Methods of proof | Mathematical terminology

Counterexample

A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "John Smith is not a lazy student" is a counterexample to the generalization “students are lazy”, and both a counterexample to, and disproof of, the universal quantification “all students are lazy.” In mathematics, the term "counterexample" is also used (by a slight abuse) to refer to examples which illustrate the necessity of the full hypothesis of a theorem. This is most often done by considering a case where a part of the hypothesis is not satisfied and the conclusion of the theorem does not hold. (Wikipedia).

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Counterexample

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From playlist Geometry

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Disproving implications with Counterexamples

Counterexamples are one of the most powerful types of proof methods in math and philosophy. When you give a counterexample, you are demonstrating that some claim if false. For instance, if I say that every prime number is odd, I can disprove that claim by observing that 2 is a prime which

From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)

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Counter Steering | The interesting physics behind it

Counter steering is an amazing technique used by many bike riders, and is very useful when making a quick turn and doing some bike stunts like this. At first, counter steering looks counter intuitive, you turn the handlebars to the left, but the motorcycle makes a quick right turn. What ar

From playlist Automobile Engineering

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Testing Syllogisms by Counterexample // Lesson 24 [INTRODUCTORY LOGIC]

Although it can feel like there are infinitely many kinds of categorical syllogisms, in fact there are only 256, and of those, only 40 are valid. So how can we confirm which ones are valid and which ones are invalid, especially if we're not already familiar with the terms of the argument?

From playlist Introductory Logic

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What is counterbalancing? | Research Methods w/ Dr. Swan

This video is the video on demand (VOD) from my Twitch livestream. There are likely several edits for flow and topic. No facecam or overlays from stream appear in this video. Video contains only Microsoft OneNote information. Topic for this stream: I discuss how to counterbalance with-gro

From playlist Research Methods

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What is an Injective Function? Definition and Explanation

An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez

From playlist Functions

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Determining clockwise vs counter clockwise rotations

👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will

From playlist Transformations

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What is the difference between rotating clockwise and counter clockwise

👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will

From playlist Transformations

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6. Ch. 2, Sections 2.4 & 2.5. Introduction to Logic, Philosophy 10, UC San Diego - BSLIF

Video lecture corresponding to _Basic Sentential Logic and Informal Fallacies_, Chapter 2, Sections 2.4 & 2.5. This is for the class Introduction to Logic, Philosophy 10, UC San Diego.

From playlist UC San Diego: PHIL 10 - Introduction to Logic | CosmoLearning.org Philosophy

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Obstruction de Brauer-Manin pour les surfaces (...) - Colliot-Thélène - Workshop 1 - CEB T2 2019

Jean-Louis Colliot-Thélène (Mathématiques, Université Paris-Sud) / 20.05.2019 Obstruction de Brauer-Manin pour les surfaces de Markoff C’est un problème difficile de décider quand une surface cubique affine a un point entier, et si les points entiers sont denses (en divers sens). Ghosh

From playlist 2019 - T2 - Reinventing rational points

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Evaluating Arguments: Study Hall Writing Composition #9: ASU + Crash Course

How can we know if our argument for something is good? How can we know if someone else is presenting valuable information in their own argument? In evaluating the arguments of others, we’ll also get better at writing arguments ourselves. That’s what we’ll discuss today in Study Hall: Compo

From playlist Study Hall: Composition

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The Riemann Hypothesis

The Riemann Hypothesis is one of the Millennium Prize Problems and has something to do with primes. What's that all about? Rather than another hand-wavy explanation, I've tried to put in some details here. Some grown-up maths follows. More information: http://www.claymath.org/publications

From playlist My Maths Videos

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Definition of an Injective Function and Sample Proof

We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil

From playlist Injective, Surjective, and Bijective Functions

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CA Geometry: Similar triangles 1 | Worked examples | Geometry | Khan Academy

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-miscellaneous/geometry-worked-examples/v/ca-geometry-similar-triangles-1 10-14, similar triangles Watch the next lesson: https://www.khanac

From playlist Worked examples | Geometry | Khan Academy

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Properties of Real Numbers

I introduce the basic Properties of Real Numbers: Commutative Property of Addition and Multiplication, Associative Property of Addition and Multiplication, Identity Property of Multiplication, Identity Property of Addition, Zero Product Property, and Multiplying by Negative One. I also d

From playlist Algebra 1

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Inductive Reasoning

http://mathispower4u.wordpress.com/

From playlist Introduction to Proof

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Geneva Drive Counter

http://www.mekanizmalar.com This video show the working principles of a odometer in two dimension by using Geneva Drive. Actual odometer work somewhat similar fashion but it is hard to describe it in 2D animation.

From playlist Indexing

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How to Debug a Property Proving Counterexample

Property proving with Simulink Design Verifier™ is a static analysis technique that uses formal methods to prove whether a given property will always be valid. This technique can help you formally verify that specific requirements implemented in your design will always be met. If a propert

From playlist Embedded Systems | Developer Tech Showcase

Related pages

Loss function | Counterexamples in Topology | Rhombus | Minimal counterexample | Ganea conjecture | Conjecture | Shape | Tait's conjecture | Witsenhausen's counterexample | Imre Lakatos | Mathematical proof | State variable | Composite number | Control theory | Natural number | Mathematics | Euler's sum of powers conjecture | Seifert conjecture | Hilbert's fourteenth problem | Prime number | Parity (mathematics) | Universal quantification | Pólya conjecture | Geometry | Deductive reasoning | Contradiction