Re: Replacement of Cardinality

Le 03/08/2024 à 21:54, Jim Burns a écrit :

On 8/3/2024 10:23 AM, WM wrote:

I recognized lately that you use
the wrong definition of NUF.
>
Here is the correct definition:
There exist NUF(x) unit fractions u, such that
for all y >= x: u < y.

Here is an equivalent definition:
There exist NUF(x) unit fractions u, such that
u < x
 

Note that the order is ∃ u ∀ y.

 The order is ∀x ∃u ∀y
∃u ∀x ∀y is an unreliable quantifier shift.

It is not a shift but it is the definition of NUF. It excludes that ∃u ∀x>0: u < x,
Regards, WM