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subset

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subset

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Fromsub- +‎set.

subset (pluralsubsets)

(set theory, of a set S) AsetA such that everyelement ofA is also an element ofS.
The set ofintegers is asubset of the set ofreal numbers.
The set $\lbrace a,b\rbrace$ is a both asubset and apropersubset of $\lbrace a,b,c\rbrace$ while the set $\lbrace a,b,c\rbrace$ is asubset of $\lbrace a,b,c\rbrace$ but not a propersubset 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 setD of the first four letters of the alphabet, was asubset of the setA of all the letters of the alphabet, becauseA includes all the members ofD.
- 1997, Wolfgang Filter, K. Weber,Integration Theory,Chapman & Hall,page 5:
  Let $A {\displaystyle A}$ be asubset of the topological space $X {\displaystyle X}$ 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,page280:
  We say that a set $S {\displaystyle S}$ has afinite partition intosubsets $S_{1},\dots ,S_{n}$ , if $S=S_{i}\cup \dots \cup S_{n}$ , where thesubsets are pairwise disjoint, that is, $S_{i}\cap S_{j}=\emptyset$ , if $i\neq j$ . (We do not require that thesubsets be nonempty.)
A group of things or people, all of which are in a specified larger group.
We asked asubset of the population of the town for their opinion.

(set theory):
- The subsetrelation is denoted⊆ (⊂ forproper subset), and one writesA ⊆B for "A is asubset ofB".
- It is permissible forA to contain no elements: theempty set is a subset of every set (including itself).

set whose elements are within another given set

group contained in a larger group

subset (third-person singular simple presentsubsets,present participlesubsetting,simple past and past participlesubsetted)

(transitive) To take a subset of.
(transitive, computing, typography) To extract only the portions of (afont) that are needed to display a particulardocument.