heltallige

Heltallige is a term used in Norwegian-language mathematics and related fields to describe properties related to heltall, the integers. In mathematics, an integer is a whole number that can be written without a fractional part, including positive numbers, negative numbers, and zero. The standard symbol for the set of all integers is Z, and it is defined as Z = {…, -2, -1, 0, 1, 2, …}.

Heltallige numbers form a closed set under the basic arithmetic operations of addition, subtraction, and multiplication. This means that the result of adding, subtracting, or multiplying any two integers is always an integer. Division, however, does not always yield an integer; a quotient is an integer only when one integer is divisible by another without remainder. Parity is a common property associated with heltallige numbers: an integer is even if it can be written as 2k for some k in Z, and odd if it can be written as 2k + 1.

In practice, the term is used across several related concepts. Subsets include natural numbers (often non-negative integers) and, depending on convention, whole numbers (which may or may not include zero). Heltallige numbers are central in number theory, combinatorics, and computer science, where integer arithmetic and modular arithmetic are fundamental. In computing, integers are represented as data types with fixed storage sizes (for example, 8, 16, 32, or 64 bits), with considerations for sign (signed vs unsigned) and potential overflow.

Examples of heltallige numbers are -3, 0, 7, and 42. A non-integer such as 3.5 is not considered heltallige. See also: natural numbers, rational numbers, real numbers, and complex numbers.