Piecewise Syndetic Set
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, piecewise syndeticity is a notion of largeness of subsets of the natural numbers. Let mathcal{P}_f(mathbb{N}) denote the set of finite subsets of mathbb{N}. Then a set S sub mathbb{N} is called piecewise syndetic if there exists G in mathcal{P}_f(mathbb{N}) such that for every F in mathcal{P}_f(mathbb{N}) there exists an x in mathbb{N} such that x+F subset bigcup_{n in G} (S-n) where S-n = {m in mathbb{N}: m+n in S }. Informally, S is piecewise syndeti...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, piecewise syndeticity is a notion of largeness of subsets of the natural numbers. Let mathcal{P}_f(mathbb{N}) denote the set of finite subsets of mathbb{N}. Then a set S sub mathbb{N} is called piecewise syndetic if there exists G in mathcal{P}_f(mathbb{N}) such that for every F in mathcal{P}_f(mathbb{N}) there exists an x in mathbb{N} such that x+F subset bigcup_{n in G} (S-n) where S-n = {m in mathbb{N}: m+n in S }. Informally, S is piecewise syndetic if S contains arbitrarily long intervals with gaps bounded by some fixed bound b.
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