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

Le 18/07/2024 à 23:42, Jim Burns a écrit :

On 7/18/2024 4:55 PM, WM wrote:

But if
for all points x > 0
there are ℵo smaller unit fractions,
then
for the interval (0, oo)
there are ℵo smaller unit fractions.

 No.

Like Bob. No reason to continue.

For each point x > 0
there are
step.down non.⅟⌈⅟x⌉.step.up well.ordered.by.>
unit.fractions in (0,x] which,
because
step.down non.⅟⌈⅟x⌉.step.up well.ordered.by.>
are ℵ₀.many.

Of all unit fractions left of any x > 0, ℵ₀ are the same, finitely many are different.

 No unit fractions are smaller than (0,∞)

Right. That means Fritsches x are not all x.

 

Or is there a point in (0, oo) which
is not an x > 0?

 No, but
there is no point x in (0,∞) such that

irrelevant. All x > 0 are there and nothing else.
Regards, WM