integer, whole-valued positive or negative number or 0. The integers are generated from the set of counting numbers 1, 2, 3,… and the operation of subtraction. When a counting number is subtracted from itself, the result is zero; for example, 4 − 4 = 0. When a larger number is subtracted from a smaller number, the result is a negative whole number; for example, 2 − 3 = −1. In this way, every integer can be derived from the counting numbers, resulting in a set of numbers closed under the operation of subtraction (see group theory).