subset

English

Etymology

From sub- +‎ set.

Pronunciation

• (UK) IPA^(key): /ˈsʌbˌsɛt/

• Audio (US):

  (file)

Noun

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 $\lbrace a,b\rbrace$ is a both a subset and a proper subset of $\lbrace a,b,c\rbrace$ while the set $\lbrace a,b,c\rbrace$ is a subset of $\lbrace a,b,c\rbrace$ but not a proper subset of $\lbrace a,b,c\rbrace$.

   • 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 $A$ be a subset of the topological space $X$ and take $x\in X$.

   • 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 $S$ has a finite partition into subsets $S_{1},\dots ,S_{n}$, if $S=S_{i}\cup \dots \cup S_{n}$, where the subsets are pairwise disjoint, that is, $S_{i}\cap S_{j}=\emptyset$, if $i\neq j$. (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.

Usage notes

• (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).

Synonyms

• subclass

Antonyms

• superclass
• superset

Derived terms

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

 

Translations

set whose elements are within another given set

• Bulgarian: подмножество n (podmnožestvo)
• Catalan: subconjunt m
• Chinese:

  Mandarin: 子集 (zh) (zǐjí)

• Czech: podmnožina (cs) f
• Danish: delmængde c
• Dutch: deelverzameling
• Estonian: alamhulk
• Finnish: osajoukko (fi)
• French: sous-ensemble (fr) m
• Georgian: ქვესიმრავლე (kvesimravle)
• German: Untermenge f, Teilmenge (de) f
• Greek: υποσύνολο (el) n (yposýnolo)
• Hebrew: תת קבוצה
• Hindi: उपसमुच्चय (upasmuccay)
• Hungarian: részhalmaz (hu)
• Icelandic: hlutmengi n
• Irish: fo-thacar m
• Italian: sottoinsieme (it) m
• Japanese: 部分集合 (ja) (ぶぶんしゅうごう, bubun jūgō)
• Korean: 부분집합 (ko) (bubunjiphap)
• Macedonian: подмно́жество n (podmnóžestvo)
• Pannonian Rusyn: подмножество n (podmnožestvo)
• Polish: podzbiór (pl) m
• Portuguese: subconjunto (pt) m
• Romanian: submulțime (ro) f
• Russian: подмно́жество (ru) n (podmnóžestvo)
• Slovene: podmnožica f
• Spanish: subconjunto m
• Swedish: delmängd (sv) c
• Tagalog: kubtangkas
• Ukrainian: підмножина́ f (pidmnožyná)
• Vietnamese: tập hợp con, tập con
• Welsh: is-set f

group contained in a larger group

• Finnish: osajoukko (fi)
• French: sous-ensemble (fr) m
• Italian: sottogruppo m
• Kurdish:

  Northern Kurdish: binkom f

• Polish: podgrupa f
• Portuguese: subconjunto (pt) m, subgrupo (pt) m
• Romanian: subgrup n, subclasă (ro) f
• Russian: подгру́ппа (ru) f (podgrúppa)
• Welsh: is-set f, isgasgliad m

Verb

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.