Re: Replacement of Cardinality (infinite middle)

On 8/29/2024 6:46 PM, Ross Finlayson wrote:

On 08/19/2024 12:27 PM, Ross Finlayson wrote:

On 08/18/2024 09:56 PM, Jim Burns wrote:

Definition.
⎛ An order ⟨B,<⟩ of B is finiteᵖᵍˢˢ  iff
⎜ each non.empty subset S ⊆ B holds
⎝ both min[<].S and max[<].S

Why is it you think that Stackel's definition of finite
and "not Dedekind's definition of countably infinite"
don't agree?

I don't think they disagree, normally.
Note: If you mean Dedekind's definition of infinite,
it isn't limited to countably.infinite.

The entire idea here that there's a particular _regularity_
due dispersion and modularity only courtesy division down
from a fixed-point, that "Peano's axioms" don't give integers,
they only give increments, i.e. not necessarily constant increments,
that there's more than one _regularity_, REQUIRED, is another
little fact of mathematics missing from your neat little hedgerow.

>
..., REQUIRED, ....

Things missing from my neat little hedgerow are
missing because I intend for them to be missing.
My neat little hedgerow has no weeds.
It has not had and will not have weeds.
And weeds would not be an improvement.
My neat little hedgerow is well.ordered;
each non.empty subset holds a minimum.
In my neat little hedgerow,
each Little Bunny Foo Foo has a successor,
scooping up the field mice and bopping them on the head,
and is a successor, except the first, named 0.
Successors are non.0 non.doppelgänger non.final.
You are welcome to talk about something else, Ross.
Note, though, that,
if you are talking about something else,
then you are talking about something else.
Non.triangles are not counter.examples to triangles.
Non.Bunny.Foo.Foos are not counter.examples to Bunny.Foo.Foos.
Have a nice day.