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

On 11/2/2024 5:23 PM, WM wrote:

On 02.11.2024 19:45, Jim Burns wrote:

On 11/2/2024 6:15 AM, WM wrote:

On 02.11.2024 01:55, Richard Damon wrote:

Infinite sets do not need to have both ends in them.

>
Between 0 and 1 there are unit fractions.
Hence there must be a first one.

>
A.
⎛ S can be given a total ordering which is
⎜ well-ordered both forwards and backwards.
⎜ That is, every non-empty subset of S has
⎝ both a least and a greatest element in the subset.
[1]
>
A. isn't true of all sets.

>
It is true for all sets of
separated points on the real line.

⎛ The union of ⟦0,n⟧ which are doubly.well.ordered
⎜ is not a doubly.well.ordered set.
⎜
⎜ The union of ⟦0,n⟧ which are doubly.well.ordered
⎝ holds only separated points on the real line.
----
j+1 = min.{k:j<k}
j-1 = max.{i:i<j}