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Sum, or addition, of numbers has the following properties:

Commutative: a + b = b + a

Associative: a + (b + c) = (a + b) + c and so either can be written as a + b + c

A set, over which addition is defined will usually (but not necessarily) contain a unique additive identity, which is denoted by 0. This has the property that, for all eelments a, in the set, a + 0 = 0 + a = a

The set may also have additive inverses. An element, a in the set, has the additive inverse, denoted by -a, such that a + (-a) = (-a) + a = 0.

Not all sets will have an identity or inverse, for example, the set of counting numbers has neither.

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