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

On 10/30/2024 2:34 PM, Ross Finlayson wrote:

On 10/30/2024 09:18 AM, Jim Burns wrote:

On 10/30/2024 1:27 AM, Ross Finlayson wrote:

That ran(EF) is complete is rather simple,
i.e. it's trivial, in as to where,
as you for whatever reason chose to simply ignore:
the LUB can be simply either max(n), or, max(n)+1,
being or making a critical point.

⎛ Necessary and sufficient conditions for finiteness
⎜
⎜ 3. (Paul Stäckel) 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.
⎝
https://en.wikipedia.org/wiki/Finite_set

That that there's
"0/d, ..., { ... infinitely-many ... }, ..., d/d",
has that the "infinitely-many" is a usual sort of word
that is among the few words that end up in "math mode",
like "lim".

Contradiction.
If there are infinitely.many between 0/d and d/d
then there isn't max.B and 1+max.B
for each non.empty subset B