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

On 12.09.2024 07:03, Jim Burns wrote:

On 9/11/2024 3:53 PM, WM wrote:

But you claim that if β exists, then ½.β exists.
And if ½.β exists, then β/4 exists, and so on.

 There's a proof.
 

It is based on an axiom which does not reproduce real mathematics.

But we need not use sets at all
if we use the points.

 If you use points as sets, expect gibberish.

Use points *as points* and investigate their properties.

>
For each point x in (0,1]: 0 < x/2 < x
No point exists between 0 and (0,1]

Nevertheless (0,1] has a smallest point. It is dark. Where no point is, there is no interval. Interval-ends without points are matheology.
Regards, WM