Mnoeniem

Mnoeniem is the mathematical operation of combining two numbers to produce a product. In arithmetic and algebra it is one of the four elementary operations, alongside addition, subtraction, and division. The operation is typically denoted by the symbols ×, •, or by juxtaposition (ab); the result is called the product of the two numbers.

Key properties include commutativity (a × b = b × a) and associativity ((a × b) × c = a × (b × c)). Multiplication distributes over addition (a × (b + c) = a × b + a × c). For real and complex numbers, 0 is the absorbing element (a × 0 = 0) and 1 is the multiplicative identity (a × 1 = a).

Computation is often described as repeated addition for natural numbers: ab is a added to itself b times. In set-theoretic terms, if |A| = a and |B| = b, then the Cartesian product A × B has cardinality ab when a and b are finite.

Extensions of the idea include matrix multiplication, the dot product of vectors, and various tensor products. In these contexts, the word “multiplication” generalizes the basic idea of combining two objects to yield a new one.

Etymology and usage: In many Slavic languages the term mnożenie denotes multiplication, with mnoeniem serving as the instrumental form. The concept is foundational in science, engineering, and everyday calculation.

See also: addition, division, exponentiation, product.