Multiplication (natural numbers)
From Mathematics
In Peano arithmetic, multiplication is defined by a recursion of addition of natural numbers.
[edit] Definition
Given an arbitrary 
, we will define 
recursively as follows: 
and 
, for all 
.
[edit] Properties
Multiplication on the natural numbers has some important properties:
- The natural number
is the multiplicative identity (proof)
- Multiplication is distributive over addition (proof)
- Multiplication is commutative (proof) and associative (proof)
