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

On 02.11.2024 20:52, Jim Burns wrote:

On 11/2/2024 1:50 PM, WM wrote:

On 02.11.2024 15:10, Jim Burns wrote:

On 11/1/2024 1:24 PM, WM wrote:

 

Hence
at least ℵ₀ points with
ℵ₀ intervals of uncountably many points
must be between 0 and x₀.

>

That cannot happen at x₀ = 0.

Each x₀ > 0 is an x₀ where it happens.

No. At least ℵ₀ points with ℵ₀ intervals of uncountably many points must be between 0 and x₀. This criterion is not satisfied by every point x > 0, but it is satisfied by every definable or visible point x > 0.
Why do you not see this requirement?
Regards, WM