Re: Replacement of Cardinality

Le 24/08/2024 à 22:16, Jim Burns a écrit :

Many of us are more familiar with necklaces which
have some minimum size of bead (or of whatever).

The unit fractions have no minimum distance but more than nothing.

 For rationals,
there is a greatest lower bound of distances
between different rationals,
but,
for a minimum distance to exist,
the greatest lower bound needs to be a distance.

For a distance to exist in every case mathematics is sufficicient:
∀n ∈ ℕ: 1/n - 1/(n+1) > 0 .

The greatest lower bound of distances is 0,

The distances between all unit fractions are positive. The GLB is to comfort blind persons who cannot think.
Regards, WM