Did you read the word "labeled".  The states considered can be complex numbers, or even quaternions, over the reals and yet still be enumerable.

Brent


On 11/27/2024 7:04 AM, John Clark wrote:
On Mon, Nov 25, 2024 at 8:37 PM Brent Meeker <[email protected]> wrote:

    /> His axiom only assumes that configurations of a physical system
    can be labeled by the natural numbers. /


*But the Real Numbers, much less the Natural Numbers, are insufficiently powerful to make quantum mechanical predictions, you need Complex Numbers: *
*
*
*Quantum theory based on real numbers can be experimentally falsified <https://arxiv.org/pdf/2101.10873> *
*
*
*John K Clark    See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>*
cvn
**






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