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Extended natural numbers — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Extended_natural_numbers
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-15T16:15:22.446Z
SHA-256 of the archived text: 8d49be301b90bc6377a97b1bc6f308146c671c6859cad2a9c3c149f3d278d2aa
Stable URL of this page: https://metraipolis.com/documento/dc_7ae034e7c141

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Extended natural numbers — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Extended_natural_numbers (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_7ae034e7c141 (Metraipolis archive dc_7ae034e7c141, sha256 8d49be301b90bc6377a97b1bc6f308146c671c6859cad2a9c3c149f3d278d2aa)

BibTeX

@misc{dc7ae034e7c141,
  title = {Extended natural numbers — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Extended_natural_numbers},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_7ae034e7c141; sha256 8d49be301b90bc6377a97b1bc6f308146c671c6859cad2a9c3c149f3d278d2aa},
  year = {2026}
}

Archived text

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

In mathematics, the extended natural numbers is a set which contains the values 0 , 1 , 2 , … {\displaystyle 0,1,2,\dots } and ∞ {\displaystyle \infty } (infinity). That is, it is the result of adding a maximum element ∞ {\displaystyle \infty } to the natural numbers. Addition and multiplication work as normal for finite values, and are extended by the rules n + ∞ = ∞ + n = ∞ {\displaystyle n+\infty =\infty +n=\infty } ( n ∈ N ∪ { ∞ } {\displaystyle n\in \mathbb {N} \cup \{\infty \}} ), 0 × ∞ = ∞ × 0 = 0 {\displaystyle 0\times \infty =\infty \times 0=0} and m × ∞ = ∞ × m = ∞ {\displaystyle m\times \infty =\infty \times m=\infty } for m ≠ 0 {\displaystyle m\neq 0} . With addition and multiplication, N ∪ { ∞ } {\displaystyle \mathbb {N} \cup \{\infty \}} is a semiring but not a ring, as ∞ {\displaystyle \infty } lacks an additive inverse. The set can be denoted by N ¯ {\displaystyle {\overline {\mathbb {N} }}} , N ∞ {\displaystyle \mathbb {N} _{\infty }} or N ∞ {\displaystyle \mathbb {N} ^{\infty }} . It is a subset of the extended real number line, which extends the real numbers by adding − ∞ {\displaystyle -\infty } and + ∞ {\displaystyle +\infty } .

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Number theory»).
Fonte: Wikipedia in inglese, voce «Extended natural numbers» — https://en.wikipedia.org/wiki/Extended_natural_numbers
Wikidata Q105759800 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q105759800
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Extended_natural_numbers?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 1364005297, consultata il 2026-10-15T15:43:31.336Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: aace77cf351d3ccf6da7785240e6ebb6deb5d90ba6dcd9e20e77463324aef147