In math, zero is part of the set of whole numbers. The whole numbers include all of the natural numbers, or positive counting numbers, plus the number zero. The whole numbers do not include any of the negative numbers.
The set of integers is more inclusive than the set of whole numbers and includes all of the positive whole numbers, the number zero, and all of the whole numbers with negative signs in front of them. The set of rational numbers is even more inclusive and consists of fractions that can be represented as an integer over a non-zero integer. The integer at the bottom of the fraction must not be zero, because division by zero is undefined.