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

On 17.10.2024 21:39, FromTheRafters wrote:

Anyway, the size of these infinite sets are equal despite outpacing and asymtotic density considerations.

The even numbers and the natural numbers have the relative sizes
|{2, 4, 6, ..., 2n}|/|{1, 2, 3, 4, 5, 6, ..., 2n} = 1/2
for every n. Only real fools can believe that the relative size changes to 1 for all numbers |E|/|ℕ| = 1. Cantor knew this. Therefore cardinality is not true for the complete sets but only for potentially infinite initial segments.
Regards, WM