Georg Cantor (eBook)

His Mathematics and Philosophy of the Infinite

Joseph Warren Dauben (Autor)

eBook Download: PDF

2020
424 Seiten
Princeton University Press (Verlag)
978-0-691-21420-7 (ISBN)

Infos

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 "e;corrupter of youth"e; 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.

Produkt-Details

• Erscheint lt. Verlag: 23.6.2020
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Naturwissenschaften
• Schlagworte: Absolute Infinite • Actual infinity • Addition • Aleph number • A priori and a posteriori • Arbitrarily large • Archimedean property • Aristotle • arithmetic • Auxiliary function • Axiom • Axiom of choice • Berlin, Germany • Bernhard Riemann • Bertrand Russell • Big O notation • Bolzano–Weierstrass theorem • Borchardt, C. W. • Burali-Forti paradox • Cantor's Diagonal Argument • Cantor set • Cantor's Theorem • cardinal number • Catholic Church • Characterization (mathematics) • Charles Hermite • coefficient • commutative property • Comparability • conjecture • consistency • Continuity • continuous function • Continuum Hypothesis • Contradiction • Countable set • counterexample • Counting • David Hilbert • Dedekind cut • Derived set (mathematics) • Derived Set(s) • Diagonal method • Disenchantment • empty set • Epistemology • Equation • Equivalence • exponentiation • Felix Bernstein (mathematician) • Felix Klein • Fermat's Last Theorem • Finitism • First principle • Fourier series • Georg Cantor • Gödel's Incompleteness Theorems • Goldscheider, F. • Gottlob Frege • Grattan-Guinness, I. • Hermite, C. • Hilbert's program • hypothesis • Infimum and supremum • Infinitesimal • irrational number • Jeiler, I. • Joseph of Arimathea • Kerry, B. • Kronecker, L. • Leopold Kronecker • Limit point • Limit points • Linear continuum • Logic • logical framework • logicism • Mathematical Induction • mathematician • Mathematics • Maxima and minima • Mutual exclusivity • Naturalness (physics) • Natural number • Neo-Thomism • Number Theory • Order type • Order types • ordinal number • paradoxes • philosophy of mathematics • point sets • Power(s) • Prime number • Principia Mathematica • Pure Mathematics • quaternions • Rational number • real number • Richard Brauer • Richard Dedekind • Riemann integral • Rosicrucianism • Russell's paradox • Schoenflies, A. • scientific notation • set theory • Sign (mathematics) • soundness • Special case • Squaring the circle • Subset • Subsets • Summa Theologica • Summation • Tautology (logic) • theologians • Theorem • theory • transcendental number • transfinite • Transfinite number • Transfinite numbers • Trigonemetric series • Trigonometric Series • Uncountable set • uniqueness theorem • Universal set • Well-order • Zermelo–Fraenkel set theory • Zermelo's theorem (game theory)
• ISBN-10: 0-691-21420-4 / 0691214204
• ISBN-13: 978-0-691-21420-7 / 9780691214207