different between subset vs pseudotriangle

English

Etymology

sub- +? set.

Pronunciation

• (UK) IPA^(key): /?s?b?s?t/

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.
   • 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.

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

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

Translations

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.

English

Etymology

pseudo- +? triangle

Noun

pseudotriangle (plural pseudotriangles)

1. (mathematics) Any subset of a plane that lies between any three mutually tangent convex sets