Dedekind: real numbers constructed through rational cuts

What changed

Proper rational cuts define real numbers, equivalent rational-endpoint partitions are identified, and the completed order supports a cut-completeness principle linked to bounded monotone convergence.

Scientific scope

Proper rational cuts define real numbers, equivalent rational-endpoint partitions are identified, and the completed order supports a cut-completeness principle linked to bounded monotone convergence. The admitted target is the cut construction, order-completeness statement and its analytic connection. Cuts are proper nonempty order partitions; equivalent rational-endpoint cuts represent the same number. The cited source is a university transcription of the 1912 fourth edition, with formula/glyph defects, rather than the 1872 facsimile. It does not prove the continuity of physical space, certify every arithmetic-operation proof or assert a modern well-order of the reals.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

• Richard Dedekind · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

• Richard Dedekind, Stetigkeit und irrationale Zahlen (1872); Radboud University literal German transcription of the fourth edition (1912)

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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