"inf" and "sup" are abbreviations of Chinese and English in mathematics, which respectively mean "lower supremum" and "upper supremum". In mathematics, all the elements of a given set have a minimum element and a maximum element, which are called the upper and lower bounds of the set respectively. The lower supremum refers to the lower bound of all elements in the set, that is, all elements are not less than the lower supremum; The supremum refers to the upper bound of all elements in a set, that is, all elements are not greater than the supremum.