FANDOM


In Peano arithmetic, multiplication is defined by a recursion of addition of natural numbers.

Definition

Given an arbitrary $ a \in \mathbb{N} $, we will define $ ab $ recursively as follows: $ a \cdot 0 = 0 $ and $ ab' = ab+a $, for all $ b \in \mathbb{N} $.

Properties

Multiplication on the natural numbers has some important properties:

See also