View source for Subset

==English==
{{wikipedia}}

===Etymology===
From {{prefix|en|sub|set}}.

===Pronunciation===
* {{IPA|en|/ˈsʌbˌsɛt/|a=UK}}
* {{audio|en|en-us-subset.ogg|a=US}}

===Noun===
{{en-noun}}

# {{lb|en|set theory|of a set S}} A [[set]] ''A'' such that every [[element]] of ''A'' is also an element of ''S''.
#: {{usex|en|The set of [[integers]] is a '''subset''' of the set of [[real numbers]].}}
#: {{usex|en|The set <math>\lbrace a, b\rbrace</math> is a both a '''subset''' and a [[proper subset|proper '''subset''']] of <math>\lbrace a, b, c\rbrace</math> while the set <math>\lbrace a, b, c\rbrace</math> is a '''subset''' of <math>\lbrace a, b, c\rbrace</math> but not a proper '''subset''' of <math>\lbrace a, b, c\rbrace</math>.}}
#* '''1963''', David B. MacNeil, ''Modern Mathematics for the Practical Man'', {{w|David Van Nostrand}}, Republished as 2013, David B. MacNeil, ''Fundamentals of Modern Mathematics: A Practical Review'', {{w|Dover Publications|Dover}}, [https://books.google.com.au/books?id=ZdfCAgAAQBAJ&pg=PA3&dq=%22subset%22%7C%22subsets%22&hl=en&sa=X&ved=0ahUKEwjd0KnqysHbAhUqGTQIHRPxAPIQ6AEI_gEwJw#v=onepage&q=%22subset%22%7C%22subsets%22&f=false 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''.
#* {{quote-book|en|year=1997|author=Wolfgang Filter; K. Weber|title=Integration Theory|publisher=w:Chapman & Hall|pageurl=https://books.google.com.au/books?id=Bteluw-7IuEC&pg=PA5&dq=%22subset%22%7C%22subsets%22&hl=en&sa=X&ved=0ahUKEwjd0KnqysHbAhUqGTQIHRPxAPIQ6AEIpgIwLg#v=onepage&q=%22subset%22%7C%22subsets%22&f=false|page=5
|passage=Let <math>A</math> be a '''subset''' of the topological space <math>X</math> and take <math>x\in X</math>.}}
#* {{quote-book|en|year=2007|author=Judith D. Sally; Paul J. Sally, Jr.|title=Roots to Research: A Vertical Development of Mathematical Problems|publisher=w:American Mathematical Society|pageurl=https://books.google.com.au/books?id=nHxBw-WlECUC&pg=PA280&dq=%22subset%22%7C%22subsets%22&hl=en&sa=X&ved=0ahUKEwjd0KnqysHbAhUqGTQIHRPxAPIQ6AEI8AEwJA#v=onepage&q=%22subset%22%7C%22subsets%22&f=false|page=280
|passage=We say that a set <math>S</math> has a ''finite partition'' into '''subsets''' <math>S_1,\dots,S_n</math>, if <math>S = S_i \cup\dots\cup S_n</math>, where the '''subsets''' are pairwise disjoint, that is, <math>S_i\cap S_j = \empty</math>, if <math>i\ne j</math>. (We do not require that the '''subsets''' be nonempty.)}}
# A group of things or people, all of which are in a specified larger group.
#: {{usex|en|We asked a '''subset''' of the population of the town for their opinion.}}

====Usage notes====
* {{sense|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====
* {{l|en|subclass}}

====Antonyms====
* {{l|en|superclass}}
* {{l|en|superset}}

====Derived terms====
{{col|en|multiplicative subset|subset classifier|proper subset<t:subset that is strictly less than the given other set>}}

====Translations====
{{trans-top|set whose elements are within another given set}}
* Bulgarian: {{t|bg|подмножество|n}}
* Catalan: {{t|ca|subconjunt|m}}
* Chinese:
*: Mandarin: {{t+|cmn|子集|tr=zǐjí}}
* Czech: {{t+|cs|podmnožina|f}}
* Danish: {{t|da|delmængde|c}}
* Dutch: {{t+|nl|deelverzameling}}
* Estonian: {{t|et|alamhulk}}
* Finnish: {{t+|fi|osajoukko}}
* French: {{t+|fr|sous-ensemble|m}}
* Georgian: {{t|ka|ქვესიმრავლე|sc=Geor}}
* German: {{t|de|Untermenge|f}}, {{t+|de|Teilmenge|f}}
* Greek: {{t+|el|υποσύνολο|n}}
* Hebrew: {{t|he|תת קבוצה|sc=Hebr}}
* Hindi: {{t|hi|उपसमुच्चय}}
* Hungarian: {{t+|hu|részhalmaz}}
* Icelandic: {{t|is|hlutmengi|n}}
* Irish: {{t|ga|fo-thacar|m}}
* Italian: {{t+|it|sottoinsieme|m}}
* Japanese: {{t+|ja|部分集合|tr=ぶぶんしゅうごう, bubun jūgō|sc=Jpan}}
* Korean: {{t+|ko|부분집합}}
* Macedonian: {{t|mk|подмно́жество|n}}
* Pannonian Rusyn: {{t|rsk|подмножество|n}}
* Polish: {{t+|pl|podzbiór|m}}
* Portuguese: {{t+|pt|subconjunto|m}}
* Romanian: {{t+|ro|submulțime|f}}
* Russian: {{t+|ru|подмно́жество|n}}
* Slovene: {{t|sl|podmnožica|f}}
* Spanish: {{t|es|subconjunto|m}}
* Swedish: {{t+|sv|delmängd|c}}
* Tagalog: {{t|tl|kubtangkas}}
* Ukrainian: {{t|uk|підмножина́|f}}
* Vietnamese: {{t|vi|tập hợp con}}, {{t|vi|tập con}}
* Welsh: {{t|cy|is-set|f}}
{{trans-bottom}}

{{trans-top|group contained in a larger group}}
* Finnish: {{t+|fi|osajoukko}}
* French: {{t+|fr|sous-ensemble|m}}
* Italian: {{t|it|sottogruppo|m}}
* Kurdish:
*: Northern Kurdish: {{t|kmr|binkom|f}}
* Polish: {{t|pl|podgrupa|f}}
* Portuguese: {{t+|pt|subconjunto|m}}, {{t+|pt|subgrupo|m}}
* Romanian: {{t|ro|subgrup|n}}, {{t+|ro|subclasă|f}}
* Russian: {{t+|ru|подгру́ппа|f}}
* Welsh: {{t|cy|is-set|f}}, {{t|cy|isgasgliad|m}}
{{trans-bottom}}

===Verb===
{{en-verb|++}}

# {{lb|en|transitive}} To take a subset of.
# {{lb|en|transitive|computing|typography}} To extract only the portions of (a [[font]]) that are needed to display a particular [[document]].