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Addition is:

Commutative ie a + b = b + a

Associative ie (a + b) + c = a + (b + c) so that they can both be written as a + b + c

Existence of Identity: There is a unique number, 0, such that a + 0 = 0 + a = a for all numbers a

Existence of Inverse: For any number a, there is a unique number b such that a + b = b + a = 0. This b is written as -a.

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