수학-칸토어 무한집합론) 이론 하나가 수학을 거의 망가뜨릴 뻔 한 이야기
하늘
수학-칸토어 무한집합론) 이론 하나가 수학을 거의 망가뜨릴 뻔 한 이야기
이론 하나가 수학을 거의 망가뜨릴 뻔 한 이야기
Veritasium 한국어 - 베리타시움
그거 아세요? 수학영상은 조회수는 가장 안나오고 만드는데는 가장 오래 걸린답니다!
근데 재밌어요!!
이론 하나 만들었다가 수학 체계가 망가져 버릴 뻔한 이야기!
영상 업로드가 안돼서 렌더링만 3번한 영상... 재밌게 봐주세요.
carlos lamas, 지방흡입 정재호 원장입니다, í , StarSeed Global, lililiiiiliillliili, Im Yongsik 님 멤버십 감사합니다.
▀▀▀
A huge thank you to Dr Asaf Karagila, Prof. Alex Kontorovich, Prof. Joel David Hamkins, Prof. Andrew Marks, Prof. Gabriel Goldberg and Prof. Elliot Glazer for their invaluable expertise and contributions to this video.
Head over and sign up to our Patreon for some exclusive behind the scenes footage, showing how the animations and illustrations for this video were made - / patreon. .
▀▀▀
0:00 1 다음은 뭘까?
2:42 다른 무한보다 큰 무한?
6:17 정렬 정리 (The Well Ordering Principle & Theorem)
10:32 체르멜로와 선택 공리
17:22 선택 공리가 논란이 되는 이유
23:16 바나흐-타르스키 역설
27:53 참 vs 거짓
29:58 당신의 증명, 당신의 선택
▀▀▀
References:
Up and Atom - • Cantor's Infinity Paradox | Set Theory
Minutephysics - • How to Count Infinity
PBS Infinite Series - • How the Axiom of Choice Gives Sizeless Set...
Vsauce - • The Banach–Tarski Paradox
Ernst Zermelo via Wikipedia - https://ve42.co/zermeloBio
Axiom of choice via Wikipedia - https://ve42.co/choiceAxiom
Georg Cantor via Wikipedia - https://ve42.co/cantorMath
Gregory H. Moore (2013). Consequences of the Axiom of Choice. Dover Publications - https://ve42.co/choiceBook
Georg Cantor (1874). On a property of the class of all real algebraic numbers. Journal für die Reine und Angewandte Mathematik - https://ve42.co/MeyerCantor1874
Heinz-Dieter Ebbinghaus (Dec 2012). Zermelo and the Heidelberg Congress 1904. Historia Mathematica - https://ve42.co/SciDirect1904
Herbert B. Enderton (1977). Elements of Set Theory. - https://ve42.co/SciDirectGCH
Additional References - https://ve42.co/AoCAdRefs
Images & Video:
Foundations of a general theory of sets by Georg Cantor via ViaLibri - https://ve42.co/grundlagen
Alfred Tarski by George Bergman via Wikimedia Commons - https://ve42.co/tarski
Alfred Tarski Offprint Group by Alfred Tarski via Bonhams - https://ve42.co/tarskipaper
La mission strasbourgeoise de Maurice Fréchet by Laurent Mazliak via Images des mathematiques - https://ve42.co/frechet
Kurt Gödel by Alfred Eisenstaedt via New Yorker - https://ve42.co/godel
Leopold Kronecker by Granger via Fine Art America - https://ve42.co/kronecker
Lashi Bandara (2006). Zermelo-Frankel Set Theory and Well Orderings. ResearchGate - https://ve42.co/zermelofrankel
Heidelberg, Germany 1936 by Wagner & Debes via Ward Maps - https://ve42.co/heidelberg
Pythagoras by J. Augustus Knapp via the marginalian - https://ve42.co/pythag
Paul Cohen by C. J. Mozzochi via C. J. Mozzochi - https://ve42.co/paulcohen
Instituto de Matemática Pura e Aplicada. Lecture 01: Introduction: a non-measurable set via Youtube - • Lecture 01: Introduction: a non-measurable...
Simons Foundation. Fields Medal: James Maynard. Youtube • Fields Medal: James Maynard
▀▀▀
Special thanks to our Patreon supporters:
Adam Foreman, Albert Wenger, Alex Porter, Alexander Tamas, Anton Ragin, Autodidactic Studios, Balkrishna Heroor, Bertrand Serlet, Blake Byers, Bruce, Dave Kircher, David Johnston, David Tseng, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, Greg Scopel, HydrochloRick, Jon Jamison, Juan Benet, Keith England, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Tj Steyn, TTST, Ubiquity Ventures, wolfee
▀▀▀
Directed by Kaela Albert
Written by Kaela Albert and Emily Zhang
Edited by Jack Saxon and Luke Molloy
Assistant Edited by James Stuart
Animated by Fabio Albertelli, Andrew Neet, Alex Zepharin, Mike Radjabov, Emma Wright and Ivy Tello
Illustrations by Jakub Misiek, Maria Gusakovich, Cainejan Esperanza, Tommy A. Steven and Emma Wright
Additional research by Emilia Gyles, Gabe Bean, Geeta Thakur and Vincent Cheng
Produced by Kaela Albert, Casper Mebius, Derek Muller, Emily Zhang, Zoe Heron, Rob Beasley Spence, and Tori Brittain
Additional Editing by Luke Molloy and James Stuart
Thumbnail contributions by Ben Powell, Peter Sheppard and Ren Hurley
Additional video/photos supplied by Getty Images and Storyblocks
Music from Epidemic Sound
Translated by Mingi Kwon, GivernyAI, CineLingo
Dubbed by Mingi Kwon
https://youtu.be/yrPr4SCjWoM
이론 하나가 수학을 거의 망가뜨릴 뻔 한 이야기
Veritasium 한국어 - 베리타시움
그거 아세요? 수학영상은 조회수는 가장 안나오고 만드는데는 가장 오래 걸린답니다!
근데 재밌어요!!
이론 하나 만들었다가 수학 체계가 망가져 버릴 뻔한 이야기!
영상 업로드가 안돼서 렌더링만 3번한 영상... 재밌게 봐주세요.
carlos lamas, 지방흡입 정재호 원장입니다, í , StarSeed Global, lililiiiiliillliili, Im Yongsik 님 멤버십 감사합니다.
▀▀▀
A huge thank you to Dr Asaf Karagila, Prof. Alex Kontorovich, Prof. Joel David Hamkins, Prof. Andrew Marks, Prof. Gabriel Goldberg and Prof. Elliot Glazer for their invaluable expertise and contributions to this video.
Head over and sign up to our Patreon for some exclusive behind the scenes footage, showing how the animations and illustrations for this video were made - / patreon. .
▀▀▀
0:00 1 다음은 뭘까?
2:42 다른 무한보다 큰 무한?
6:17 정렬 정리 (The Well Ordering Principle & Theorem)
10:32 체르멜로와 선택 공리
17:22 선택 공리가 논란이 되는 이유
23:16 바나흐-타르스키 역설
27:53 참 vs 거짓
29:58 당신의 증명, 당신의 선택
▀▀▀
References:
Up and Atom - • Cantor's Infinity Paradox | Set Theory
Minutephysics - • How to Count Infinity
PBS Infinite Series - • How the Axiom of Choice Gives Sizeless Set...
Vsauce - • The Banach–Tarski Paradox
Ernst Zermelo via Wikipedia - https://ve42.co/zermeloBio
Axiom of choice via Wikipedia - https://ve42.co/choiceAxiom
Georg Cantor via Wikipedia - https://ve42.co/cantorMath
Gregory H. Moore (2013). Consequences of the Axiom of Choice. Dover Publications - https://ve42.co/choiceBook
Georg Cantor (1874). On a property of the class of all real algebraic numbers. Journal für die Reine und Angewandte Mathematik - https://ve42.co/MeyerCantor1874
Heinz-Dieter Ebbinghaus (Dec 2012). Zermelo and the Heidelberg Congress 1904. Historia Mathematica - https://ve42.co/SciDirect1904
Herbert B. Enderton (1977). Elements of Set Theory. - https://ve42.co/SciDirectGCH
Additional References - https://ve42.co/AoCAdRefs
Images & Video:
Foundations of a general theory of sets by Georg Cantor via ViaLibri - https://ve42.co/grundlagen
Alfred Tarski by George Bergman via Wikimedia Commons - https://ve42.co/tarski
Alfred Tarski Offprint Group by Alfred Tarski via Bonhams - https://ve42.co/tarskipaper
La mission strasbourgeoise de Maurice Fréchet by Laurent Mazliak via Images des mathematiques - https://ve42.co/frechet
Kurt Gödel by Alfred Eisenstaedt via New Yorker - https://ve42.co/godel
Leopold Kronecker by Granger via Fine Art America - https://ve42.co/kronecker
Lashi Bandara (2006). Zermelo-Frankel Set Theory and Well Orderings. ResearchGate - https://ve42.co/zermelofrankel
Heidelberg, Germany 1936 by Wagner & Debes via Ward Maps - https://ve42.co/heidelberg
Pythagoras by J. Augustus Knapp via the marginalian - https://ve42.co/pythag
Paul Cohen by C. J. Mozzochi via C. J. Mozzochi - https://ve42.co/paulcohen
Instituto de Matemática Pura e Aplicada. Lecture 01: Introduction: a non-measurable set via Youtube - • Lecture 01: Introduction: a non-measurable...
Simons Foundation. Fields Medal: James Maynard. Youtube • Fields Medal: James Maynard
▀▀▀
Special thanks to our Patreon supporters:
Adam Foreman, Albert Wenger, Alex Porter, Alexander Tamas, Anton Ragin, Autodidactic Studios, Balkrishna Heroor, Bertrand Serlet, Blake Byers, Bruce, Dave Kircher, David Johnston, David Tseng, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, Greg Scopel, HydrochloRick, Jon Jamison, Juan Benet, Keith England, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Tj Steyn, TTST, Ubiquity Ventures, wolfee
▀▀▀
Directed by Kaela Albert
Written by Kaela Albert and Emily Zhang
Edited by Jack Saxon and Luke Molloy
Assistant Edited by James Stuart
Animated by Fabio Albertelli, Andrew Neet, Alex Zepharin, Mike Radjabov, Emma Wright and Ivy Tello
Illustrations by Jakub Misiek, Maria Gusakovich, Cainejan Esperanza, Tommy A. Steven and Emma Wright
Additional research by Emilia Gyles, Gabe Bean, Geeta Thakur and Vincent Cheng
Produced by Kaela Albert, Casper Mebius, Derek Muller, Emily Zhang, Zoe Heron, Rob Beasley Spence, and Tori Brittain
Additional Editing by Luke Molloy and James Stuart
Thumbnail contributions by Ben Powell, Peter Sheppard and Ren Hurley
Additional video/photos supplied by Getty Images and Storyblocks
Music from Epidemic Sound
Translated by Mingi Kwon, GivernyAI, CineLingo
Dubbed by Mingi Kwon
https://youtu.be/yrPr4SCjWoM