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

On 12.09.2024 14:35, Richard Damon wrote:

On 9/12/24 7:18 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.

Nope, that ASSUMPTION just means you can't actually have an infinite
set, as you can't get to the upper end to let you count down.

Wrong. Dark numbers prevent counting to the end. Dark numbers establish
the existence of a set where no end can be seen. That is the only way to
make infinity and completeness compatible.

1/n - 1/(n+1) > 0 thus says that no 1/n is the smallest, as there will
exist a 1/(n+1) that is smaller that that.

That is not a proof of existence. The formula says: If n and n+1 exist,
then they differ.