Chaos is the order of nature. Nature is characterized by its chaotic variables and processes. These variables and processes are described by numbers and words. Numbers in classical mathematics are static and rigid. However, nature is dynamic and evolutionary. Therefore, it is vital to propose new definitions and meanings for the numbers in order to describe properly nature behavior and therefore know its chaos. For example, the mysterious numbers zero and infinity lack precision. Infinity is defined as being always unlimited. However, when solving mathematical equations, infinity becomes limited, which is contradictory to the previous and original concept. This paper introduces infinity as a dynamic and evolutionary number, which adds meaning and precision to it. The various chaos arithmetic operations involving infinity are defined. They include addition, subtraction, multiplication, and division. This paper represents a novel and essential contribution to establish a new branch of mathematics that is chaos arithmetic.