The Canonical Order of Operations: a Separate Framework

The Canonical Order of Operations introduces a unified framework to resolve ambiguities in traditional arithmetic, particularly in handling negative values, roots, and exponents. By eliminating inconsistencies that necessitate the use of imaginary numbers and redefining the treatment of operations involving negatives, this framework preserves the integrity of real numbers without resorting to abstract constructs. Rooted in centuries of mathematical tradition, the Canonical Order replaces symbols such as the radical () with explicit fractional exponents, making these concepts more accessible and intuitive for learners. This paper explores the historical context, defines the Canonical Order, and demonstrates its potential to simplify mathematical education and computation while maintaining logical consistency.