One of the most useful tools in nonstandard analysis is the concept of a hyperfinite set. To understand a hyperfinite set, begin with an arbitrary infinite set X whose members are not sets, and form the superstructure S(X) over X. Assume that X includes the natural numbers as elements, let N denote the set of natural numbers as elements of X, and let ^* S(X) be an enlargement of S(X). By the transfer principle, the ordering < on N extends to a strict linear ordering on ^* N, which can be denoted with the symbol "<." Since ^* S(X) is an enlargement of S(X), it satisfies the concurrency principle, so that there is an element ν of ^* N such that if n element N, then n<ν. This follows because the relation < is a concurrent relation on the set of natural numbers.