Supernumber Theory and Quantum Superposition Phenomena

Abstract

Zhi Li* and Hua Li

Hyperreal numbers are a field encompassing real numbers, infinitesimals, and infinities. In the hyperreal number system, infinitesimals are not equal to zero, and operations can be performed on infinitesimals and infinities. Based on hyperreal number theory, this paper discovers that multi-level radicals that cannot be simplified have no definite value, varying in size; these can be called quantum numbers or inaccurate numbers. A special type of multi-level radical can exhibit quantum superposition phenomena similar to those in the physical world. This allows the hyperreal number system to be extended to a supernumber system, a field encompassing real numbers, infinitesimals, infinities, and inaccurate numbers. Confirming the existence and properties of quantum numbers or inaccurate numbers and classifying them as supernumbers provides a new perspective. Within this framework, the negation proves the Riemann hypothesis.

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