In mathematics and logic, a direct proof is a way of showing thetruth or falsehood of a given statement by a straightforward combination ofestablished facts, usually axioms, existing lemmas and theorems, without making any further assumptions. In order to directly prove a conditional statement of the form "If p, then q", it suffices to consider the situations in which the statement p is true. Logical deduction is employed to reason from assumptions to conclusion. The type of logic employed is almost invariably first-order logic, employing the quantifiers for all and there exists. Common proof rules used are modus ponens and universal instantiation. In contrast, an indirect proof may begin with certain hypothetical scenarios and then proceed to eliminate the uncertainties in each of these scenarios until an inescapable conclusion is forced. For example, instead of showing directly p ⇒ q, one proves its contrapositive ~q ⇒ ~p (one assumes ~q and shows that it leads to ~p). Since p ⇒ q and ~q ⇒ ~p are equivalent by the principle of transposition (see law of excluded middle), p ⇒ q is indirectly proved. Proof methods that are not direct include proof by contradiction, including proof by infinite descent. Direct proof methods include proof by exhaustion and proof by induction. (Wikipedia).
Introduction to Direct Proofs: If n is even, then n squared is even
This video introduces the mathematical proof method of direct proof provides an example of a direct proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Direct Proof: If a|b and b|c, then a|c
This video provides an example of a direct proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Introduction to Indirect Proof
This video introduces indirect proof and proves one basic algebraic and one basic geometric indirect proof. Complete Video List: http://mathispower4u.yolasite.com/
From playlist Relationships with Triangles
Introduction to Proof Methods!
The first video I've made on proof methods! I discuss what a proof is, give some general tips, show how to prove a conditional statement using the direct proof method, and use the direct proof method to do some very beginner friendly proofs! The goals of this video: 1. Help people underst
From playlist Proofs
Direct Proofs Involving Divisibility
In this video, we write direct proofs of four different statements that all involve divisibility of integers. I hope you find it helpful! Timestamps: 0:00 - Intro 0:50 - Definition 3:30 - Proof 1 6:17 - Proof 2 9:41 - Proof 3 12:48 - Proof 4 Thanks for watching! Comment below with quest
From playlist Proofs
In this first video in our mathematical proof series, (the slightly injured) Ben discusses direct proofs and shows two examples.
From playlist Basics: Proofs
Introduction to Common Mathematical Proof Methods
This video introduces the common methods of mathematical proofs and provides a basic example of a direct proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Direct Proofs: Beginner Examples (Even/Odd)
Let's prove some basic statements using the direct proof method! This is intended for beginners to direct proof or proof in general. Timestamps: 0:00 Introduction 00:50 Definitions 3:31 Example 1 8:14 Example 2 12:18 Example 3 15:53 Example 4 Thanks for watching! Comment below with quest
From playlist Proofs
The basic idea of proof by contrapositive + two examples! Comment below with questions, make sure to like / subscribe, and keep flexin' those brain muscles! Facebook: https://www.facebook.com/braingainzofficial Instagram: https://www.instagram.com/braingainzofficial
From playlist Proofs
Discrete Math - 1.7.1 Direct Proof
This is the first of several videos exploring methods of proof. In this video we will focus on direct proof by assuming "p" is true, then showing that "q" must also be true. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=P
From playlist Discrete Math I (Entire Course)
Bitcoin Q&A: Directed Acyclic Graphs (DAGs) and IOTA
What is your opinion on directed acyclic graphs (DAGs) and whether they can achieve the same level of decentralisation, security, and censorship resistance? DAGs are not vaporware, but the cryptocurrency projects using them mostly employ proof-of-stake (PoS) or proof-of-authority consensus
From playlist English Subtitles - aantonop Videos with subtitles in English
proof by contradiction and more -- Proof Writing 11
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From playlist Proof Writing
DIRECT PROOFS - DISCRETE MATHEMATICS
We introduce proofs by looking at the most basic type of proof, a direct proof. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz Discrete M
From playlist Discrete Math 1
How to Prove Math Theorems | 1st Ex: Even + Odd = Odd
Our first math proof! The main goal of this video is more about the structure of a direct proof than the specific claim, that the sum of an even integer and an odd integer is an odd integer. We will write: 1) The Assumptions 2) Definition of the Assumptions 3) Manipulations 4) Definition
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Direct Proof Examples -- How to do mathematical Proofs (PART 6)
This is the fourth video on a series of videos on: How to do mathematical proofs. The course is structured in such a way to make the transition from applied-style problems in mathematics (sometimes referred to as engineering mathematics) to pure mathematics much smoother. The course will
From playlist How to do Mathematical Proofs