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

On 9/12/2024 4:18 AM, WM wrote:

Le 12/09/2024 à 03:00, Richard Damon a écrit :
 

So, you can't "index" an unbounded set of unit fractions from 0, as there isn't a "first" unit fraction from that end.
>
We can "address" those unit fractions with the value, but we can not "index" them from 0, only from 1/1.

 If you can index all unit fractions, then you can index them from every side.

No. Thinking of using natural numbers to index them.
1 = 1/1
2 = 1/2
3 = 1/3
...
Since there is no _largest_ natural number, you cannot find the other end... See?

Fact is that NUF(x) increases from 0, but at no point it can inc4rease by more than 1 because of
∀n ∈ ℕ: 1/n - 1/(n+1) > 0
Regards, WM