QM is a solid theory that reliably predicts every known experiment dependent on it.

And it seems you need to brush up on your arithmetic theory. There is a progression in the usual number fields, Naturals (w/ or w/o 0), Integers, Rationals, Reals, Complex, Quarternions, Octonions, Sedenions, etc.

• Naturals have a starting point, countability, no negatives, no inverse elements and no algebraic closure.
• Integers sacrifice a starting points to gain negative elements.
• Rationals sacrifice finiteness of subsets to gain inverse elements.
• Reals sacrifice uniqueness