Re: Replacement of Cardinality

On 7/30/24 1:39 PM, WM wrote:

Le 30/07/2024 à 03:20, Richard Damon a écrit :

On 7/29/24 9:15 AM, WM wrote:

Le 29/07/2024 à 11:01, Mikko a écrit :
>

He also notes that what we have learned from finite quatities does
not apply to infinity.

>
Unit fractions are isolated. They have distances. The function "unit fractions between 0 and x" can nowhere grow by more than 1.

>
Unless it just jumps to infinity because it isn't actually correctly defined.

 It is correctly defined. Try to define the function Number of UnitFractions between 0 and x as you like it but in accordance with mathematics ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.
 Regards, WM

And you equation proves that there is no smallest unit fraction as your mathematics also says that you statement is equivalent to
∀n ∈ ℕ: 1/n > 1/(n+1) so there does not exist a smallest unit fraction, since part of the definition of the Natural numbers is that
∀n ∈ ℕ: there exist n+1 ∈ ℕ