In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite sets in ZF. The axiom schema is motivated by the idea that whether a class is a set depends only on the cardinality of the class, not on the rank of its elements. Thus, if one class is "small enough" to be a set, and there is a surjection from that class to a second class, the axiom states that the second class is also a set. However, because ZFC only speaks of sets, not proper classes, the schema is stated only for definable surjections, which are identified with their defining formulas. (Wikipedia).
Zermelo Fraenkel Separation and replacement
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axioms of separation and replacement and some of their variations. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50fRP2_SbG2oi
From playlist Zermelo Fraenkel axioms
Expanding and Factorising (4 of 4: What is Substitution?)
More resources available at www.misterwootube.com
From playlist Formulae and Equations
Ex 2: Solve a System of Equations Using Substitution
This video provides an example of how to solve a system of linear equation using the substitution method. Complete Library: http://www.mathispower4u.com Search by Topic: http://www.mathispower4u.wordpress.com
From playlist Solving Systems of Equations Using Substitution
From playlist 1. Solving One-Variable Equations and Inequalities
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
Set Theory 1.1 : Axioms of Set Theory
In this video, I introduce the axioms of set theory and Russel's Paradox. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5ITQHUW
From playlist Set Theory
Foundations S2 - Seminar 8 - Light discussion of soundness, completeness, first vs second order
A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. In this seminar Billy leads a discussion of soundness, completeness and first vs second-order logic, as a recap of some of what has been discussed over the past few months in the seminar. The webpage f
From playlist Foundations seminar
Topology Without Tears - Video 2c - Infinite Set Theory
This is the final part, part (c), of Video 2 in a series of videos supplementing the online book "Topology Without Tears" which is available at no cost at www.topologywithouttears.net
From playlist Topology Without Tears
How ISPs Violate the Laws of Mathematics
Get a free trial of Audible at https://audible.com/minutephysics or by texting 'minutephysics' to 500500 Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics Link to Patreon Supporters: http://www.minutephysics.com/supporters/ MinutePhysics is on twitter - @minutephysic
From playlist MinutePhysics
Live CEOing Ep 374: Language Design in Wolfram Language [AxiomaticTheory]
In this episode of Live CEOing, Stephen Wolfram discusses upcoming improvements of AxiomaticTheory for the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen
From playlist Behind the Scenes in Real-Life Software Design
Anthony Bordg - How to Do Maths Without Dependent Types
What can be done when formalising mathematics without dependent types? I will give you new insights into this question by exploring the capability and possible limitations of the Isabelle/HOL proof assistant. I will explain what we learnt formalising Grothendieck's schemes using only Isabe
From playlist Workshop Schlumberger 2022 : types dépendants et formalisation des mathématiques
Calculus Introduction to U-Substitution
In this lesson, I introduce the concept of u-substitution for integrals with a brief review of substitution techniques in Algebra first. This technique is also known as integration by substitution.
From playlist Calculus
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
Live CEOing Ep 401: Language Design in Wolfram Language [AxiomaticTheory, Echo, FoldWhile, & More]
In this episode of Live CEOing, Stephen Wolfram reviews the design of upcoming functionality for the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfra
From playlist Behind the Scenes in Real-Life Software Design
Solving Systems of Linear Equations Using Substitution (L12.2)
The lesson explains how to solve a system of linear equation using the substitution method. All solutions are verified. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist Solving Systems of Equations Using Substitution
Ex 1: Solve a System of Equations Using Substitution
This video provides an example of how to solve a system of linear equation using the substitution method. Complete Library: http://www.mathispower4u.com Search by Topic: http://www.mathispower4u.wordpress.com
From playlist Solving Systems of Equations Using Substitution
Relations and Functions | Axiomatic Set Theory, Section 2.1
In this video we define and prove a few basic theorems about relations and functions. My Twitter: https://twitter.com/KristapsBalodi3 Intro:(0:00) Ordered Pairs:(1:43) IMAGE-in that!:(3:33) Composition: (7:57) Functions:(11:05) Special thanks to Alex Stephens
From playlist Axiomatic Set Theory
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
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
Ex 3: Solve a System of Equations Using Substitution
This video provides an example of how to solve a system of linear equation using the substitution method. Complete Library: http://www.mathispower4u.com Search by Topic: http://www.mathispower4u.wordpress.com
From playlist Solving Systems of Equations Using Substitution