What is infinity? Does infinity exist in the real world? Or is it just an abstraction, something that exists only in our minds? In this video, we will talk about the mathematical concept of infinity, starting in ancient Greece and going up to the present day. 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 of them remained open: is there any 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 PRISONERS' PROBLEM AND THE 100 HATS • THE PRISONERS' PROBLEM AND THE 100 HATS ... ???? GÖDEL'S INCOMPLETENESS: Mathematics is NOT Perfect • GÖDEL'S INCOMPLETENESS: Mathematics is NOT... ???? THE HARDEST QUESTION IN THE HISTORY OF GOOGLE • THE HARDEST QUESTION IN THE HISTORY OF... ???? WOULD YOU PASS A AMAZON INTERVIEW? AND MICROSOFT? • WOULD YOU PASS an AMAZON INTERVIEW? ???? THE (almost) IMPOSSIBLE PROBLEM 3 Houses Problem • THE (almost) IMPOSSIBLE PROBLEM 3 Houses Problem? ???? A GAME that NOBODY CAN WIN. Here's why. • A GAME that NOBODY CAN WIN. ... ???? THE LEGENDARY CIRCLE SQUARE PROBLEM • THE LEGENDARY CIRCLE SQUARE PROBLEM? ???? TIME'S ARROW: Why can't you remember the future? • TIME'S ARROW: Why Don't You ... ???? The (TRUE) ORIGIN of COMPLEX NUMBERS • The (TRUE) ORIGIN of COMPLEX NUMBERS ... ???? JOSEPHUS' PROBLEM (and its incredible story) • JOSEPHUS' PROBLEM (and its incredible ... ???? A BRIEF HISTORY of MEASURE and INTEGRATION • A BRIEF HISTORY of MEASURE and INTEGRATION ... ???? POINCARÉ CONJECTURE: a 1 MILLION DOLLAR problem • POINCARÉ CONJECTURE: a 1 MILLION DOLLAR problem ... ???? ARISTOTLE'S WHEEL PARADOX • ARISTOTLE'S WHEEL PARADOX ???? ARE YOU RATIONAL? (Allais' Paradox and Prospect Theory) • ARE YOU RATIONAL? (Allais' Paradox... ???? THE BIRTHDAY PARADOX • THE BIRTHDAY PARADOX (how do you ... ???? PRISONERS' DILEMMA and NASH'S EQUILIBRIUM • PRISONERS' DILEMMA and NASH'S EQUILIBRIUM... ???? ST. PETERSBURG PARADOX: HOW MUCH IS INFINITE MONEY WORTH? • ST. PETERSBURG PARADOX: HOW MUCH IS INFINITE MONEY WORTH? ???? Mathematics and Sports Betting: HOW TO BREAK THE BANK? • Mathematics and Sports Betting: HOW TO BREAK THE BANK? ???? WHY (scientifically) THERE IS NO SCIENTIFIC PROOF • WHY (scientifically) THERE IS NO SCIENTIFIC PROOF ... ???? WAS MATHEMATICS DISCOVERED or INVENTED? • MATHEMATICS was DISCOVERED or INVENTED... ???? WHAT IS IT LIKE TO DO A DOCTORATE IN MATHEMATICS AT IMPA • WHAT IS IT LIKE TO DO A DOCTORATE IN MATHEMATICS... ???? HOW IS THE ENEM SCORE REALLY CALCULATED? • TRI: the MATHEMATICS behind the ENEM SCORE... ???? PageRank: HOW GOOGLE's Mathematical ALGORITHM works • PageRank: HOW GOOGLE's Mathematical ALGORITHM works... ???? WHY DO YOU HAVE FEWER FRIENDS than your friends? • WHY DO YOU HAVE FEWER FRIENDS than your ... ???? THE ILLUSION of the MAJORITY • The ILLUSION of the MAJORITY ???? WHAT is MATHEMATICS FOR? When will you actually use it? • WHAT is MATHEMATICS FOR? When you... ???? THE PROBLEM with the VOLUME FORMULAS that INTRIGUED GAUSS • The BIG PROBLEM with the VOLUME FORMULAS ... ???? WHY are there only 5 PLATO SOLIDS in 3D? • WHY are there only 5 PLATO SOLIDS in 3D? ???? What is NON-EUCLIDEAN GEOMETRY? - History of Geometry • What is NON-EUCLIDEAN GEOMETRY? - H... ???? THE RING PARADOX • THE RING PARADOX ???? The SECRET Mathematics of things • Where is the Advanced Mathematics in our... ???? HOW was PI CALCULATED (with a matchbox)? • HOW TO CALCULATE PI by throwing MATCH... ???? 3 PARADOXES OF INFINITY • 3 PARADOXES OF INFINITY ???? Hilbert's INFINITY Hotel: How to Count Infinity? • Hilbert's INFINITY Hotel: a PARADOX...