Editing Maths (section)

==Peano Arithmetic==
The axioms that define the natural numbers. - Good Math pg5.

* Initial Value Rule - There is one object called 0 and 0 is a natural number.
* Successor rule: For every natural number n there is exactly one other natural number called its sucessor, s(n).
* Uniqueness Rule: No two natural numbers have the same sucessor.
*Equality Rules: Numbers can be compared for equality.
** Equality is reflexive: - Every number is equal to itself
** Equality is symmetric: a=b then b=a
** Equality is transitive: if a=b and b=c then a=c
* Induction rule: For P, P is true for all natural numbers if.
** 1. P is true about 0. P(0)=true.
** 2. If you assume P is true for a natural number n(P(n) is true). Then you can prove that P is true for the sucessor s(n) of n, P(s(n) == true.

===Addition===
* Commutative: n+m = m+n
* Identity: n+0 = 0+n=n
* Recursion: m+s(n) = s(m + n)