Pomnoenie

Pomnoenie is the mathematical operation of combining two quantities to produce a product. In its simplest form, multiplying two numbers a and b yields ab. The concept generalizes beyond numbers to other mathematical objects and underpins much of arithmetic, algebra, and applied sciences.

Notation varies by context. In most mathematics, multiplication is written as juxtaposition (ab), a times sign (a × b), or, in programming, with symbols such as a * b. For integers, rationals, reals, and complexes the operation follows familiar rules of counting repeated addition.

Core properties include commutativity (a × b = b × a), associativity ((a × b) × c = a × (b × c)), and distributivity over addition (a × (b + c) = a × b + a × c). There is a multiplicative identity, 1, and multiplying by 0 yields 0. Negative numbers affect the sign according to parity, so multiplying two negatives gives a positive result.

Generalizations include matrix multiplication, which is associative but not generally commutative, and scalar multiplication in vector spaces. Exponentiation is defined as repeated multiplication. In higher algebra, multiplication interacts with structure such as rings and fields, shaping how elements combine.

The term pomnoenie is used in some Slavic languages to denote multiplication, with spelling and usage varying by language. Etymology generally traces to roots related to increasing or combining quantities. This operation remains foundational in everyday arithmetic, science, engineering, computing, and finance.