The term "limit inferior" is commonly used in mathematics and refers to the smallest number that a sequence can approach as the index goes to infinity. There are several synonyms for this term, such as "infimum," "lower bound," and "greatest lower bound." The infimum is the greatest number that is less than or equal to all of the elements in a set of numbers. A lower bound is any number that is less than or equal to all of the elements in a set of numbers. Finally, the greatest lower bound is the largest lower bound of a set of numbers. No matter which term is used, all synonyms describe the same concept in mathematical terms.