A cardinal number is a number used for counting real objects or counting things. It represents "how many" or "number of" elements in a set or group. In mathematics, a cardinal number is the number of elements of a set. For a finite set, its cardinal number, or cardinality, is a natural number. Cardinal numbers are also known as "counting numbers" or "cardinals". They are the counting numbers that start from 1 and go on sequentially and are not fractions. The smallest cardinal number is 1, and examples of cardinal numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, and so on. The intuition behind the formal definition of cardinal is the construction of a notion of the relative size or "bigness" of a set, without reference to the kind of members which it has. In order to compare the sizes of larger sets, it is necessary to appeal to more refined notions.