Mathematical proofs | Methods of proof
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. This is a method of direct proof. A proof by exhaustion typically contains two stages: 1. * A proof that the set of cases is exhaustive; i.e., that each instance of the statement to be proved matches the conditions of (at least) one of the cases. 2. * A proof of each of the cases. The prevalence of digital computers has greatly increased the convenience of using the method of exhaustion (e.g., the first computer-assisted proof of four color theorem in 1976), though such approaches can also be challenged on the basis of mathematical elegance. Expert systems can be used to arrive at answers to many of the questions posed to them. In theory, the proof by exhaustion method can be used whenever the number of cases is finite. However, because most mathematical sets are infinite, this method is rarely used to derive general mathematical results. In the Curry–Howard isomorphism, proof by exhaustion and case analysis are related to ML-style pattern matching. (Wikipedia).
Ben discusses proof by exhaustion and goes through some examples.
From playlist Basics: Proofs
Proof: a³ - a is always divisible by 6 (2 of 2: Proof by exhaustion)
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From playlist The Nature of Proof
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
Inequality Proofs: Setting Out
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From playlist The Nature of Proof
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
Discrete Math - 1.8.1 Proof by Cases
Exploring a method of proof by exhaustion known as proof by cases. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz
From playlist Discrete Math I (Entire Course)
Two examples of using the proof by cases method. Leave any questions / comments below! Keep flexin' those brain muscles! Facebook: https://www.facebook.com/braingainzofficial Instagram: https://www.instagram.com/braingainzofficial
From playlist Proofs
Proof by Exhaustion - PROOF - New A-Level Maths Year 1
An introduction and examples of mathematical proof by exhaustion, for the new AS Level maths! ==================================== Welcome to AS Level Maths / A Level Maths Year 1 With Melv, supporting students on the new specification for AQA, Edexcel and OCR MEI! CHECK OUT MY T SHIRTS
From playlist AS Level Maths Pure - AQA, Edexcel and OCR MEI
Year 12/AS Pure Chapter 7.4 (Algebraic Methods)
This lesson directly follows on from the previous lesson (7.3) and continues to explores methods of mathematical proof. Here, we focus on two particular methods of proof: 𝒑𝒓𝒐𝒐𝒇 𝒃𝒚 𝒆𝒙𝒉𝒂𝒖𝒔𝒕𝒊𝒐𝒏 and 𝒑𝒓𝒐𝒐𝒇 𝒃𝒚 𝒅𝒆𝒅𝒖𝒄𝒕𝒊𝒐𝒏. This lesson is meant as preparation for Exercise 7E, page 152 of the Pears
From playlist Year 12/AS Edexcel (8MA0) Mathematics: FULL COURSE
A-Level Maths: A1-04 [Introducing Proof by Exhaustion]
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From playlist A-Level Maths A1: Proof
A-Level Maths: A1-05 [Proof by Exhaustion Examples]
Navigate all of my videos at https://sites.google.com/site/tlmaths314/ Like my Facebook Page: https://www.facebook.com/TLMaths-1943955188961592/ to keep updated Follow me on Instagram here: https://www.instagram.com/tlmaths/ My LIVE Google Doc has the new A-Level Maths specification and
From playlist A-Level Maths A1: Proof
Proof by Exhaustion Examples - New A-Level Maths Year 1
Some example questions on proof by exhaustion for the new A-Level maths including a proof that all cube numbers are a multiple of 9, or 1 more or less! ==================================== Welcome to AS Level Maths / A Level Maths Year 1 With Melv, supporting students on the new specific
From playlist AS Level Maths Pure - AQA, Edexcel and OCR MEI
New Methods in Finsler Geometry - 23 May 2018
http://www.crm.sns.it/event/415 Centro di Ricerca Matematica Ennio De Giorgi The workshop has limited funds to support lodging (and in very exceptional cases, travel) costs of some participants, with priority given to young researchers. When you register, you will have the possibility to
From playlist Centro di Ricerca Matematica Ennio De Giorgi