Infinity | Axioms of set theory

Axiom of infinity

In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set, namely a set containing the natural numbers. It was first published by Ernst Zermelo as part of his set theory in 1908. (Wikipedia).

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What is infinity ?

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

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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

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Infinity root of infinity

A classic calculus 1 limit problem, evaluating the limit of x-th root of x as x goes to infinity. This is an inf^0 indeterminate form example. We will have to convert the x-root of x to x^(1/x) and then write x as e^ln(x) and use L'Hopital's Rule. Try this next: what do you think what (inf

From playlist Calculus Limits

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Limits At Infinity

http://mathispower4u.wordpress.com/

From playlist Limits

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Calculus 1: Limits & Derivatives (12 of 27) When the Limit = Infinity (Vertical Asymptotes)

Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the limit of a function where the limit = infinity because of the vertical asymptotes. Next video in the series can be seen at: http://youtu.be/CRj1Uyyjn3Q

From playlist CALCULUS 1 CH 1 LIMITS & DERIVATIVES

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Zermelo Fraenkel Infinity

This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axiom of infinity, and give some examples of models where it does not hold. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50fRP2_SbG

From playlist Zermelo Fraenkel axioms

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Introduction to Infinite Limits in Calculus 1

Introduction to Infinite Limits in Calculus 1

From playlist Calculus 1 Exam 1 Playlist

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Calculus 2.6 Limits at Infinity

My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart

From playlist Calculus

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Introduction to Limits at Infinity (Part 1)

This video introduces limits at infinity. https://mathispower4u.com

From playlist Limits at Infinity and Special Limits

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How To Count Past Infinity

Support Vsauce, your brain, Alzheimer's research, and other YouTube educators by joining THE CURIOSITY BOX: a seasonal delivery of viral science toys made by Vsauce! A portion of all proceeds goes to Alzheimer's research and our Inquisitive Fellowship, a program that gives money and resour

From playlist Knowledge

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Set Theory 1.2 : Ordinals

In this video, I introduce the Von Neumann construction of the ordinals, including ones that are infinite/transfinite! Email : fematikaqna@gmail.com Subreddit : https://reddt.com/r/Fematika Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Set Theory

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Axioms of Constructive Set Theory Explained

In this video we're going to discuss the various axiom schemes of constructive set theories and how they relate to type theory. I cover BCST, ECST, IKP, KPI, KP, CST, CZF, IZF, Mac Lane, Z and variants equi-consistent to ETCS from category theory, and then of course ZF and ZFC. The text I

From playlist Logic

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Zermelo Fraenkel Introduction

This lecture is part of an online course on the Zermelo Fraenkel axioms of set theory. This lecture gives an overview of the axioms, describes the von Neumann hierarchy, and sketches several approaches to interpreting the axioms (Platonism, von Neumann hierarchy, multiverse, formalism, pra

From playlist Zermelo Fraenkel axioms

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Colloquium MathAlp 2018 - Patrick Dehornoy

La théorie des ensembles cinquante ans après Cohen : On présentera quelques résultats de théorie des ensembles récents, avec un accent sur l'hypothèse du continu et la possibilité de résoudre la question après les résultats négatifs bien connus de Gödel et Cohen, et sur les tables de Lave

From playlist Colloquiums MathAlp

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The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories - Emily Riehl

Vladimir Voevodsky Memorial Conference Topic: The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories Speaker: Emily Riehl Affiliation: Johns Hopkins University Date: September 12, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

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IMS Public Lecture - Can Every Mathematical Problem Be Solved?

Menachem Magidor, The Hebrew University of Jerusalem, Israel

From playlist Public Lectures

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Defining Infinity | Infinite Series

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Set theory is supposed to be a foundation of all of mathematics. How does it handle infinity? Learn through active problem-solving at Brilliant: https://brilliant.org/I

From playlist An Infinite Playlist

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Linear Algebra 4.1 Real Vector Spaces

My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul

From playlist Linear Algebra

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The definition of limit at infinity (Ch2 Pr8)

A gentle introduction to the formal "epsilon-M" definition for the limit of a function at infinity. This is Chapter 2 Problem 8 from the UNSW MATH1131/1141 Calculus notes. Presented by Dr Daniel Mansfield.

From playlist Mathematics 1A (Calculus)

Related pages

Axiom schema of specification | Power set | Hereditarily finite set | Equality (mathematics) | Closure (mathematics) | Infinite set | Gödel's incompleteness theorems | Isomorphism | Axiom of extensionality | Identity function | Empty domain | Formal language | Peano axioms | Empty set | Ordinal number | Zermelo–Fraenkel set theory | Axiom of power set | Natural number | Mathematics | Paul Halmos | Set (mathematics) | Second-order logic | Second-order arithmetic | Successor ordinal | Axiom of union | Mathematical induction | Singleton (mathematics) | Existential quantification | Zermelo set theory | Axiom | Cardinality | Von Neumann universe | Finitism | Epsilon-induction