Construction of the real numbers

Real Numbers

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From playlist Integers

What is a Rational Number?

Construction of the rational numbers In this video, I construct the rational numbers starting from the integers, using equivalence relation and equivalence classes. After this video, you can finally understand what 1/2 really means! Enjoy! Check out my Real Numbers Playlist: https://www.

From playlist Real Numbers

What is a number ?

Construction of Natural Numbers In this, I rigorously define the concept of a natural number, using Peano's axioms. I also explain why those axioms are the basis for the principle of mathematical induction. Enjoy! Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=

From playlist Real Numbers

Set Theory (Part 14a): Constructing the Complex Numbers

Please leave your thoughts and questions below! In this video, we will extend the real numbers to the complex numbers and investigate the algebraic structure of the complex numbers after defining addition and multiplication of these new objects. We will also begin to see how complex numbe

From playlist Set Theory by Mathoma

What is a real number?

Ordered Fields In this video, I define the notion of an order (or inequality) and then define the concept of an ordered field, and use this to give a definition of R using axioms. Actual Construction of R (with cuts): https://youtu.be/ZWRnZhYv0G0 COOL Construction of R (with sequences)

From playlist Real Numbers

Identifying Sets of Real Numbers

This video provides several examples of identifying the sets a real number belongs to. Complete Video Library: http://www.mathispower4u.com Search by Topic: http://www.mathispower4u.wordpress.com

From playlist Number Sense - Properties of Real Numbers

Ex: Determine a Real, Imaginary, and Complex Number

This video explains how decide if a number is best described by the set of real, imaginary, or complex numbers. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com

From playlist Performing Operations with Complex Numbers

How to construct the (true) complex numbers I | Famous Math Problems 21a | N J Wildberger

The usual story of complex numbers needs to be strengthened and enlarged for the 21st century! Supposing that the complex numbers are a quadratic field extension of the "real numbers" is clearly inadequate, as the arithmetic of "real numbers" is mostly absent, and essentially vacuous. Noti

From playlist Famous Math Problems

Geometry of Complex Numbers (2 of 6: Real vs. Complex)

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From playlist Introduction to Complex Numbers

Visual Group Theory, Lecture 6.7: Ruler and compass constructions

Visual Group Theory, Lecture 6.7: Ruler and compass constructions Inspired by philosophers such as Plato and Aristotle, one of the chief purposes of ancient Greek mathematics was to find exact constructions for various lengths, using only the basic tools of a ruler and compass. However, t

From playlist Visual Group Theory

Representations of p-adic groups for non-experts - Jessica Fintzen

Short Talks by Postdoctoral Members Topic: Representations of p-adic groups for non-experts Speaker: Jessica Fintzen Affiliation: University of Cambridge and Duke University; Member, School of Mathematics Date: October 1, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Wolfram Physics Project: Working Session Tuesday, Nov. 2, 2021 [Topos Theory]

This is a Wolfram Physics Project working session about Topos Theory in the Wolfram Model. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/

From playlist Wolfram Physics Project Livestream Archive

SHM - 16/01/15 - Constructivismes en mathématiques - Henri Lombardi

Henri Lombardi (LMB, Université de Franche-Comté), « Foundations of Constructive Analysis, Bishop, 1967 : une refondation des mathématiques, constructive, minimaliste et révolutionnaire »

From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques

Henri Lombardi: A geometric theory for the constructive real number system and for o-minimal struct

Title: Henri Lombardi: A geometric theory for the constructive real number system and for o-minimal structures The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: We work in a pure constructive context, minimalist, à la Bish

From playlist Workshop: "Constructive Mathematics"

Jessica Fintzen - 1/2 Supercuspidal Representations: Construction, Classification, and Characters

We have seen in the first week of the summer school that the buildings blocks for irreducible representations of p-adic groups are the supercuspidal representations. In these talks we will explore explicit exhaustive constructions of these supercuspidal representations and their character

From playlist 2022 Summer School on the Langlands program

Five Stages of Accepting Constructive Mathematics - Andrej Bauer

Andrej Bauer University of Ljubljana, Slovenia; Member, School of Mathematics March 18, 2013 Discussions about constructive mathematics are usually derailed by philosophical opinions and meta-mathematics. But how does it actually feel to do constructive mathematics? A famous mathematician

From playlist Mathematics

Micaela Mayero - Overview of real numbers in theorem provers: application with real analysis in Coq

Recorded 15 February 2023. Micaela Mayero of the Galilee Institute - Paris Nord University presents "An overview of the real numbers in theorem provers: an application with real analysis in Coq" at IPAM's Machine Assisted Proofs Workshop. Abstract: Formalizing real numbers in a formal proo

From playlist 2023 Machine Assisted Proofs Workshop

Representations of p-adic groups - Jessica Fintzen

Workshop on Representation Theory and Geometry Topic: Representations of p-adic groups Speaker: Jessica Fintzen Affiliation: University of Cambridge and Duke University; Member, School of Mathematics Date: April 02, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

Geometric Impossibilities, Part 3: Modern Field Theory

In this third installment, we talk about some basic results in the theory of fields, setting us up to discuss the proof of the famous impossibilities.

From playlist Geometric Impossibilities

Imaginary Numbers, Functions of Complex Variables: 3D animations.

Visualization explaining imaginary numbers and functions of complex variables. Includes exponentials (Euler’s Formula) and the sine and cosine of complex numbers.

From playlist Physics