Concept

Constructive set theory

Related lectures (32)

Cartesian Product MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Covers the concept of the Cartesian product, emphasizing the order of elements in pairs.

Cartesian Product in Linear Algebra

Explores the Cartesian product in linear algebra and the method of induction for proving propositions.

Abstract Concepts: Semi-Ring

Explores the concept of a commutative semi-ring based on set theory properties.

Commutation Groups: Euler's Totient Function

Explores commutative groups, Euler's Totient Function, and Cartesian products in group theory.

Lifting properties and model categories

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

Limits and colimits: Two examples

Focuses on the pushout and pullback constructions in sets, illustrating colimits and limits with explicit examples.

Set Difference: Definition and Examples

Explains set difference and complement calculation with clear examples.

Recap of Group Theory

Provides a recap of group theory, defining a group as a set with a multiplication operation.

The Pigeonhole Principle: Basics and Applications

Covers the Pigeonhole Principle, its applications, and examples of its guarantees.

Counting Basics: Set Theory and Permutations

Covers the main rules of counting for combinatorial objects and introduces various counting techniques.

Real Numbers: Sets and Operations

Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.

Linear Algebra: Injective Functions

Focuses on injective functions in linear algebra, demonstrating how to verify properties and prove injectivity.

Crystallography: Describing Periodic Structures

Covers crystallography, lattice structures, vectors, and diffraction patterns.

Set Theory: Introduction and Operations

Covers the foundation of mathematics through set theory concepts like membership and unions.

Set Theory: Operations and Functions

Covers set theory operations and functions, including injections and surjections.

Formal Languages: Concepts

Covers the basics of formal languages, including alphabets, words, and languages, as well as operations like concatenation and reversal.

Linear Algebra: Propositions and Sets

Covers propositions indexed by vectors, proof by induction, and Cartesian products of sets.

Sigma Field: Random Variables

Explores sigma fields generated by random variables and their connection to measurable functions.

Group Actions on Sets

Explores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.

Logical Structure: Choice and Bar Induction Principles

Covers the logical structure of principles equivalent to choice and bar induction, focusing on generalized dependent choice and its implications in mathematics.