Elementary Number Theory: Well-Ordering Principle

Показать описание

This video describes the well-ordering principle of the natural numbers and gives several examples. An extension to this axiom is discussed at the end of the video.

Рекомендации по теме

Комментарии

Increible video, fabulosa su capacidad para explicar. Gracias.

lugo

Lovely. Clear. Straightforward. Great job

elias.n

Thank you so much. Learning from this precise video is very joyful.

phoenixschwarz

Satisfying 👍 explanation, that you for posting such fundamental topic.

Junaidii

Thanks for this lecture. It was very helpful.

valeriereid

The following is the set theoretic (and more efficient) way to describe the well ordering principle
(as david hilbert once said, let no one prevent you from entering cantor's cartoon world).

N is a well ordered set under the usual ordering <=.
What is a well ordered set? A set with the property that every subset has a minimum.
The "well ordering principle" is a mutant of ordinal set theory and leads to confusion.
It seems redundant.
"The well ordering principle says that the set of natural numbers is well ordered."
So then just say that N is well ordered.

maxpercer

This video is superb. Thanks a million times

LeVraiment

Please make more video. your video is abstuly amazing

Pohgox-XXIII

What are the applications of this principle?

animesock

What us the purpose of having Well-Ordering Principle to start with?

AlulaZagway

At 21:41, can't you define a bijective function to map the finite part to a subset of the natural numbers anyway? and then compare the two minimums?

NeelSandellISAWESOME

@ 0:28 States that the WOP is only true for NN, which is false. The WOP holds for any subset of ZZ bounded from below or bounded from above.

MathinD

I liked the part in 19:45, on the extension of the well-ordering principle. I came up with an example that would work visually. Make the set A be the set of complex numbers with the restriction that you have a helix of growing radius such that at every revolution it crosses the real axis, with the starting point being the (1, 0). At all of those crossings the complex number hs an image on the set of natural numbers. Given that we start from the element that maps to 1, the first natural number according to your convention, the set A is non-empty. So, the well-ordering principle applies. Yeah?

ioannisnobelis

Sir can u give me notes of elementary number theory by David Burton chapters 2, 3 and 4

arshadmahmood

Elementary Number Theory: Well-Ordering Principle

Elementary Number Theory: Well-Ordering Principle

Well Ordering Principle explaination with proof (Number Theory)

Use the Well-ordering Principle to Prove √3 Is Irrational

Discrete Math - 5.2.1 The Well-Ordering Principle and Strong Induction

Well Ordering Principle in Number Theory

Well Ordering Principle of Elementary Number Theory by S.B Malik Pure math

Well Ordering Property of Set of Natural numbers N

Well Ordering Principle ||Basic Number Theory

Number Theory Lecture 1 || Well Ordering Principle || Division Algorithm || Discrete Mathematics✍

Well Ordering Principle & Archimedean Property

Number Theory: The Division Algorithm

Well ordering principle, Bezout Theorem || Math Olympiad, I.S.I. C.M.I. Entrance || Number Theory

The Well Ordering Principle

Equivalences: Induction - Strong Induction - Well Ordering Principle | Algebra

Well Ordering Principle / Division Algorithm Theorem / Number Theory

Mathematical Induction (from Elementary Number Theory by D. M. Burton, 5th Edition) (Part 1)

S1 B.Sc; Number Theory; Lecture 1-The Well-Ordering Principle

Well ordering principle

Well-Ordering Principle

Well Ordering Principle (Number Theory B.Sc)

Well-Ordering Axiom (1)

well ordering principle and linear combination in number theory

Introduction to Well-Ordering Principle

Basis for Proving Using Well-Ordering Principle