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

On 11/2/24 5:28 PM, WM wrote:

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
 

But there are uncountably many real numbers between ANY two different Real Numbers, and thus between 0 and any real number that is not zero. This is because the Real Numbers are uncountably Dense.
Your problem is your eyesight isn't good enough to see that every Real Number is actually visable, it is only your own stupidity that keeps you from seeing them.