Examples of subsets thumb|The regular polygons form a subset of the polygons. The set A = {1, 2} is a proper subset of B = {1, 2, 3}, thus both expressions and are true. The set D = {1, 2, 3} is a subset (but a proper subset) of E = {1, 2, 3}, thus is true, and is not true (false). The set {x: x is a prime number greater than 10} is a proper subset of {x: x is an odd number greater than 10} The set of natural numbers is a proper subset of the set of rational numbers; likewise, the set of points in a line segment is a proper subset of the set of points in a line. These are two examples in which both the subset and the whole set are infinite, and the subset has the same cardinality (the concept that corresponds to size, that is, the number of elements, of a finite set) as the whole; such cases can run counter to one's initial intuition. The set of rational numbers is a proper subset of the set of real numbers. In this example, both sets are infinite, but the latter set has a larger cardinality (or ) than the former set.
Examples of subsets thumb|The regular polygons form a subset of the polygons. The set A = {1, 2} is a proper subset of B = {1, 2, 3}, thus both expressions and are true. The set D = {1, 2, 3} is a subset (but a proper subset) of E = {1, 2, 3}, thus is true, and is not true (false). The set {x: x is a prime number greater than 10} is a proper subset of {x: x is an odd number greater than 10} The set of natural numbers is a proper subset of the set of rational numbers; likewise, the set of points in a line segment is a proper subset of the set of points in a line These are two examples in which both the subset and the whole set are infinite, and the subset has the same cardinality (the concept that corresponds to size, that is, the number of elements, of a finite set) as the whole; such cases can run counter to one's initial intuition. The set of rational numbers is a proper subset of the set of real numbers. In this example, both sets are infinite, but the latter set has a larger cardinality (or ) than the former set.