Abstract Concepts: Semi-Ring

This lecture introduces the concept of a commutative semi-ring, which is defined based on properties similar to those of set theory. The instructor explains how operations like addition and multiplication in N exhibit analogous properties, leading to the abstraction of a semi-ring. The lecture covers the definition of a commutative semi-ring with two operations, illustrating examples where properties like associativity, commutativity, and the existence of neutral elements are satisfied. The properties discussed in the lecture precisely define N as a commutative semi-ring, distinguishing it from a ring by the absence of subtraction. The previous chapter's exploration of the power set of a set X, equipped with union and intersection operations, serves as an example of a commutative semi-ring.