 Elementary algebra ordinarily works with real or complex values. However its general methods, if not always its specific operations and laws, are equally applicable to other numeric domains such as the natural numbers, the integers, the integers modulo some integer \(n\), the rationals, the quaternions, the Gaussian integers, the \(p\)-adic numbers, and so on. They are also applicable to many nonnumeric domains such as the subsets of a given set under the operations of union and intersection, the words over a given alphabet under the operations of concatenation and reversal, the permutations of a given set under the operations of composition and inverse, etc. Each such algebraic structure, or simply algebra, consists of the set of its elements and operations on those elements obeying the laws holding in that domain, such as the set \(Z = \{0, \pm 1, \pm 2, \ldots \}\) of integers under the integer operations \(x+y\) of addition, \(xy\) of multiplication, and \(-x\), negation, or the set \(2^X\) of subsets of a set \(X\) under the set operations \(X\cup Y\) of union, \(X\cap Y\) of intersection, and \(X'\), complement relative to \(X\).