Hausdorff Paradox

← paradoks.kyo.fyi

Felix Hausdorff (1914) membuktikan sebelum Banach-Tarski: permukaan bola S² bisa dipartisi menjadi empat himpunan A, B, C, D di mana A, B, C masing-masing kongruen satu sama lain, dan A kongruen dengan B∪C. Ini menghasilkan kontradiksi ukuran: satu bagian seharusnya memiliki ukuran yang sama dengan gabungan dua bagian lain.

Hausdorff Paradox secara eksplisit menggunakan Axiom of Choice untuk mengkonstruksi partisi ini. Menjadi tonggak dalam teori ukuran dan geometri: menunjukkan bahwa tidak semua himpunan di ruang Euclidean bisa diberi ukuran yang konsisten (non-measurable sets).

← Kembali ke Daftar Paradoks

Kumpulan Paradoks — Index Barbershop Paradox What the Tortoise Said to Achilles Catch-22 Drinker Paradox Paradox of Free Choice Paradox of Entailment Lottery Paradox Raven Paradox Ross' Paradox Temperature Paradox Unexpected Hanging Paradox Barber Paradox Bhartrhari's Paradox Berry Paradox Crocodile Dilemma Paradox of the Court Curry's Paradox Epimenides Paradox Grelling–Nelson Paradox Hilbert–Bernays Paradox I Know That I Know Nothing Kleene–Rosser Paradox Knower Paradox Liar Paradox Card Paradox No-no Paradox Pinocchio Paradox Quine's Paradox Yablo's Paradox Opposite Day Richard's Paradox Russell's Paradox Ship of Theseus Sorites Paradox All Horses Are the Same Color Ant on a Rubber Rope Cramer's Paradox Elevator Paradox Interesting Number Paradox Potato Paradox Burali-Forti Paradox Cantor's Paradox Abelson's Paradox Accuracy Paradox Berkson's Paradox Freedman's Paradox Friendship Paradox Inspection Paradox Lindley's Paradox Low Birth Weight Paradox Simpson's Paradox Will Rogers Phenomenon Bertrand's Box Paradox Bertrand's Paradox Birthday Paradox Borel's Paradox Boy or Girl Paradox False Positive Paradox Grice's Paradox Intransitive Dice Monty Hall Problem Necktie Paradox Proebsting's Paradox Sleeping Beauty Problem Two-envelope Paradox Galileo's Paradox Hilbert's Paradox of the Grand Hotel Skolem's Paradox Zeno's Paradoxes Benardete's Paradox Grim Reaper Paradox Grandi's Series Ross–Littlewood Paradox Thomson's Lamp Banach–Tarski Paradox Coastline Paradox Coin Rotation Paradox Gabriel's Horn Hausdorff Paradox Hooper's Paradox Nikodym Set Sphere Eversion Three Prisoners Problem Abilene Paradox Apportionment Paradox Arrow's Paradox Buridan's Ass Chainstore Paradox Decision-making Paradox Ellsberg Paradox Fenno's Paradox Fredkin's Paradox Green Paradox Hedgehog's Dilemma Inventor's Paradox Kavka's Toxin Puzzle Motivation Crowding Theory Morton's Fork Newcomb's Paradox No-show Paradox Paradox of Voting Parrondo's Paradox Preparedness Paradox Prevention Paradox Prisoner's Dilemma Achilles and the Tortoise Archer's Paradox Arrow Paradox Aristotle's Wheel Paradox Carroll's Paradox D'Alembert's Paradox Knudsen Paradox Denny's Paradox Dichotomy Paradox Feynman Sprinkler Hydrostatic Paradox Norton's Dome Painlevé Paradox Stokes' Paradox Tea Leaf Paradox Upstream Contamination Cool Tropics Paradox Irresistible Force Paradox The Moving Rows Paradox of Place Algol Paradox Faint Young Sun Paradox Olbers' Paradox GZK Paradox Paradox of Youth Bentley's Paradox Boltzmann Brain Fermi Paradox Heat Death Paradox Faraday Paradox Two Capacitor Paradox Aharonov–Bohm Effect Bell's Theorem Double-slit Experiment Einstein–Podolsky–Rosen Paradox Hardy's Paradox Klein Paradox Quantum Zeno Effect Schrödinger's Cat Paradox Uncertainty Principle Bell's Spaceship Paradox Black Hole Information Paradox Twin Paradox Gibbs Paradox Kauzmann's Paradox Loschmidt's Paradox Maxwell's Demon Mpemba Effect Faraday Paradox (Electrochemistry) SAR Paradox Antarctic Paradox C-value Enigma Cole's Paradox Gray's Paradox Hormesis Lek Paradox Lombard's Paradox Paradox of Enrichment Paradox of the Pesticides Paradox of the Plankton Sherman Paradox Charlesworth's Paradox Washburn's Paradox Levinthal Paradox Exercise Paradox French Paradox Glucose Paradox Hispanic Paradox Israeli Paradox Mexican Paradox Obesity Paradox Peto's Paradox Pulsus Paradoxus Second Wind Bootstrap Paradox Predestination Paradox Temporal Paradox Grandfather Paradox Polchinski's Paradox Bracketing Paradox Code-talker Paradox Moravec's Paradox Movement Paradox Sayre's Paradox Paradox of Analysis When a White Horse Is Not a Horse Buridan's Bridge Paradox of Fiction Fitch's Paradox Paradox of Free Will Goodman's Paradox Paradox of Hedonism Liberal Paradox Meno's Paradox Mere Addition Paradox Moore's Paradox Paradox of Nihilism Omnipotence Paradox Polanyi's Paradox Preface Paradox Problem of Evil Rule-following Paradox Paradox of Tolerance Paradox of Democracy Paradox of Freedom Tzimtzum Allais Paradox Arrow Information Paradox Bertrand Paradox (Economics) Braess's Paradox Deaton Paradox Demographic-economic Paradox Downs–Thomson Paradox Easterlin Paradox Edgeworth Paradox European Paradox Gibson's Paradox Giffen Paradox Grossman-Stiglitz Paradox Icarus Paradox Jevons Paradox Leontief Paradox Lerner Paradox Lucas Paradox Mandeville's Paradox Mayfield's Paradox Metzler Paradox Paradox of Prosperity Paradox of Thrift Paradox of Toil Paradox of Value Productivity Paradox Scitovsky Paradox Service Recovery Paradox St. Petersburg Paradox Paradox of Plenty Gender Paradox Gender-equality Paradox Identical Twins Paradox Ironic Process Theory Meat Paradox Moral Paradox Outcomes Paradox Paradox of Suspense Region-beta Paradox Sad Clown Paradox Self-absorption Paradox Solomon's Paradox Stockdale Paradox Willpower Paradox Wollheim's Paradox Progress Paradox Stability–instability Paradox Air Conditioning Paradox Bonini's Paradox Buttered Cat Paradox Intentionally Blank Page Observer's Paradox Taeuber Paradox Blub Paradox