smallest

Smallest is the superlative form of the adjective small. It is used to identify the least size, extent, amount, or degree within a defined group. In ordinary language, it compares objects or quantities by describing which has the fewest or least amount.

In mathematics, smallest often refers to a minimum or to the least element in a set. In a totally ordered set, a smallest element is one that is less than or equal to every other element in the set; if such an element exists, it is unique. Finite nonempty sets always have a smallest element under standard ordering, while infinite or unbounded sets may not. For example, the real numbers do not have a smallest element in the whole line, but the set {0} has 0 as its smallest element. The interval (0,1) has no smallest element because every member has a smaller member still within the interval.

Related concepts include the minimum value of a function (the smallest value it attains on its domain) and the infimum, which is the greatest lower bound and may not be attained. In computer science, “smallest” is used in algorithms and data structures to describe operations like finding the minimum element in a collection.

Common examples include the smallest prime number (2) and, in the solar system, the smallest planet (Mercury by size, under current classifications). The term is widely used across disciplines to denote the least among comparable items.