High Quality Content by WIKIPEDIA articles! Julius Wilhelm Richard Dedekind (October 6, 1831 – February 12, 1916) was a German mathematician who did important work in abstract algebra (particularly ring theory), algebraic number theory and the foundations of the real numbers. While teaching calculus for the first time at the Polytechnic, Dedekind came up with the notion now called a Dedekind cut, now a standard definition of the real numbers. The idea behind a cut is that an irrational number divides the rational numbers into two classes (sets), with all the members of one class (upper) being strictly greater than all the members of the other (lower) class. In 1888, he published a short monograph titled Was sind und was sollen die Zahlen? ("What are numbers and what should they be?"), which included his definition of an infinite set.

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