halvtalsmultipel

Halvtalsmultipel is a term used in Swedish mathematics to describe a number that is a multiple of a half-number. A half-number is any number of the form n/2 where n is an integer. Therefore a halvtalsmultipel is any number that can be written as n/2 with n ∈ Z; equivalently, it is an element of the additive subgroup 1/2 Z of the rational numbers.

The set of halvtalsmultipler includes all integers and all half-integers: ..., -3/2, -1, -1/2, 0, 1/2, 1, 3/2, 2, ...

Properties and structure: The halvtalsmultipel set is closed under addition and subtraction, making it an additive subgroup of the rational numbers. It is not closed under ordinary multiplication: the product of two halvtalsmultipler is typically a quarter-integer. In notation, the set can be written as { n/2 : n ∈ Z } or 1/2 Z.

Context and usage: The term appears in Swedish-language mathematical texts and curricula. In English-language contexts, the concept is usually described as half-integers or as multiples of one half. It is relevant in discussions of number theory, lattice points, and problems involving steps of size 1/2 on the number line.

See also: Half-integer; 1/2; Integer; Additive subgroup; Lattice.