Concept

Relation (mathematics)

In mathematics, a binary relation on a set may, or may not, hold between two given set members. For example, "is less than" is a relation on the set of natural numbers; it holds e.g. between 1 and 3 (denoted as 1

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https://en.wikipedia.org/wiki/Relation_(mathematics)

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Related courses (2)

CS-101: Advanced information, computation, communication I

Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics a

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The goal of this course is to give an introduction to the theory of distributions and cover the fundamental results of Sobolev spaces including fractional spaces that appear in the interpolation theor

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Cartesian product

In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. In terms of set-builder notation, that is A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product rows × columns is taken, the cells of the table contain ordered pairs of the form (row value, column value).

Element (mathematics)

In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. Writing means that the elements of the set A are the numbers 1, 2, 3 and 4. Sets of elements of A, for example , are subsets of A. Sets can themselves be elements. For example, consider the set . The elements of B are not 1, 2, 3, and 4. Rather, there are only three elements of B, namely the numbers 1 and 2, and the set . The elements of a set can be anything. For example, is the set whose elements are the colors , and .

Universe (mathematics)

In mathematics, and particularly in set theory, , type theory, and the foundations of mathematics, a universe is a collection that contains all the entities one wishes to consider in a given situation. In set theory, universes are often classes that contain (as elements) all sets for which one hopes to prove a particular theorem. These classes can serve as inner models for various axiomatic systems such as ZFC or Morse–Kelley set theory. Universes are of critical importance to formalizing concepts in inside set-theoretical foundations.

Official source

https://en.wikipedia.org/wiki/Relation_(mathematics)

About this result

Related courses (2)

CS-101: Advanced information, computation, communication I

MATH-502: Distribution and interpolation spaces

Related lectures (9)

Relations: Definitions and Properties

Explains binary relations, reflexive, symmetric, antisymmetric, and transitive relations on a set.

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Relations: Reflexive, Symmetric, Antisymmetric, Transitive

Explains binary relations on a set and their properties with illustrative examples.

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Experimental and ab initio derivation of interface stress in nanomultilayered coatings: Application to immiscible Cu/W system with variable in-plane stress

Pandula Manura Liyanage, Claudia Cancellieri, Giacomo Lorenzin

Interface stress is a fundamental descriptor for interphase boundaries and is defined in strict relation to the interface energy. In nanomultilayers with their intrinsically high interface density, the functional properties are dictated by the interface st ...

Elsevier2024

Absolute Structure from Scanning Electron Microscopy

Philip Johannes Walter Moll

The absence of centrosymmetry in chiral and polar crystal structures is the reason for many technical relevant physical properties like optical birefringence or ferroelectricity. Other chirality related properties that are actually intensively investigated ...

Nature Research2020

Asset Pricing When 'This Time Is Different'

Pierre Collin Dufresne

Recent evidence suggests that younger people update beliefs in response to aggregate shocks more than older people. We embed this generational learning bias in an equilibrium model in which agents have recursive preferences and are uncertain about exogenou ...

Oxford Univ Press Inc2017

Related concepts (15)

Cartesian product

Element (mathematics)

Universe (mathematics)