Beiträge zur Begründung der transfiniten Mengenlehre

Cantor, G. (1895). Beiträge zur Begründung der transfiniten Mengenlehre. Mathematische Annalen, 46, 481-512.

Type

Journal article

Intellectual base

Primary research

Year

1895

Volume

46

Pages

481-512

DOI

10.1007/bf02124929

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/BF02124929

Cited from

mathematics

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Cardinality
  • establishes \(|A| < |\mathcal{P}(A)|\) for every set (the power set strictly dominates), which yields an unbounded hierarchy of ever-larger infinities and forecloses any "set of all sets" (Cantor's paradox); (3) cardinality delivers
• Order
  • Mathematical formalization arrived very late: Cantor's work on ordinal numbers (from the 1870s) developed the transfinite extension of well-orderings, consolidated in his Beiträge zur Begründung der transfiniten Mengenlehre (Cantor, 1895–1897)

    This sourceOriginal exposition of ordinal numbers and transfinite orderings; the foundational source for well-ordered transfinite extension of order theory.

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