heltall

Heltal, in Swedish mathematical terminology, denotes the set of integers, written as Z in mathematical notation. This includes all whole numbers positive, negative, and zero: ..., -2, -1, 0, 1, 2, and so on. The term is commonly translated as “integers” in English. Heltal are closed under addition, subtraction, and multiplication, meaning the result of any of these operations on integers is always an integer. Zero is the additive identity, and every integer has an additive inverse (for example, the inverse of 7 is -7). Division of integers does not, in general, yield an integer.

Integers are foundational in number theory and algebra. They form a ring under the usual addition and multiplication, with properties such as distributivity and the existence of multiplicative and additive identities. They can be classified as even or odd and as positive, negative, or zero. In modular arithmetic, integers are studied modulo a fixed modulus to understand remainders and congruences.

Relation to other number sets is a standard part of the structure of number systems. The natural numbers (which may or may not include zero, depending on convention) are a subset of the integers. Every integer is a rational number, since it can be expressed as a quotient with denominator 1, and every rational is a real number, so integers are contained in the real numbers.

In practice, integers are represented in decimal notation with an optional leading minus sign and a sequence of digits. They are used to model discrete quantities in mathematics, computer science, and related fields.