Re: Replacement of Cardinality (infinite middle)

On 8/19/2024 3:27 PM, Ross Finlayson wrote:

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

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[...]

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I mean it's a great definition that finite has that
there exists a normal ordering that's a well-ordering

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...in both directions...
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and that all the orderings of the set are well-orderings.

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...in both directions...
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That's a great definition of finite and now it stands
for itself in enduring mathematical definition in defense.

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...for comfortably more than a century.
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Why is it you think that Stackel's definition of finite
and "not Dedekind's definition of countably infinite"
don't agree?

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They mostly agree.
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Given the Axiom of Choice
(let us say, if an inaccessible cardinal exists),
they completely agree.
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My impression from somewhere is that,
if they disagree,
they disagree on some very weird sets.
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https://en.wikipedia.org/wiki/Finite_set
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[...] is another little fact of mathematics
missing from your neat little hedgerow.

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I mark my neat little hedgerow, and
I describe what's true everywhere inside the hedgerow.
That allows me to learn about
what's inside the hedgerow,
even though it's infinite and I am finite.
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I like doing that.
It isn't wrong for me to do that.
I will continue doing that.
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