Sujet : Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.mathDate : 02. Nov 2024, 14:03:16
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vg57ul$3pvqd$1@dont-email.me>
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Am 02.11.2024 um 13:30 schrieb joes:
Am Fri, 01 Nov 2024 11:07:27 +0100 schrieb WM:
On 31.10.2024 21:46, joes wrote:
>
At single points a function has a single value, not a jump.
It jumps in case of NUF by 1 at a unit fraction with respect to the
foregoing unit fraction and the many points between both.
Whether you define your pathological function with < or <=, at every
point it has one value (note it doesn't have the SAME value at every
point [...]).
In the case of NUF, [we have:]
NUF(x) = 0 for x = 0 and
NUF(x) = aleph_0 for all x e IR, x > 0.
Instead of NUF we might consider the function
NNN(x) = card {n e IN: n > x} (x e IR*)
"number of natural numbers larger than x"
defined on the extended reals (R* = IR u {-oo, oo}).
THERE we would have:
NNN(x) = 0 for x = oo.
NNN(x) = aleph_0 for all x e IR*, x < oo.
Math is too hard for Mückenheim.