fjölföldun

Fjölföldun is the Icelandic term for the arithmetic operation commonly known as multiplication. In its simplest sense, it combines two numbers to produce a product. For natural numbers, it can be understood as repeated addition: a times b equals adding a to itself b times. In real-number arithmetic, multiplication is defined by a consistent set of rules that extend this idea to fractions, decimals, and irrational numbers.

In mathematical notation, fjölföldun is usually written as a × b, ab, or a · b. The standard properties include commutativity (a × b = b × a), associativity ((a × b) × c = a × (b × c)), and distributivity over addition (a × (b + c) = ab + ac). The multiplicative identity is 1, since a × 1 = a for any a, and the zero property states that a × 0 = 0. In most contexts, multiplication follows the order of operations, having priority over addition.

Applications of fjölföldun are widespread. It is used to compute areas (length × width), scale quantities, and perform financial calculations. In higher mathematics, multiplication extends to more abstract structures, such as matrix multiplication and scalar multiplication of vectors, each with its own definitions and properties. Matrix multiplication, for example, combines rows and columns to produce a new matrix and is generally not commutative, though it is associative.

Historically, multiplication has roots in ancient civilizations and has evolved with notation. The modern multiplication symbol × became common in Europe during the early modern period and remains a standard representation in education and science.