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

On 11/1/24 1:33 PM, WM wrote:

On 01.11.2024 16:04, Jim Burns wrote:
 

Here,
you say: the smallest exists.
That does not pop the smallest into existence.

 I say: All exist. That implies the smallest.

Nope. That if your finite thinking.
When "All" is infinite, it doesn't need to have both ends.
That is your problem.

>
It contracts our discourse to
lines which have a smallest.

 Yes.
 The other alternative would consist of variable sets.

No, it means coming to grips of the somewhat non-intuative nature of infinity. Since we can never have seen infinity, we don't have a natural basis to understand it.

Why?
It is a point on the real line,
well separated from its neighbour.

>
You can contract our discourse to
real lines with smallest points,
but they will also be
real lines without smallest points,

 That happens when Cantor's actual infinity is treated like potential infinity. Best example: Hilberts hotel.
 Regards, WM
 

No, Hilberts Hotel gives us a way to use the potential infinity that we have better able to understand to see the rules of what Actual Infinity follows.