Metraipolis › archive › dc_09ed2cd63a72

Piecewise syndetic set — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Piecewise_syndetic_set
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T16:13:14.126Z
SHA-256 of the archived text: eaeaf7bf2bfd460697c1b47c0e3dba7e8fc6dccededfb02b53400d23ef87ee09
Stable URL of this page: https://metraipolis.com/documento/dc_09ed2cd63a72

How to cite

Piecewise syndetic set — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Piecewise_syndetic_set (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_09ed2cd63a72 (Metraipolis archive dc_09ed2cd63a72, sha256 eaeaf7bf2bfd460697c1b47c0e3dba7e8fc6dccededfb02b53400d23ef87ee09)

BibTeX

@misc{dc09ed2cd63a72,
  title = {Piecewise syndetic set — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Piecewise_syndetic_set},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_09ed2cd63a72; sha256 eaeaf7bf2bfd460697c1b47c0e3dba7e8fc6dccededfb02b53400d23ef87ee09},
  year = {2026}
}

Archived text

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

In mathematics, piecewise syndeticity is a notion of largeness of subsets of the natural numbers. A set S ⊂ N {\displaystyle S\subset \mathbb {N} } is called piecewise syndetic if there exists a finite subset G of N {\displaystyle \mathbb {N} } such that for every finite subset F of N {\displaystyle \mathbb {N} } there exists an x ∈ N {\displaystyle x\in \mathbb {N} } such that x + F ⊂ ⋃ n ∈ G ( S − n ) {\displaystyle x+F\subset \bigcup _{n\in G}(S-n)} where S − n = { m ∈ N : m + n ∈ S } {\displaystyle S-n=\{m\in \mathbb {N} :m+n\in S\}} . Equivalently, S is piecewise syndetic if there is a constant b such that there are arbitrarily long intervals of N {\displaystyle \mathbb {N} } where the gaps in S are bounded by b.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Combinatorics»).
Fonte: Wikipedia in inglese, voce «Piecewise syndetic set» — https://en.wikipedia.org/wiki/Piecewise_syndetic_set
Wikidata Q7191426 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q7191426
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Piecewise_syndetic_set?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 1378036121, consultata il 2026-10-07T15:46:11.013Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 1bf02ed53e3713a5fa3a1308e2a2ae09324772b3ec455d7388fd3ceaf7c911c7