à 15:49, Moebius a écrit :
Am 04.07.2024 um 15:19 schrieb WM:
Le 03/07/2024 à 23:58, Moebius a écrit :
>
Why do you adhere to the [...] idea that every x > 0 is larger than [the sum of] ℵo finite distances?
>
Because it is true?
>
<bla bla bla> Useless to discuss with you further.
 Da gibt's auch nicht zu "diskutieren", Mückenheim.
 Hinweis: Für jedes x e IR mit x > 0 gibt es (abzählbar) unendlich viele Stammbrüche s, so dass s < x ist. Die Summe der (abzählbar) unendlich vielen Abstände zwischen diesen Stammbrüchen ist dann natürlich < x.
Andere Möglichkeit: Man betrachtet einfach die (abzählbar) unendlich vielen Intervalle [x/4, x/2], [x/8, x/4], [x/16, x/8], ... Die (abzählbar) unendlich vielen "finite distances" d_1 = x/2 - x/4, d_2 = x/4 - x/8, usw. summieren sich dann genau zu x/2 auf: SUM_(n=1..oo) d_n = x/2. Und x/2 ist bekanntlich kleiner als x (für x e IR, x > 0).

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