In Peano arithmetic, Addition is defined recursively.


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}.


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

See also

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