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

On 10/19/2024 02:57 PM, FromTheRafters wrote:

WM used his keyboard to write :

On 19.10.2024 20:22, Alan Mackenzie wrote:

WM <wolfgang.mueckenheim@tha.de> wrote:

>

An infinite set is one which has a proper subset which can be
put into 1-1 correspondence with the original set.  That is the
definition.

>
According to Dedekind every set {1, 2, 3, ..., n} is in correspondence
with the set {2, 4, 6, ..., 2n} which covers twice the interval,
containing numbers not in the original set. This does not change when
the whole set ℕ is multiplied by 2. The result covers twice the
interval, containing numbers not in the original set ℕ.

>
Intervals now? Discrete ones or real ones?

The usual term for how an interval could be anything
less is called a "de-generate" interval, that it's not
generated by infinite divisibility a generate (n.),
sort of like "quasi-invariant", "pseudo-differential",
"degenerate interval", this kind of thing.
I.e. that's the term for that concept the idea.
If you have it, ....