Mathematically, an identity is an equation that holds no matter how the variables are taken. The relationship between two analytic expressions. Given two analytic expressions, if any number of the common parts (or subsets of the common parts) of their domains or the values of arrays are equal (see function), the two analytic expressions are said to be the same. For example, X2-Y2 and (x+y) (x-y) have A2-B2 = (a+b) (a-b) for any set of real numbers (a, b), so X2-Y2 and (x+y) (x-y) are the same. Whether two analytic expressions are the same or not depends on the specified number set, because the same two analytic expressions are the same in one number set and may be different in the other. For example, and x are the same in a non-negative real number set, but different in a real number set.