Stetigkeit und irrationale Zahlen¶
Dedekind, R. (1872). Stetigkeit und irrationale Zahlen. Essays on the Theory of Numbers.
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Primes¶
- Infinity
- Dedekind's foundational work in (1872) on completion via cuts
This sourceFormal definition of infinite sets via self-bijection; Dedekind cuts for real-number completion.
SupportedVerified against the work's full text
Dedekind's tract, prefaced March 1872, defines cuts of the rationals, locates their incompleteness in cuts no rational produces, and creates an irrational number for each.
“In dieſer Eigenſchaft, daß nicht alle Schnitte durch rationale Zahlen hervorgebracht werden, beſteht die Unvollſtändigkeit oder Unſtetigkeit des Gebietes R aller rationalen Zahlen.”
- Dedekind's foundational work in (1872) on completion via cuts
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