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

On 9/20/2024 2:27 PM, WM wrote:

On 19.09.2024 21:15, Jim Burns wrote:

On 9/19/2024 9:02 AM, WM wrote:

On 19.09.2024 13:44, Richard Damon wrote:

On 9/19/24 7:22 AM, WM wrote:

There are infinitely many points with no extension
filling the space.

>
Right,
and none "next" to another, because
there is always another in between them.

>
"always another" is potential infinity.

>
For each finite ordinal ξ,
always another finite ordinal ξ∪{ξ} > ξ exists.

>
Potential infinity.

ξ ⟼ ξ∪{ξ}
is one.to.one
from finite ordinals
to (proper subset) nonzero finite ordinals

The set ω of all and only finite ordinals
holds all and only finite ordinals.

>
And there is no gap before ω.

ω-1 requires impossibilities:
a gap between ω and (hypothetical) ω-1