The symbol \mathbbZ represents the set of all integers, which includes positive numbers, negative numbers, and zero. This set can be expressed as \..., -3, -2, -1, 0, 1, 2, 3, ...\. Integers are used in various mathematical contexts, such as counting, ordering, and performing arithmetic operations. In mathematics, \mathbbZ is a fundamental building block for number theory and algebra. It is closed under addition, subtraction, and multiplication, meaning that performing these operations on integers will always yield another integer. The set \mathbbZ is also an example of a ring, which is a structure that allows for the study of algebraic properties.