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sub- +‎ set.



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   is a both a subset and a proper subset of   while the set   is a subset of   but not a proper subset of  .
    • 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   be a subset of the topological space   and take  .
    • 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   has a finite partition into subsets  , if  , where the subsets are pairwise disjoint, that is,  , if  . (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.

Usage notesEdit

  • (set theory):
    • The subset relation is denoted ( for proper subset), and one writes AB 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).


Derived termsEdit

  • proper subset (subset that is strictly less than the given other set)



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.