Although such a definition was known to Bernard Bolzano, he was prevented from publishing his work in any but the most obscure journals by the terms of his political exile from the University of Prague in 1819.
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the various (but equivalent) constructions of the real numbers by Dedekind and Cantor resulting in the modern axiomatic definition of the real number field;
Friedrich Dedekind (1524–1598), German humanist, theologian, and bookseller
In number theory, Dedekind function can refer to any of three functions, all introduced by Richard Dedekind
After Rademacher's death, Grosswald edited and completed the notes and published them in the Carus Mathematical Monographs series as Dedekind Sums.
Dieudonné, who was one of the founding members of the Bourbaki group, credits a precise and general modern definition of a function to Dedekind in his work
In the second half of the nineteenth century, the calculus was reformulated by Augustin-Louis Cauchy, Bernard Bolzano, Karl Weierstrass, Cantor, Dedekind, and others using the (ε, δ)-definition of limit and set theory.
John Stillwell, Introduction to Theory of Algebraic Integers by Richard Dedekind.