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Another important property of the set of real numbers links addition and multiplication in two distributive laws as follows:
a(b + c) = ab + ac
(b + c)a = ba + ca
Any set of elements with an equality relation and for which two operations (such as addition and multiplication) are defined, and which obeys all the laws for addition A-1 through A-5, the laws for multiplication M-1 through M-5, and the distributive laws, constitutes a field.