Re: how

On 5/19/2024 11:46 AM, WM wrote:

Le 17/05/2024 à 21:08, Jim Burns a écrit :

On 5/17/2024 10:08 AM, WM wrote:

Between each pair of unit fractions,
there is a finite distance.

>
Before each unit fraction ⅟n,
there is a smaller unit fraction ⅟(n+1).

>
These two conditions
cannot be satisfied simultaneously.

No.
1.
Between each pair of unit fractions,
there is a finite distance.
For ⅟m≠⅟n: |⅟n-⅟m|>0
because ⅟m≠⅟n
2.
Before each unit fraction ⅟n,
there is a smaller unit fraction ⅟(n+1).
For each n countable.to from 0
n⁺¹ is countable.to from n
n⁺¹ is countable.to from 0  through n
n < n⁺¹
n < n⁺¹
n⋅⅟n⁺¹⋅⅟n < n⁺¹⋅⅟n⁺¹⋅⅟n
⅟n⁺¹ < ⅟n
"Infinite" does not mean "humongous".