Sujet : Re: There is a first/smallest integer (in Mückenland)
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.mathDate : 17. Jul 2024, 15:56:08
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v78m28$1sk3g$1@dont-email.me>
References : 1 2
User-Agent : Mozilla Thunderbird
Am 17.07.2024 um 16:43 schrieb WM:
Le 17/07/2024 à 13:37, Moebius a écrit :
WM> All unit fractions are separated. Therefore there is a first one
>
Moebius> All integers are separated. Therefore there is a first one [?]
>
WM> This is true but difficult to understand.
Can you explain how NUF(x) can [jump] from 0 [at x = 0] to [aleph_0] [at any] point x [> 0] although all unit fractions are separated by finite distances [...]
Yes, of course: For each and every x e IR, x > 0 there are countably-infinitely many unit fractions which are <= x. (Hint: No first one.)
Not that hard, is it?
Relevance concerning your nonsensical claim "This is true but difficult to understand"? - None.
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