Definition of "subset"

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.

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

Let A {\displaystyle A} be a subset of the topological space X {\displaystyle X} and take x ∈ X {\displaystyle x\in X} .

1997, Wolfgang Filter, K. Weber, Integration Theory, Chapman & Hall, page 5

We say that a set S {\displaystyle S} has a finite partition into subsets S 1 , … , S n {\displaystyle S_{1},\dots ,S_{n}} , if S = S i ∪ ⋯ ∪ S n {\displaystyle S=S_{i}\cup \dots \cup S_{n}} , where the subsets are pairwise disjoint, that is, S i ∩ S j = ∅ {\displaystyle S_{i}\cap S_{j}=\emptyset } , if i ≠ j {\displaystyle i\neq j} . (We do not require that the subsets be nonempty.)

2007, Judith D. Sally, Paul J. Sally, Jr., Roots to Research: A Vertical Development of Mathematical Problems, American Mathematical Society, page 280