Addition (natural numbers)

In Peano arithmetic, Addition is defined recursively.

Definition

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

Properties

Addition on the Natural Numbers has two important properties: commutativity and associativity. Also, multiplication is distributive over addition.

See also

• Peano Arithmetic
• Recursions
• Multiplication
• Associative property of addition on the natural numbers
• Commutative property of addition on the natural numbers
• Distributive property of multiplication over addition on the natural numbers