Concept

Transitive relation

Related lectures (23)

Relations: Definitions and Properties

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

Relations: Reflexive, Symmetric, Antisymmetric, Transitive

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

Sets and Functions

Introduces binary relations, functions, and various types of relations in sets.

Force-extension relation of a polymer

Explores the force-extension relation of polymers through experiments and models.

Binary Relations and Cartesian Products

Explores binary relations, Cartesian products, and applications between sets, emphasizing their properties and significance.

Möbius inversion: posets

Covers the Möbius inversion for posets, defining partially ordered sets and explaining the incidence algebra.

Equivalence Relations and Partitions

Discusses equivalence relations, partitions, reflexivity, symmetry, transitivity, and set cardinality.

Logical Expressions and Equivalence Relations

Covers logical expressions, sets, elements, and equivalence relations.

Relations and Sequences

Covers relations, sequences, and posets, emphasizing properties like anti-symmetry and transitivity, and introduces arithmetic and geometric progressions.

Equivalence Relations: Classes, Partitions

Covers equivalence relations, classes, and partitions of a set.

Equivalence Relations: Relations, Sequences and Summations

Explores equivalence relations, functions, subsets, and De Morgan's laws.

Equivalence Relations

Covers the concept of equivalence relations and how to determine them.

Relations in Computer Science

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

Group Actions on Lattices

Explores group actions on lattices, emphasizing GL₂(Q) and GL₂(Ag) compatibility and alternative formulations.

Partial Ordering: Relations, Sequences, Summation

Introduces partial orderings, lattices, and lexicographic orderings on Cartesian products.

Understanding Equivalence Relations and Integer Construction

Covers the construction of integers through equivalence relations and their properties in mathematics.

Equivalence Classes and Relations

Covers equivalence classes, relations, quotient sets, and functions properties.

Cyclic Groups: Structure and Applications

Explores cyclic groups, generators, isomorphisms, and the discrete logarithm problem in depth, highlighting their importance and applications.

Equivalence Relations: Classes, Partitions

Explains equivalence relations, classes, and partitions in sets.

Introduction to Real Numbers

Introduces the properties and structure of real numbers, emphasizing completeness and the Archimedean property.