Cantor: algebraic numbers are countable but the reals are not

What changed

Mathematics gained a rigorous distinction between different sizes of infinite collections.

Scientific scope

The 1874 paper; not the later diagonal proof, cardinal arithmetic, continuum hypothesis or the full later axiomatization of set theory.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. This records the 1874 paper, not Cantor’s later diagonal argument or the full later development of set theory.

Contributors

• Georg Cantor · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Cantor 1874 paper, English translation

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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