Infinity | Philosophy of mathematics

In the philosophy of mathematics, the abstraction of actual infinity involves the acceptance (if the axiom of infinity is included) of infinite entities as given, actual and completed objects. These might include the set of natural numbers, extended real numbers, transfinite numbers, or even an infinite sequence of rational numbers. Actual infinity is to be contrasted with potential infinity, in which a non-terminating process (such as "add 1 to the previous number") produces a sequence with no last element, and where each individual result is finite and is achieved in a finite number of steps. As a result, potential infinity is often formalized using the concept of limit. (Wikipedia).

Definition of infinity In this video, I define the concept of infinity (as used in analysis), and explain what it means for sup(S) to be infinity. In particular, the least upper bound property becomes very elegant to write down. Check out my real numbers playlist: https://www.youtube.co

From playlist Real Numbers

Can You Define the Immeasurable?

What is infinity? Can you define something that, by definition, has no boundaries? A subject extensively studied by philosophers, mathematicians, and more recently, physicists and cosmologists, infinity still stands as an enigma of the intellectual world. We asked people from all walks of

From playlist Mathematics

What’s the biggest number you can think of? Well, what about one more than that number? We can’t really comprehend the idea of infinity, but it’s still a useful concept in science. Brian Greene explains more. Subscribe to our YouTube Channel for all the latest from World Science U. Visit

From playlist Science Unplugged: Physics

How many kinds of infinity are there?

A lot. List with links: http://vihart.com/how-many-kinds-of-infinity-are-there/

From playlist Doodling in Math and more | Math for fun and glory | Khan Academy

Touching Infinity: It's Not Out of Reach

The conventional way to represent the Real Number system is to think of the numbers as corresponding to points along an infinite straight line. The problem is that in this representation there is no place for "infinity". Infinity is not a real number. This video shows an alternate visua

From playlist Lessons of Interest on Assorted Topics

To check out the physics courses that I mentioned (many of which are free!) and to support this channel, go to https://brilliant.org/Sabine/ and create your Brilliant account. The first 200 will get 20% off the annual premium subscription. Correction: At 4 mins 44 seconds, it should be t

From playlist Philosophy of Science

It's a concept which intrigues mathematicians, but scientists aren't so keen on it. More at http://www.sixtysymbols.com/

From playlist From Sixty Symbols

This video provides a description of infinity with several examples. http://mathispower4u.com

From playlist Linear Inequalities in One Variable Solving Linear Inequalities

Charles Rezk - 4/4 Higher Topos Theory

Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RezkNotesToposesOnlinePart4.pdf In this series of lectures I will give an introduction to the concept of "infinity

From playlist Toposes online

Charles Rezk - 3/4 Higher Topos Theory

Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RezkNotesToposesOnlinePart3.pdf In this series of lectures I will give an introduction to the concept of "infinity

From playlist Toposes online

How to visualize infinity in concrete terms.

From playlist Summer of Math Exposition 2 videos

Christina Sormani: A Course on Intrinsic Flat Convergence part 5

The lecture was held within the framework of the Hausdorff Trimester Program: Optimal Transportation and the Workshop: Winter School & Workshop: New developments in Optimal Transport, Geometry and Analysis

From playlist HIM Lectures 2015

Indeterminate Forms In this video, I introduce the concept of indeterminate forms and explain why it is necessary to even have calculus. Then, I go over the main forms, all while emphasizing that in each of them, there is a tug-of-war situation going on. Enjoy! Check out my Calculus Play

From playlist Calculus

Charles Rezk - 1/4 Higher Topos Theory

Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RezkNotesToposesOnlinePart1.pdf In this series of lectures I will give an introduction to the concept of "infinity

From playlist Toposes online

Transformations of Functions | Preparing for Precalculus Part 3

I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. If I helped you in this video, I would love to have you subscribe. My subscribers are my

From playlist Preparing for Precalculus

Higher Algebra 10: E_n-Algebras

In this video we introduce E_n-Algebras in arbitrary symmetric monoidal infinity-categories. These interpolate between associated algebras (= E_1) and commutative algebras (= E_infinity). We also establish some categorical properties and investigate the case of the symmetric monoidal infin

From playlist Higher Algebra

A subject extensively studied by philosophers, mathematicians, and now recently, physicists, infinity is a uniquely universal enigma within the academic world. Thinkers clash over questions such as: Does infinity exist? What types of infinity are there? Watch the Full Program Here: https:

From playlist Mathematics

Theorems about sequences -- Calculus II

This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.

From playlist Calculus II