Re: Replacement of Cardinality

On 8/25/24 3:41 PM, WM wrote:

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

But the sum of the infinite series adding up the terms of
1/n - 1/(n+1)
never gets to 1, so you never need to stop.
You logic just condemns Achilles to never be able to pass the tortoise as every time he reaches where the tortoise was, the tortoise has moved some more so Achilles needs to move again.