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Aleph number — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Aleph_number
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-08T05:53:32.730Z
SHA-256 of the archived text: 76c2c5b4e02b0dbb19d88ee98a66d7d2ff51b1ccf988b978a9032c44c79cc022
Stable URL of this page: https://metraipolis.com/documento/dc_03ea443df3c8

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Aleph number — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Aleph_number (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_03ea443df3c8 (Metraipolis archive dc_03ea443df3c8, sha256 76c2c5b4e02b0dbb19d88ee98a66d7d2ff51b1ccf988b978a9032c44c79cc022)

BibTeX

@misc{dc03ea443df3c8,
  title = {Aleph number — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Aleph_number},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_03ea443df3c8; sha256 76c2c5b4e02b0dbb19d88ee98a66d7d2ff51b1ccf988b978a9032c44c79cc022},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Aleph_number. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets. They were introduced by the mathematician Georg Cantor and are named after the symbol he used to denote them, the Hebrew letter aleph (ℵ). The smallest cardinality of an infinite set is that of the natural numbers, denoted by ℵ0 (read aleph-nought, aleph-zero, or aleph-null); the next larger cardinality of a well-ordered set is ℵ1, then ℵ2, then ℵ3, and so on. Continuing in this manner, it is possible to define an infinite cardinal number ℵα for every ordinal number α, as described below. The concept and notation are due to Georg Cantor, who defined the notion of cardinality and realized that infinite sets can have different cardinalities. The aleph numbers differ from the infinity (∞) commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the extended real number line.

Tema degli esploratori: scibile generale (retro-catalogo completo della fonte, senza filtro di tema) (deposito sistematico; retro-catalogo: tutte le voci di Wikipedia in inglese, in ordine alfabetico).
Fonte: Wikipedia in inglese, voce «Aleph number» — https://en.wikipedia.org/wiki/Aleph_number
Wikidata Q908627: «simbolo usato in matematica per indicare la cardinalità del numerabile» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q908627
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Aleph_number?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1382894017, consultata il 2026-11-08T05:48:03.651Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 2443e71a5f5b26d3a19b040513a1554609e6c3f3346fe96d0517a5dc013a93ca