In number theory, Dedekind function can refer to any of three functions, all introduced by Richard Dedekind
Ideals generalize Ernst Eduard Kummer's ideal numbers, devised as part of Kummer's 1843 attempt to prove Fermat's Last Theorem.
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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;
The discrepancy between rationals and reals was finally resolved by Eudoxus of Cnidus, a student of Plato, who reduced the comparison of irrational ratios to comparisons of multiples (rational ratios), thus anticipating Richard Dedekind's definition of real numbers.
John Stillwell, Introduction to Theory of Algebraic Integers by Richard Dedekind.