Re: There is a first/smallest integer (in Mückenland)

On 7/18/2024 2:28 PM, WM wrote:

Le 18/07/2024 à 19:00, Jim Burns a écrit :

Jumps "at" a point are between
 nearby points.
WM admitted that much in a recent post,
but changed what "change" means to him.

>
A claim for all x > 0 is
a claim for all points of the interval (0, oo).
The claim
"between 0 and every point of (0, oo) NUF(x) = ℵo"
implies the existence of
ℵo unit fractions between 0 and (0, oo)
and is false.

The unit.fractions between 0 and different points x
are not the same unit.fractions.
For each x > 0
the unit fractions in (0,x] are
step.down non.max.step.up well.ordered.by.>
That order is the same type as ℕ
step.up non.min.step.down well.ordered.by.<
Anything with the order.type of ℕ holds ℵ₀.many.
For each x > 0
max.(⅟ℕ∩(0,x]) = ⅟⌈⅟x⌉
The sets ⅟ℕ∩(0,x] are different.
The order.type of each ⅟ℕ∩(0,x] is the same.
step.down non.⅟⌈⅟x⌉.step.up well.ordered.by.>
Each ⅟ℕ∩(0,x] holds ℵ₀.many.
Infinite does not mean humongous.