The Fundamental Theorems of Hyper-Operations
Renny Barrett · Preprints.org · 2019
We examine the extensions of the basic arithmetical operations of addition and multiplication on the natural numbers into higher-rank hyper-operations also on the natural numbers. We go on to define the concepts of prime and composite numbers under these hyper-operations and derive some results about factorisation, resulting in fundamental theorems analogous to the Fundamental Theorem of Arithmetic.