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

On 9/12/24 7:39 AM, WM wrote:

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.

No, it is based on the axiom that produces the real mathematics, not you toy set that is all you can think of,

 

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.

Which means you need to start with the definition of what the points are.

>
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.

Except you can't define such a smallest point, and in fact, due to the normal property of points, there can't be a smallest in an unbounded from below set of points.

 Regards, WM