Dedekind cuts and ideals
Construcción de los números reales (cortaduras) e ideales
- Date
- 1872 · confidence high
- Place
- Brunswick, Germany
- Credited to
- Richard Dedekind (Stetigkeit und irrationale Zahlen, 1872; ideals, 1871); alternative construction by Cantor using Cauchy sequences
- People
- 👤 Julius Wilhelm Richard Dedekind1831–1916
- Field
- Knowledge & symbols
What was discovered
A rigorous definition of the reals as cuts of rationals, which underpins the continuity of the line, and a theory of ideals that restores unique factorisation in rings of algebraic integers.
Cantor's construction using Cauchy sequences dates from the same year, 1872.
What it led to
- the arithmetisation of analysis
- commutative algebra
- algebraic number theory
- the axiomatic definition of the natural numbers (1888)
Built on
- Method of exhaustion and theory of proportionsc. 370 BCE
- Kummer (ideal numbers)
- Weierstrass