Z_4
Z_4 is a mathematical structure known as a group, specifically a cyclic group of order 4. It consists of the set of integers 0, 1, 2, 3 with addition defined modulo 4. This means that when the sum exceeds 3, it wraps around to 0. For example, 2 + 3 equals 1 in Z_4.
In Z_4, each element can be generated by adding 1 repeatedly. The group is closed under addition, meaning that adding any two elements from the set will always yield another element in the set. This property, along with the existence of an identity element (0) and inverses for each element, confirms that Z_4 satisfies the group axioms.