Re: Replacement of Cardinality

On 8/13/2024 3:21 PM, Chris M. Thomasson wrote:

On 8/13/2024 7:27 AM, WM wrote:

Le 12/08/2024 à 20:34, Jim Burns a écrit :

On 8/12/2024 9:47 AM, WM wrote:

Before the bound there is the end,
perhaps dark.

>

0 is
greatest.lower.bound β of visibleᵂᴹ unit.fractions

>
Yes. But the smallest unit fractions comes before.

>
This irks me a bit.
The smallest unit fractions?
How do you define them?
What if
your version of "small" is _larger_ than
somebody else's version of "small"?
Is hyper small smaller than super small?

"It depends".
Note that super.duper small is
between hyper.small and super.small.
OMG.small and WTF.small are left as
an exercise for the reader.
I think that
delta.epsilonics finesses the question
by first picking what 'small' is, ε > 0
then defining
what continuity and its ilk need to be
in relation to _the picked small_ ε > 0