Mathematician:Julius Wilhelm Richard Dedekind

Mathematician

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.

Used the thinking behind the resolution of Galileo's Paradox to underpin the definition of an infinite set.

A student of Carl Friedrich Gauss.

One of the earliest mathematicians to accept the ideas of Georg Cantor.

Nationality

German

History

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

Theorems and Definitions

• Dedekind's Theorem

• Dedekind Completeness Property
• Dedekind Completion
• Dedekind Cut, also known as a Dedekind Section
• Dedekind Domain
• Dedekind-Infinite
• Dedekind Number
• Dedekind Ring

• Dedekind-MacNeille Completion (with Holbrook Mann MacNeille)

• Dedekind-Peano Axioms (with Giuseppe Peano)

• Cantor-Dedekind Hypothesis (with Georg Ferdinand Ludwig Philipp Cantor)

Results named for Julius Wilhelm Richard Dedekind can be found here.

Definitions of concepts named for Julius Wilhelm Richard Dedekind can be found here.

Axioms named for Julius Wilhelm Richard Dedekind can be found here.

Publications

• 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 known as

Usually referred to as Richard Dedekind.

Some sources render his name as Richard Julius Wilhelm Dedekind.

Sources

• John J. O'Connor and Edmund F. Robertson: "Julius Wilhelm Richard Dedekind": MacTutor History of Mathematics archive

• 1937: Eric Temple Bell: Men of Mathematics: Chapter $\text{XXVII}$
• 1939: E.G. Phillips: A Course of Analysis (2nd ed.) ... (previous) ... (next): Chapter $\text {I}$: Number: $1.1$ Introduction
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Dedekind, Julius Wilhelm Richard (1831-1916)
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($\text {1815}$ – $\text {1897}$): Footnote $5$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Dedekind, Julius Wilhelm Richard (1831-1916)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Dedekind, Julius Wilhelm Richard (1831-1916)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Dedekind, (Julius Wilhelm) Richard (1831-1916)