Os INFINITOS e a HIPÓTESE DO CONTÍNUO

What is infinity? Does infinity exist in the real world? Or is it merely an abstraction, something that exists only in our minds? In this video, we'll discuss the mathematical concept of infinity, beginning in ancient Greece and continuing through modern times. How do we count infinity? Are there different types of infinities? How do we tell if one infinity is greater than another? How many infinities are there? These questions were answered by Georg Cantor, but one remained open: is there an infinity between the countable infinity of natural numbers and the continuum of real numbers? The so-called Continuum Hypothesis said no, and proving it was the first problem on Hilbert's legendary list of 23 problems. The answer only came decades later, with the work of Gödel and Cohen. Become a member and help me continue producing this type of content: https://www.youtube.com/temciencia/join ========================================== Script, presentation, and editing: Daniel Nunes My Instagram:   / tem.ciencia   ===================================== WATCH ALSO: 🔴 THE PRISONER PROBLEM AND THE 100 HATS    • O PROBLEMA DOS PRISIONEIROS E OS 100 CHAPÉUS   🔴 GÖDEL'S INCOMPLETUDE: Mathematics is NOT Perfect    • INCOMPLETUDE DE GÖDEL: a Matemática NÃO é ...   🔴 THE HARDEST QUESTION IN THE HISTORY OF GOOGLE    • A QUESTÃO MAIS DIFÍCIL DA HISTÓRIA DO GOOGLE   🔴 YOU WOULD YOU PASS AN INTERVIEW with AMAZON? And MICROSOFT?    • VOCÊ PASSARIA numa ENTREVISTA da AMAZON? E...   🔴 THE (ALMOST) IMPOSSIBLE PROBLEM | The 3-Square Problem    • O PROBLEMA (quase) IMPOSSÍVEL | Problema d...   🔴 A GAME NOBODY CAN WIN. Here's why.    • Um JOGO que NINGUÉM CONSEGUE VENCER. Eis o...   🔴 THE LEGENDARY SQUARING THE CIRCLE Problem    • O LENDÁRIO Problema da QUADRATURA do CÍRCULO   🔴 TIME'S ARROW: Why can't you remember the future?    • A SETA DO TEMPO: Por que você não se lembr...   🔴 The (TRUE) ORIGIN of COMPLEX NUMBERS    • A (VERDADEIRA) ORIGEM dos NÚMEROS COMPLEXOS   🔴 The JOSEPHUS PROBLEM (and its incredible story)    • O PROBLEMA de JOSEFO (e sua incrível histó...   🔴 A BRIEF HISTORY of MEASURE and INTEGRATION    • Uma BREVE HISTÓRIA da MEDIDA e da INTEGRAÇÃO   🔴 POINCARÉ CONJECTURE: A MILLION DOLLAR Problem    • CONJECTURA DE POINCARÉ: um problema de 1 M...   🔴 ARISTOTLE'S WHEEL PARADOX    • O PARADOXO DA RODA DE ARISTÓTELES   🔴 ARE YOU RATIONAL? (Allais' Paradox and Prospect Theory)    • VOCÊ É RACIONAL? (Paradoxo de Allais e a T...   🔴 THE BIRTHDAY PARADOX    • O PARADOXO DO ANIVERSÁRIO (como você nunca...   🔴 PRISONERS' DILEMMA and NASH'S EQUILIBRIUM    • DILEMA dos PRISIONEIROS e o EQUILÍBRIO de ...   🔴 ST. PETERSBURG PARADOX: HOW MUCH IS INFINITE MONEY WORTH?    • PARADOXO DE SÃO PETERSBURGO: QUANTO VALE D...   🔴 Math and Sports Betting: HOW TO BREAK THE BANK?    • Matemática e Apostas Esportivas: COMO QUEB...   🔴 WHY (Scientifically) THERE IS NO SCIENTIFIC PROOF    • POR QUE (cientificamente) NÃO EXISTE COMPR...   🔴 Was MATHEMATICS DISCOVERED or INVENTED?    • A MATEMÁTICA foi DESCOBERTA ou INVENTADA?   🔴 WHAT IS IT LIKE TO GET A DOCTORATE IN MATHEMATICS AT IMPA    • COMO É FAZER UM DOUTORADO EM MATEMÁTICA NO...   🔴 HOW IS THE ENEM SCORE REALLY CALCULATED?    • TRI: a MATEMÁTICA por trás da NOTA do ENEM   🔴 PageRank: HOW GOOGLE'S Mathematical ALGORITHM works    • PageRank: COMO funciona o ALGORITMO Matemá...   🔴 WHY DO YOU HAVE FEWER FRIENDS THAN YOUR FRIENDS?    • POR QUE VOCÊ tem MENOS AMIGOS que os seus ...   🔴 THE ILLUSION OF MAJORITY    • A ILUSÃO da MAIORIA   🔴 WHAT IS MATHEMATICS FOR? When will you actually use it?    • PRA QUE serve a MATEMÁTICA? Quando você ir...   🔴 THE PROBLEM with VOLUME FORMULAS that INTRUSTED GAUSS    • O GRANDE PROBLEMA com as FÓRMULAS de VOLUME   🔴 WHY are there only 5 PLATONIC SOLIDS in 3D?    • POR QUE só existem 5 SÓLIDOS DE PLATÃO em 3D?   🔴 What is NON-EUCLIDEAN GEOMETRY? - History of Geometry    • O que é GEOMETRIA NÃO EUCLIDIANA? - Histór...   🔴 THE RING PARADOX    • O PARADOXO DO ANEL   🔴 The SECRET Math of Things    • Onde está a Matemática Avançada no nosso d...   🔴 HOW WAS PI CALCULATED (with a matchbox)?    • COMO CALCULAR o PI arremessando FÓSFOROS? ...   🔴 3 PARADOXES OF INFINITY    • 3 PARADOXOS DO INFINITO   🔴 Hilbert's INFINITY Hotel: How to Count Infinity?    • O Hotel INFINITO de Hilbert: um PARADOXO d...