Introducing Infinity | Set Theory, Section 3.1
In this video we define inductive sets, the natural numbers, the axiom of infinity, and the standard order relation on the natural numbers. My Twitter: https://twitter.com/KristapsBalodi3 Intro (0:00) Defining Natural Numbers as Sets (1:19) Definition of Inductive Sets (5:07) The Axiom o
From playlist Axiomatic Set Theory
Set Theory (Part 7): Natural Numbers and Induction
Please feel free to leave comments/questions on the video and practice problems below! In this video, I discuss the von Neumann construction of the natural numbers and relate the idea of natural numbers to inductive sets. The axiom of infinity is also introduced here as one of the ZFC axi
From playlist Set Theory by Mathoma
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
Higher Inductive Types - Peter Lumsdaine
Peter Lumsdaine Dalhousie University; Member, School of Mathematics October 1, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
The perfect number of axioms | Axiomatic Set Theory, Section 1.1
In this video we introduce 6 of the axioms of ZFC set theory. My Twitter: https://twitter.com/KristapsBalodi3 Intro: (0:00) The Axiom of Existence: (2:39) The Axiom of Extensionality: (4:20) The Axiom Schema of Comprehension: (6:15) The Axiom of Pair (12:16) The Axiom of Union (15:15) T
From playlist Axiomatic Set Theory
RA1.3. Peano Axioms and Induction
Real Analysis: We consider the Peano Axioms, which are used to define the natural numbers. Special attention is given to Mathematical Induction and the Well-Ordering Principle for N. (Included is an example of how to show a triple equivalence.)
From playlist Real Analysis
Petra Hozzova - Automation of Induction in Saturation - IPAM at UCLA
Recorded 17 February 2023. Petra Hozzova of Technische Universität Wien, Institute of Logic and Computation, presents "Automation of Induction in Saturation" at IPAM's Machine Assisted Proofs Workshop. Abstract: Induction in saturation-based first-order theorem proving is a new exciting di
From playlist 2023 Machine Assisted Proofs Workshop
Axiom of Regularity (Foundation) vs. Induction
Previous video on regularity: https://youtu.be/AqjctCRGxhw Errata: In 56:27 I say Regularity, but I meant to say Replacement. Text and links: https://gist.github.com/Nikolaj-K/bc9f67d685bcc7d1300372cfabceed9b
From playlist Logic
Topology Without Tears - Video 4d - Writing Proofs in Mathematics
This is part (d) of the fourth video in a series of videos which supplement my online book "Topology Without Tears" which is available free of charge at www.topologywithouttears.net Video 4 focusses on the extremely important topic of writing proofs. This video is about Mathematical Induc
From playlist Topology Without Tears
Well-Ordering and Induction: Part 1
This was recorded as supplemental material for Math 115AH at UCLA in the spring quarter of 2020. In this video, I prove the equivalence of the principle of mathematical induction and the well-ordering principle.
From playlist Well Ordering and Induction
Introduction to University Mathematics - Oxford Mathematics 1st Year Student Lecture
This course is taken in the first two weeks of the first year of the Oxford Mathematics degree. It introduces the concepts and ways of mathematical thinking that students need in the years ahead. Much of the context will be familiar from high school but the way we think and write about i
From playlist Oxford Mathematics Student Lectures - Introduction to University Mathematics
Regularity and non-standard models of arithmetic #PaCE1
Follow-up video: https://youtu.be/7HKnOOvssvs Discussed text, including all links: https://gist.github.com/Nikolaj-K/101c2712dc832dec4991bf568869abc8 Curt's call: https://youtu.be/V93GQaDtv8w Timestamps: 00:00:00 Introduction 00:02:55 Wittgenstein and predicates (optional) 00:11:12 Skolems
From playlist Logic
Recursively Defined Sets - An Intro
Recursively defined sets are an important concept in mathematics, computer science, and other fields because they provide a framework for defining complex objects or structures in a simple, iterative way. By starting with a few basic objects and applying a set of rules repeatedly, we can g
From playlist All Things Recursive - with Math and CS Perspective
Fundamentals of Mathematics - Lecture 15: Dedekind-Peano vs Peano Arithmetic
This is the class where we talk about the Extra Credit. course page: http://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton - UVM
From playlist Fundamentals of Mathematics