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

On 9/12/2024 1:48 PM, WM wrote:

On 12.09.2024 14:29, FromTheRafters wrote:

After serious thinking WM wrote :

But the endpoints of open intervals
will remain dark forever.

>
Open intervals simply don't contain endpoints,
dark or otherwise.

>
You simply don't know about them.

The boundary ∂A of set A is
the set of points x such that
each open set Oₓ ∋ x
holds points in A and points not.in A
A closed set contains all of its boundary.
An open set contains none of its boundary.
The topology in which
intervals holding endpoints are open
is a topology in which
the intersection of two (open) intervals
  is open,
a one.point interval.intersection
  is open,
the arbitrary union of (open) one.point intervals
  is open, and
all sets are open.
We call that the discrete topology.
Yes, it is an actual topology.
It is not what anyone else considers
the standard topology of ℝ
⎛ Axioms for topological.space X
⎜
⎜ The intersection of two open sets is open.
⎜
⎜ The union of arbitrarily.many open sets is open.
⎜
⎝ {} and X are open.