subset

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subset

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From sub- +‎ set.

• (UK) IPA^(key): /ˈsʌbˌsɛt/

• Audio (US):

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subset (plural subsets)

1. (set theory, of 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 ${\displaystyle \lbrace a,b\rbrace }$ is a both a subset and a proper subset of ${\displaystyle \lbrace a,b,c\rbrace }$ while the set ${\displaystyle \lbrace a,b,c\rbrace }$ is a subset of ${\displaystyle \lbrace a,b,c\rbrace }$ but not a proper subset of ${\displaystyle \lbrace a,b,c\rbrace }$.

   • 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.

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

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

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

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

2. 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.

• (set theory):
  • The subset relation is denoted ⊆ (⊂ for proper subset), and one writes A ⊆ B for "A is a subset of B".
  • It is permissible for A to contain no elements: the empty set is a subset of every set (including itself).

• subclass

• superclass
• superset

subset (third-person singular simple present subsets, present participle subsetting, simple past and past participle subsetted)

1. (transitive) To take a subset of.
2. (transitive, computing, typography) To extract only the portions of (a font) that are needed to display a particular document.