Leseprobe
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Georg Cantor
Joseph Warren Dauben
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Naturwissenschaften, Medizin, Informatik, Technik / Naturwissenschaften allgemein
Beschreibung
One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula.
Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradoxes in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by recurring attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.
Kundenbewertungen
Trigonometric series, Disenchantment, Mathematician, Conjecture, Russell's paradox, Zermelo's theorem (game theory), Set theory, Sign (mathematics), Gödel's incompleteness theorems, Felix Klein, Irrational number, Ordinal number, Axiom, David Hilbert, Linear continuum, Cardinal number, Continuum hypothesis, Characterization (mathematics), Number theory, Counting, Infinitesimal, Pure mathematics, Principia Mathematica, Addition, Mathematical induction, Axiom of choice, Bertrand Russell, Coefficient, Naturalness (physics), Derived set (mathematics), Gottlob Frege, Cantor's diagonal argument, Cantor set, Cantor's theorem, Countable set, Contradiction, Fermat's Last Theorem, Georg Cantor, Arbitrarily large, Theory, Subset, Transfinite number, Continuous function, Soundness, Mathematics, Well-order, Transfinite, Logical framework, Real number, Hilbert's program, Order type, Rational number, Scientific notation, Zermelo–Fraenkel set theory, Comparability, Prime number, Finitism, Archimedean property, Big O notation, Burali-Forti paradox, Limit point, Commutative property, Uniqueness theorem, Exponentiation, Special case, Natural number, Bernhard Riemann, Infimum and supremum, Dedekind cut, Theorem