Cayley-Dickson construction

The Cayley-Dickson construction is a method in mathematics that creates larger, more complex number systems from existing ones. Starting with real numbers, it builds complex numbers, then quaternions, octonions, and beyond, each with new properties and dimensions. This process involves pairing elements from the previous system and defining new addition and multiplication rules, often leading to systems with unique features like non-commutativity (order matters) or non-associativity (grouping matters). It’s a systematic way to explore and generate advanced algebraic structures that extend our understanding of numbers and their interactions.