Integer

The integers (Latin, integer, literally, "untouched," whole, entire, i.e. a whole number) are the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.

More formally, the integers are the only integral domain whose positive elements are well-ordered, and in which order is preserved by addition. Like the natural numbers, the integers form a countably infinite set. The set of all integers is usually denoted in mathematics by a boldface Z (or blackboard bold, \mathbb{Z}, or Unicode ℤ), which stands for Zahlen (German for "numbers").

The term rational integer is used in algebraic number theory to distinguish these "ordinary" integers, embedded in the field of rational numbers, from other "integers" such as the algebraic integers.