Mathematician:Julius Wilhelm Richard Dedekind

Julius Wilhelm Richard Dedekind was a German mathematician who worked in the fields of abstract algebra, and algebraic number theory.

Most noted for his work on the foundations of the real numbers. One of the earliest mathematicians to accept the ideas of Georg Cantor.

Nationality
German

History

 * Born: 6 Oct 1831, Braunschweig, duchy of Braunschweig (now Germany)
 * Died: 12 Feb 1916, Braunschweig, duchy of Braunschweig (now Germany)

Theorems and Definitions

 * Dedekind's Theorem
 * Dedekind Cut
 * Dedekind Complete
 * Dedekind Completion
 * Dedekind-MacNeille Completion (with Holbrook Mann MacNeille)


 * Dedekind-Infinite


 * Refined Peano's Axioms (of Giuseppe Peano), so they are also known as the Dedekind-Peano Axioms

Books and Papers

 * 1872: Stetigkeit und irrationale Zahlen ("Continuity and irrational numbers") in which he introduced the concept of what is now called the Dedekind cut.
 * 1888: Was sind und was sollen die Zahlen? ("What are numbers and what should they be?") in which is included the definition of an infinite set.

Also see

 * : Chapter $\text{XXVII}$