multiplication

Ordinary multiplication of numbers is just repeated addition. To multiply a number \(a\) by a number \(b\), simply add together \(b\) copies of \(a\). For instance, \(2\times 3\) is just \(2+2+2\). We call the result of a multiplication the product, and we call the numbers being multiplied together the multiplicands.

Multiplication of natural numbers is formally defined by the Peano Axioms.

Multiplication of ordinary numbers is commutative and associative. However, in more abstract settings a notion of multiplication may be defined in which commutativity and/or associativity do not hold. Multiplication also has distinct properties for transfinite ordinals and cardinals.