Gentzen's consistency proof is a result of proof theory in mathematical logic, published by Gerhard Gentzen in 1936. It shows that the Peano axioms of first-order arithmetic do not contain a contradiction (i.e. are "consistent"), as long as a certain other system used in the proof does not contain any contradictions either. This other system, today called "primitive recursive arithmetic with the additional principle of quantifier-free transfinite induction up to the ordinal ε0", is neither weaker nor stronger than the system of Peano axioms. Gentzen argued that it avoids the questionable modes of inference contained in Peano arithmetic and that its consistency is therefore less controversial. (Wikipedia).
Every Subset of a Linearly Independent Set is also Linearly Independent Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A proof that every subset of a linearly independent set is also linearly independent.
From playlist Proofs
In this video, I give a cool proof of the product rule based only on properties of logarithms. Enjoy! Cool Product rule proof: https://youtu.be/sBMpfLpNGFc Subscribe to my channel: https://youtube.com/drpeyam Check out my TikTok channel: https://www.tiktok.com/@drpeyam Follow me on Insta
From playlist Calculus
Hugo Herbelin: Computing with Markov's principle
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Computing with Markov's principle via a realizability interpretation is standard, using unbounded search as in Kleene's realizability or by selecting the first valid wit
From playlist Workshop: "Proofs and Computation"
Benno van den Berg: Two observations on intuitionistic logic and arithmetic
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: This talk will consist of two parts. In the first part I explain a convenient formalisation of arithmetic in finite types, with both extensional and intensional models,
From playlist Workshop: "Proofs and Computation"
Sam Buss: Expanders in VNC^1 and Monotone Propositional Proofs
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: We give a combinatorial analysis of a variant of the iterative expander construction due to Reingold, Vadhan, and Wigderson [2002], and show that this analysis can be fo
From playlist Workshop: "Proofs and Computation"
Arnold Beckmann: Hyper Natural Deduction
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: We introduce Hyper Natural Deduction as an extension of Gentzen's Natural Deduction system by communication like rules. The motivation is to obtain a natural deduction li
From playlist Workshop: "Proofs and Computation"
Proof: a³ - a is always divisible by 6 (2 of 2: Proof by exhaustion)
More resources available at www.misterwootube.com
From playlist The Nature of Proof
Here I show that the ratio of two continuous functions is continuous. I do it both by using epsilon-delta and the sequence definition of continuity. Interestingly, the proof is similar to the proof of the quotient rule for derivatives. Enjoy! Reciprocals of limits: https://youtu.be/eRs84C
From playlist Limits and Continuity
Methods of Proof | A-level Mathematics
The four main types of proof you need to be familiar with in A-level mathematics: - proof by deduction - proof by exhaustion - proof by counter-example - proof by contradiction ❤️ ❤️ ❤️ Support the channel ❤️ ❤️ ❤️ https://www.youtube.com/channel/UCf89Gd0FuNUdWv8FlSS7lqQ/join 100 g
From playlist A-level Mathematics Revision
Second Order Recurrence Formula (1 of 3: Prologue - considering the old course)
More resources available at www.misterwootube.com
From playlist Further Proof by Mathematical Induction
In this video, I show you a really cool proof of the quotient rule, using just ln and the chain rule (Chen Lu). And I do it all in Russian! Enjoy :) Subscribe to my channel: https://www.youtube.com/c/drpeyam
From playlist Random fun
Here I show that the product of two continuous functions is continuous. I do it both by using epsilon-delta and the sequence definition of continuity. Interestingly, the proof is similar to the proof of the product rule for derivatives. Enjoy! Product of limits: https://youtu.be/4pvFRvtMq
From playlist Limits and Continuity
Gödel's Second Incompleteness Theorem, Proof Sketch
In order for math to prove its own correctness, it would have to be incorrect. This result is Gödel’s second incompleteness theorem, and in this video, we provide a sketch of the proof. Created by: Cory Chang Produced by: Vivian Liu Script Editor: Justin Chen, Brandon Chen, Zachary Greenb
From playlist Infinity, and Beyond!
Proofs, Circuits, Communication, and Lower Bounds in Complexity Theory - Robert Robere
Computer Science/Discrete Mathematics Seminar II Topic: Proofs, Circuits, Communication, and Lower Bounds in Complexity Theory Speaker: Robert Robere Affiliation: Member, School of Mathematics Date: February 11, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
What if Current Foundations of Mathematics are Inconsistent? | Vladimir Voevodsky
Vladimir Voevodsky, Professor, School of Mathematics, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/voevodsky In this lecture, Professor Vladimir Voevodsky begins with Gödel's second incompleteness theorem to discuss the possibility that the formal theory of f
From playlist Mathematics
Billy Price and Will Troiani present a series of seminars on foundations of mathematics. In this seminar Billy starts the proof of the completeness theorem. You can join this seminar from anywhere, on any device, at https://www.metauni.org. This video was filmed in Deprecation (https://
From playlist Foundations seminar
Title: Consistent Systems of Linear Differential and Difference Equations April 2016 Kolchin Seminar Workshop
From playlist April 2016 Kolchin Seminar Workshop
Proving a Relation is an Equivalence Relation | Example 2
In this video, we practice another example of proving a relation is in fact an equivalence relation. Enjoy! Instagram: https://www.instagram.com/braingainzofficial
From playlist Proofs
We know that God exists because math is consistent and we know... - Kojman
Menachem Kojman Ben Gurion University of the Negev; Member, School of Mathemtics April 6, 2011 MATHEMATICAL CONVERSATIONS "We know that God exists because mathematics is consistent and we know that the devil exists because we cannot prove the consistency." -- Andre Weil For more videos,
From playlist Mathematics