Richard Dedekind (nonfiction)

Richard Dedekind.

Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to abstract algebra (particularly ring theory), algebraic number theory and the definition of the real numbers.

While teaching calculus for the first time at the Polytechnic school, Dedekind developed the notion now known as a Dedekind cut (German: Schnitt), now a standard definition of the real numbers. The idea of a cut is that an irrational number divides the rational numbers into two classes (sets), with all the numbers of one class (greater) being strictly greater than all the numbers of the other (lesser) class.

In 1888, he published a short monograph titled Was sind und was sollen die Zahlen? ("What are numbers and what should they be?" Ewald 1996: 790), which included his definition of an infinite set.

He also proposed an axiomatic foundation for the natural numbers, whose primitive notions were the number one and the successor function. The next year, Giuseppe Peano, citing Dedekind, formulated an equivalent but simpler set of axioms, now the standard ones.

In 1872, while on holiday in Interlaken, Dedekind met Georg Cantor. Thus began an enduring relationship of mutual respect, and Dedekind became one of the very first mathematicians to admire Cantor's work concerning infinite sets, proving a valued ally in Cantor's disputes with Leopold Kronecker, who was philosophically opposed to Cantor's transfinite numbers.

In the News

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  August 31, 1899: Georg Cantor writes to Dedekind, remarking that his "diagonal process" could be used to show that the power set of a set has more elements than the set itself.

Fiction cross-reference

• Crimes against mathematical constants
• Gnomon algorithm
• Mathematician
• Mathematics

Nonfiction cross-reference

• Georg Cantor (nonfiction)
• Mathematician (nonfiction)
• Mathematics (nonfiction)

External links:

• Richard Dedekind @ Wikipedia