TEORÍA de la DIMENSIÓN [El Origen]

The problem of correctly defining the intuitive idea of ​​dimension is an ancient one. The Greeks were already grappling with it, and throughout history, eminent philosophers and scientists such as Galileo, Leibniz, and Bolzano also attempted to solve it. But without a doubt, the father of dimension theory is George Cantor, who in 1877 discovered, to his amazement, that there are exactly as many points on a segment as there are in a square, which led him to say, "I SEE IT, BUT I DON'T BELIEVE IT." In this video, we'll look at Cantor's approach and the objection his friend Richard Dedekind encountered. Along the way, we'll review a few things about recurring decimals and functions. Don't miss it! 00:00 Introduction 01:00 Cantor's Bijection 03:26 Decimal Numbers, Generating Fractions 10:39 Dedekind's Objection 14:49 Final Question RECOMMENDED REFERENCES In Martin Gardner's work, one can approach the concept of infinity if one is not too familiar with it. Particularly in: 1. MATHEMATICAL CARNIVAL. Martin Gardner. Alianza Editorial 📘 ➡️ https://amzn.to/34cjOHY Chapter 3 is devoted to introducing the cardinals aleph zero and aleph one (the cardinal of the continuum if we accept the continuum hypothesis). The Cantor bijection discussed in this video also appears in: 2. WHEEL, LIFE, AND OTHER MATHEMATICAL FUN. Martin Gardner. Labor 📘 ➡️https://amzn.to/2SqvRyE In chapter 4, "Alephs and Superhuman Tasks," the video uses another, slightly more specialized reference as a source: 3. HISTORY OF TOPOLOGY. Edited by I. M. James, North-Holland 📘 ➡️https://amzn.to/2QU5GAg Chapter 1, written by T. Crilly and D. Johnson, discusses the emergence of topological dimension theory and describes the history told in this video. For a more comprehensive reference on cardinality, a good reference is the book: 4. HILBERT'S TENTH PROBLEM. AN INTRODUCTION TO LOGIC, NUMBER THEORY AND COMPUTABILITY. M. Ram Murty, Brandon Fodden. American Mathematical Society 📘 ➡️https://amzn.to/34egLPt Chapter 1, "Cantor and Infinity," is a good compendium (with exercises) on infinite cardinals. The links included in this bibliography are affiliate links. If you purchase any of the books through these links, we may receive a small commission from that sale. This will help keep ARCHIMEDES TUBE going, but it will not affect the price you pay, which will remain the same. If you liked the video, like and sub it! :D http://bit.ly/ArchiSub 📸 Follow us on Instagram! http://bit.ly/InstaSub 😃 Twitter:   / archimedestub   WEB: https://www.archimedestub.com/ 👕👚 Very cool math t-shirts ➡️https://www.camisetasdematematicas.com/ 📚 Math books ➡️ https://www.amazon.es/shop/archimedes...