Dedekind, Richard - Richard Dedekind, b. Oct. 6, 1831, d. Feb. 12, 1916, was a German mathematician known for his study of CONTINUITY and definition of the real numbers in terms of Dedekind "cuts"; his analysis of the nature of number and mathematical induction, including the definition of finite and infinite sets; and his influential work in NUMBER THEORY, particularly in algebraic number fields. Among his most notable contributions to mathematics were his editions of the collected works of Peter DIRICHLET, Carl GAUSS, and Georg Riemann. Dedekind's study of Dirichlet's work led to his own study of algebraic number fields, as well as his introduction of ideals. He developed this concept into a theory of ideals that is of fundamental importance in modern algebra. Dedekind also introduced such fundamental concepts as RINGS. Author: J. W. Dauben
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