n. 1. also called signed number or directed number. a number that may be expressed as the sum or difference of two natural numbers; a member of the set {..., -3, -2, -1, 0, 1, 2, 3,...}, usually denoted Z. The integers are the closure of the natural numbers under subtraction, and are identified with the rational numbers with denominator 1. 2. an algebraic integer. The usual integers are then referred to as rational integers if a distinction is necessary.