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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