Lecture

Linear Algebra: Sets and Subsets

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Description

This lecture covers the fundamental concepts of sets and subsets in the context of linear algebra, including the definition of sets, subsets, and operations on subsets. The instructor explains the language of logic used in defining sets and explores the properties of sets and their elements. The lecture also delves into the concepts of unions, intersections, and complements of sets, providing examples to illustrate these operations.

Official source

Ontological neighbourhood

Mathematics

Mathematical logic: Set theory

Related concepts (32)

Language

Language is a structured system of communication that consists of grammar and vocabulary. It is the primary means by which humans convey meaning, both in spoken and written forms, and may also be conveyed through sign languages. The vast majority of human languages have developed writing systems that allow for the recording and preservation of the sounds or signs of language. Human language is characterized by its cultural and historical diversity, with significant variations observed between cultures and across time.

Computer graphics

Computer graphics deals with generating s and art with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by computer graphics hardware. It is a vast and recently developed area of computer science. The phrase was coined in 1960 by computer graphics researchers Verne Hudson and William Fetter of Boeing.

Disjoint sets

In mathematics, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two or more sets is called disjoint if any two distinct sets of the collection are disjoint. This definition of disjoint sets can be extended to families of sets and to indexed families of sets.

Family of sets

In set theory and related branches of mathematics, a collection of subsets of a given set is called a family of subsets of , or a family of sets over More generally, a collection of any sets whatsoever is called a family of sets, set family, or a set system. A family of sets may be defined as a function from a set , known as the index set, to , in which case the sets of the family are indexed by members of .

Set (mathematics)

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.

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