Integers are the counting numbers, their negatives, and zero: ..., −3, −2, −1, 0, 1, 2, 3, ... They have no fractional or decimal part. The set is denoted by Z, from the German word "Zahlen" meaning numbers.

Integers extend the natural numbers to include negatives, which makes subtraction always possible. They are closed under addition, subtraction, and multiplication: combining two integers gives another integer. Division, however, can produce fractions, so integers are not closed under division.

Integers appear in temperature readings, bank balances, elevations, and scores. In number theory, properties of integers—primality, divisibility, congruences—are studied in depth. In computer science, integer types have fixed ranges determined by the number of bits used. The concept is elementary but foundational.

• Whole numbers including negatives and zero
• Denoted by Z
• Closed under addition, subtraction, multiplication
• Central to number theory and computing