What is an integer?

An integer is a whole number that can be positive, negative, or zero. An Integer is naturally defined as a number that can be written without a fractional component.


Integers are: 45, 89, 6, 0, and -543, -87.

Numbers that are not integers are: 6.50, 9 1/2, and -8.152 .

The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, …), also called whole numbers or counting numbers, and their additive inverses (the negative integers, i.e., −1, −2, −3, …).

The set of integers is often denoted by a boldface letter ‘Z’ (“Z“) or blackboard bold ℤ.

ℤ is a subset of the set of all rational numbers ℚ, which in turn is a subset of the real numbers ℝ. Like the natural numbers, ℤ is countably infinite.

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