Z_3 is a mathematical notation that represents the set of integers modulo 3. This means it includes the numbers 0, 1, 2, where any integer can be reduced to one of these three values based on its remainder when divided by 3. For example, the number 5 is equivalent to 2 in Z_3 because 5 divided by 3 leaves a remainder of 2. In Z_3, addition and multiplication are performed using modulo 3 arithmetic. For instance, adding 1 and 2 results in 0, since 3 modulo 3 equals 0. This structure is an example of a finite field, which is important in various areas of mathematics, including abstract algebra and cryptography.