Re: how

Le 16/06/2024 à 21:41, Moebius a écrit :

| For all real numbers x > 0: there are infinitely many unit fractions u such that u < x [true]
 

For every definable x > 0 this is true, but the function NUF(x) concerns all x > 0 and falsifies it.

 | There are infinitely many unit fractions u such that for all real numbers x > 0: u < x [false]

Unit fractions are real numbers.

Therefore the statement:
For every x > 0 there are ℵo smaller unit fractions,
implying the statement
For every x > 0 there are 2 smaller unit fractions,
is false because 2 unit fractions are real x > 0 which cannot be smaller than every x > 0.
Regards, WM