Mathematics, Sciences, Set theoryOf a set S A set A such that every element of A is also an element of S.
The set of integers is a subset of the set of real numbers.
The set #92;lbracea,b#92;rbrace is a both a subset and a proper subset of #92;lbracea,b,c#92;rbrace while the set #92;lbracea,b,c#92;rbrace is a subset of #92;lbracea,b,c#92;rbrace but not a proper subset of #92;lbracea,b,c#92;rbrace.
3 more examples
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#92;inX.1997, Wolfgang Filter, K. Weber, Integration Theory, Chapman & Hall, page 5:
We say that a set S has a finite partition into subsets S#95;1,#92;dots,S#95;n, if S#61;S#95;i#92;cup#92;dots#92;cupS#95;n, where the subsets are pairwise disjoint, that is, S#95;i#92;capS#95;j#61;#92;empty, if i#92;nej. (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:
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A group of things or people, all of which are in a specified larger group.
We asked a subset of the population of the town for their opinion.
Interestingly, this [the core lexicon] is not all of the words of the language: It turns out that most of the words in a language from an industrialized culture come from narrow semantic domains, such that only a subset of speakers know them.2025, Edward A. F. Gibson, “Introduction” (chapter 1), in Syntax: A Cognitive Approach, MIT Press, →DOI, →ISBN, page 2: