In mathematics, a Heilbronn set is an infinite set S of natural numbers for which every real number can be arbitrarily closely approximated by a fraction whose denominator is in S. For any given real number and natural number , it is easy to find the integer such that is closest to . For example, for the real number and we have . If we call the closeness of to the difference between and , the closeness is always less than 1/2 (in our example it is 0.15926...). A collection of numbers is a Heilbronn set if for any we can always find a sequence of values for in the set where the closeness tends to zero.
More mathematically let denote the distance from to the nearest integer then is a Heilbronn set if and only if for every real number and every there exists such that .[1]
^Montgomery, Hugh Lowell (1994). Ten lectures on the Interface Between Analytic Number Theory and Harmonic Analysis. CBMS Regional Conference Series in Mathematics. Vol. 84. Providence Rhode Island: American Mathematical Society. ISBN 0-8218-0737-4.
In mathematics, a Heilbronnset is an infinite set S of natural numbers for which every real number can be arbitrarily closely approximated by a fraction...
Heilbronn (German pronunciation: [haɪlˈbʁɔn] ) is a city in northern Baden-Württemberg, Germany, surrounded by Heilbronn District. From the late Middle...
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town in the district of Heilbronn in the Baden-Württemberg region of southern Germany. It lies north of the city of Heilbronn, on the river Neckar. Bad...
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as Franconian, although not speaking the dialect. Heilbronn-Franconia's largest city of Heilbronn and its surrounding areas are South Franconian-speaking...
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Soviet Union M ; currently France Döttling, Fabian 4627253 1980-08-04 Heilbronn 2003 Germany M also spelled Doettling Dourerassou, Jonathan 628050 1989-04-10...
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mounting an open-air version of Heinrich von Kleist's play Das Käthchen von Heilbronn. Unable to stay alone in hiding, she joins him there but in no time is...
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