Re: How many different unit fractions are lessorequal than all unit fractions?

On 09.09.2024 21:05, Jim Burns wrote:

On 9/9/2024 6:39 AM, WM wrote:

ℵo unit fractions cannot exist without
1, 2, 3, ... unit fractions before.

 Each unit.fraction has 1,2,3,... unit.fraction before.
 It is incorrect (it is a quantifier shift)
to conclude from that correct claim
that
🛇 there are 1,2,3,... unit.fractions before each

It is a property of real points on the positive real line, that every sequence has a beginning. What alternative configuration can the points have in your opinion.
This is the first question:
Do ℵo unit fractions exist smaller than any x > 0,
as Fritsche claims?
The second question concerns a weaker claim:
Do ℵo unit fractions exist smaller than any 1/n > 0?
If you deny the second you cannot approve the first question.
Regards, WM
Regards, WM