Addition is the operation which produces the sum of two (or more) numbers. The order of
addition does not affect the result.
There is a number 0, called zero,
such that the sum of any number a and zero is a.
Corresponding to each number a, there is a number (-a), called the opposite of a, such
that the sum of a and (-a) is zero.
Also, for any two numbers a, b there is a unique number x such that a + x = b, namely, x
= b + (-a), more commonly written x = b - a.
A set with an addition law satisfying the above properties, and such that all sums lie
in the set, is called an additive group.
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