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

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.

If you augment ⅟ℕ with more elements that is a different set.
A. is still not true of ⅟ℕ
If you, nonetheless, assert A.
A. is true of _all the sets in the discourse_
Because A. is not true of ⅟ℕ,
⅟ℕ is not in the discourse.
After A., claims about "sets" are not claims about ⅟ℕ

cannot happen at points in smaller distance than uncountable many points
from zero.