Beiträge zur Begründung der transfiniten Mengenlehre

Cantor, G. (1897). Beiträge zur Begründung der transfiniten Mengenlehre. Mathematische Annalen, 49(2), 481-512.

Type

Journal article

Intellectual base

Primary research

Year

1897

DOI

10.1007/bf02124929

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
• Well-Foundedness (Well-Ordering)
  • Well-foundedness is not finiteness — well-founded sets need not be finite, as Cantor (1897) showed in his Beiträge by constructing the transfinite ordinals as canonical infinite well-ordered sets.

    This sourceDevelops transfinite induction and the order-type classification of well-ordered sets.

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