Minimum

In relation to sets

If a chain is finite, then it will always have a maximum and a minimum. If a chain is infinite, then it need not have a maximum or a minimum. For example, the set of natural numbers has no maximum, though it has a minimum. If an infinite chain S is bounded, then the closureCl(S) of the set occasionally has a minimum and a maximum, in which case they are called the greatest lower bound and the least upper bound of the set S, respectively.