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syndetic

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syndetic
syndetic, a. (sɪnˈdɛtɪk) [ad. Gr. συνδετικός, f. συνδεῖν to bind together.] a. Serving to unite or connect; connective, copulative. The incorrect form synderique in quot. 1621 is due to the Fr. orig. (nerfs synderiques, which is copied by Cotgrave).1621 Lodge Summary Du Bartas i. 280 The Tendons..wh... Oxford English Dictionary
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Syndetic
Syndetic may refer one of the following Syndetic set, in mathematics Syndetic coordination, in linguistics wikipedia.org
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Syndetic set
Definition A set is called syndetic if for some finite subset of where . Thus syndetic sets have "bounded gaps"; for a syndetic set , there is an integer such that for any . wikipedia.org
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synderique
synderique error for syndetique, syndetic. Oxford English Dictionary
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Syndeton
Syndeton (from the Greek συνδετόν "bound together with") or syndetic coordination in grammar is a form of syntactic coordination of the elements of a sentence In syndetic coordination with more than two conjuncts, the conjunction is placed between the two last conjuncts: "I will need bread, cheese and ham". wikipedia.org
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Is the set $\phi(\mathbb{N})$ syndetic? A set $A \subset \mathbb{N}$ is said to be syndetic if the gaps in $A$ are bounded. > Is the set $\phi(\mathbb{N})$ syndetic? (where $\phi$ denotes de Euler totient function) ...
Assuming that $\phi(\mathbb{N})$ is a syndetic set we have that the totient numbers (i.e. the numbers that are of the form $\phi(n)$ for some $n$) have * * That asymptotic is very interesting, because it shows that the problem is more or less equivalent to the trivial one: > Is the set of primes a syndetic
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syndeton
syndeton Gram. (ˈsɪndɪtən) [Back-formation from asyndeton and polysyndeton: cf. syndetic a.] (See quots. 1954, 1972.)1954 Pei & Gaynor Dict. Linguistics 210 Syndeton, a phrase or construction in which the elements are linked together by connecting particles. 1971 Computers & Humanities V. 262 The fr... Oxford English Dictionary
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Piecewise syndetic set
Properties A set is piecewise syndetic if and only if it is the intersection of a syndetic set and a thick set. Partition regularity: if is piecewise syndetic and , then for some , contains a piecewise syndetic set. wikipedia.org
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Thickly syndetic set Somewhere I read that, S is thickly syndetic if for every natural number N the positions where length N runs from a syndetic set. I can't understand this definition. Please help me to understand t...
Let me fix it: a set $S$ of natural numbers is thickly syndetic, if for every natural number $n$, the positions **of** length-$n$ runs in $S$ form a syndetic If $S$ is thickly syndetic, then the set of the numbers $i$ that start length-$n$ runs in $S$ must be syndetic, separately for every $n$.
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Ergodic Ramsey theory
See also IP set Piecewise syndetic set Ramsey theory Syndetic set Thick set References Ergodic Methods in Additive Combinatorics Vitaly Bergelson wikipedia.org
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Prove there are uncountably many syndetic sets Here is a sketch of my thought of proving it but I encounter some problems. Following the thought of Cantor's diagonal argument so firstly using indicator functions $1_s$...
each $\sigma=\langle b_n:n\in\Bbb N\rangle\in\\{0,1\\}^{\Bbb N}$ let $$S(\sigma)=\\{2n:n\in\Bbb N\\}\cup\\{2n+1:b_n=1\\}\;;$$ clearly $S(\sigma)$ is syndetic Thus, there are $2^\omega=\mathfrak{c}$ syndetic subsets of $\Bbb N$.
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Ricardo L. Castro
Known for his monographs on architects Rogelio Salmona and Arthur Erickson, his design philosophy was published in Syndetic Modernisms (2014). Syndetic Modernisms co-authored with Robert Mellin and Carlos Rueda Plata. wikipedia.org
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Tom Brown (mathematician)
of Periodic Groups' In 1963 as a graduate student, he showed that if the positive integers are finitely colored, then some color class is piece-wise syndetic wikipedia.org
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Strengthening Poincaré Recurrence Let $(X, B, \mu, T)$ be a measure preserving system. For any set $B$ of positive measure, $E = \\{n \in \Bbb N |\; \mu(B \; \cap \;T^{-n}B) > 0\\}$ is syndetic. This exercise comes ...
**Hint:** If the set was not syndetic, then the sequence $$ \frac1n\sum_{k=0}^{n-1}\mu(B\cap T^{-k}B) $$ would have zero as an accumulation point (take
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List of exceptional set concepts
large Large set (Ramsey theory) Meagre set Measure zero Natural density Negligible set Nowhere dense set Null set, conull set Partition regular Piecewise syndetic set Schnirelmann density Small set (combinatorics) Stationary set Syndetic set Thick set Thin set (Serre) Exceptional Exceptional wikipedia.org
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