Sujet : Re: Replacement of Cardinality
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logic sci.mathDate : 13. Aug 2024, 15:21:57
Autres entêtes
Organisation : Nemoweb
Message-ID : <t_rVz7RU7M3aHZTB1TQJS59Ez0I@jntp>
References : 1 2 3 4 5 6 7 8 9 10
User-Agent : Nemo/0.999a
Le 12/08/2024 à 19:44, Jim Burns a écrit :
On 8/12/2024 9:50 AM, WM wrote:
Le 11/08/2024 à 19:56, Jim Burns a écrit :
What causes an exception: nₓ ∈ ℕ:
⅟nₓ > 0 without ⅟(nₓ+1) > 0 ?
>
The end of the positive axis.
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. The function NUF(x) is a step-function. It can increase from 0 at x = 0 to greater values, either in a step of size 1 or in a step of size more than 1. But increase by more than 1 is excluded by the gaps between unit fractions. (Note the universal quantifier there, according to which never – in no limit and in no accumulation point – two unit fractions occupy the same point x.) Therefore the step size can only be 1, resulting in a real coordinate x with NUF(x) = 1.
Regards, WM
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