Definable real number

What are Real Numbers? | Don't Memorise

Watch this video to understand what Real Numbers are! To access all videos on Real Numbers, please enroll in our full course here - https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=3YwrcJxEbZw&utm_term=%7Bkeyword%7D In this video, w

From playlist 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

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

Tutorial - What is an imaginary number

http://www.freemathvideos.com In this video playlist you will learn everything you need to know with complex and imaginary numbers

From playlist Complex Numbers

Algebraic numbers are countable

Transcendental numbers are uncountable, algebraic numbers are countable. There are two kinds of real numbers: The algebraic numbers (like 1, 3/4, sqrt(2)) and the transcendental numbers (like pi or e). In this video, I show that the algebraic numbers are countable, which means that there

From playlist Real Numbers

Real Numbers

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From playlist Integers

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

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From playlist Introduction to Complex Numbers

What are imaginary numbers?

Imaginary numbers are any numbers that include the imaginary number i. A mix of imaginary and real numbers gives you what’s called a complex number. The primary reason we use imaginary numbers is to give us a way to find the root (radical) of a negative number. There’s no way to use real

From playlist Popular Questions

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

Cardinality of the Continuum

What is infinity? Can there be different sizes of infinity? Surprisingly, the answer is yes. In fact, there are many different ways to make bigger infinite sets. In this video, a few different sets of infinities will be explored, including their surprising differences and even more surpris

From playlist Summer of Math Exposition 2 videos

Analytic Continuation and the Zeta Function

Where do complex functions come from? In this video we explore the idea of analytic continuation, a powerful technique which allows us to extend functions such as sin(x) from the real numbers into the complex plane. Using analytic continuation we can finally define the zeta function for co

From playlist Analytic Number Theory

What is General Relativity? Special Lecture: Tangent Spaces and Coordinate Basis

What is General Relativity? Special Lecture: Tangent Spaces and Coordinate Basis This is a LONG lecture covering a narrow but important topic: tangent spaces and the coordinate basis. It is intended for anyone who has trouble understanding why a manifold has a vector space at every point

From playlist What is a Manifold?

Construction of the Real Numbers

Dedekind Cuts In this video, I rigorously construct the real numbers from the rational numbers using so-called Dedekind Cuts. It might seem complicated at first, but the advantage is that we can construct the real numbers without using any axioms. More importantly, in the next video, we u

From playlist Real Numbers

What is a Tensor 3: Dual Spaces

What is a Tensor? Dual Spaces

From playlist What is a Tensor?

11/16/2019, Jonathan Kirby, University of East Anglia

Jonathan Kirby, University of East Anglia Local Definability of Holomorphic Functions Given a collection F of complex or real analytic functions, one can ask what other functions are obtainable from them by finitary algebraic operations. If we just mean polynomial operations we get some

From playlist Fall 2019 Kolchin Seminar in Differential Algebra

Are the real numbers... REAL?

The first video in a series which will build up to defining the p-adic numbers. In this episode, we break down our intuitive understanding of the real numbers, and build it back up again using the formality of Cauchy sequences. #some2 #SoME2 My Twitter: https://twitter.com/KristapsBalodi

From playlist Summer of Math Exposition 2 videos

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

Who Gives a Sheaf? Part 2: A non-example

In this video we compare two pre-sheaves, one which is a sheaf, and one which is not.

From playlist Who Gives a Sheaf?

What is a complex number

http://www.freemathvideos.com In this video playlist you will learn everything you need to know with complex and imaginary numbers

From playlist Simplify Rational Expressions

Peter Scholze - Liquid vector spaces

Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ (joint with Dustin Clausen) Based on the condensed formalism, we propose new foundations for real functional analysis, replacing complete locally convex vector spaces with a vari

From playlist Toposes online