Sujet : Re: Replacement of Cardinality
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.logic sci.mathDate : 13. Aug 2024, 18:32:17
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v9g5b2$3ukli$6@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12
User-Agent : Mozilla Thunderbird
Am 13.08.2024 um 19:02 schrieb Jim Burns:
On 8/13/2024 10:21 AM, WM wrote:
Le 12/08/2024 à 19:44, Jim Burns a écrit :
There is no ⅟nₓ before the end of the positive axis
without ⅟(nₓ+1) before the end of the positive axis.
>
You cannot see it. It is dark.
No number can be seen, dark or not.
resulting in a real coordinate x with NUF(x) = 1.
Assume NUF(x0) = 1 with x0 e IR. This means that there is exactly one unit fraction u such that u < x0. Let's call this unit fraction u0. Then (by definition) there is a (actually exactly one) natural number n such that u0 = 1/n. Let n0 e IN such that u0 = 1/n0. But then (again by definition) 1/(n0 + 1) is a unit fraction which is smaller than u0 and hence smaller than x0. Hence NUF(x0) > 1. Contradiction!
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