Set, for short, is a basic concept in mathematics and the main research object of set theory. The basic theory of set theory was founded in19th century. The simplest statement about set is the definition in naive set theory (the most primitive set theory), that is, set is "a certain pile of things" and the "things" in set are called elements. A modern set is usually defined as a whole consisting of one or more definite elements.

cardinal number

The number of elements in a set is called the cardinality of the set, and the cardinality of the set A is called the card (a). When it is finite, the set A is called finite, otherwise it is infinite. Generally speaking, a set with finite elements is called a finite set, and a set with infinite elements is called an infinite set.