The set of integers is a subset of the set of real numbers.

The set {a,b} is a both a subset and a proper subset of {a,b,c} while the set {a,b,c} is a subset of {a,b,c} but not a proper subset of {a,b,c}.

1963, David B. MacNeil, Modern Mathematics for the Practical Man, David Van Nostrand, Republished as 2013, David B. MacNeil, Fundamentals of Modern Mathematics: A Practical Review, Dover, page 3,
In the foregoing example, the set D of the first four letters of the alphabet, was a subset of the set A of all the letters of the alphabet, because A includes all the members of D.

Let A be a subset of the topological space X and take x∈X.

We say that a set S has a finite partition into subsets S_1,…,S_n, if S=S_i∪…∪S_n, where the subsets are pairwise disjoint, that is, S_i∩S_j= empty , if i ne j. (We do not require that the subsets be nonempty.)

We asked a subset of the population of the town for their opinion.

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