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

On 25.09.2024 20:40, Jim Burns wrote:

On 9/25/2024 11:51 AM, WM wrote:

That means NUF increases by 1
at every point occupied by a unit fraction.

 There are numbers (cardinalities) which increase by 1
and other numbers (cardinalities), which
don't increase by 1.

No. Every countable set is countable, i.e., it increases one by one.

For each positive point x
for each number (cardinality) k which can increase by 1
there are more.than.k unit.fractions between 0 and x

That is a misinterpretation of the law valid for small numbers.

 For each positive point x
the number (cardinality) of unit.fractions between 0 and x
is not
any number (cardinality) which increases by 1
Instead, it is
a number (cardinality) which doesn't increase by 1.

For every x NUF increases by not more than 1.

Each positive point is undercut by
some finite.unit.fraction.

Repetition is apparently what you (JB) think mathematics is!
Prove that ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 is wrong or agree.
Regards, WM