Minimal counting systems and commutative monoids
Chris Preston
TL;DR
This paper explores how to derive addition and multiplication on natural numbers using fundamental properties of commutative monoids, providing a foundational algebraic perspective.
Contribution
It introduces a novel approach to defining natural number operations through elementary commutative monoid results, bridging algebraic structures and number theory.
Findings
Addition and multiplication derived from monoid properties
Elementary results suffice for natural number operations
Provides a foundational algebraic framework
Abstract
These notes present an approach to obtaining the basic operations of addition and multiplication on the natural numbers in terms of elementary results about commutative monoids.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Algebra and Logic · Rings, Modules, and Algebras