Decomposing rational numbers
نویسندگان
چکیده
منابع مشابه
Decomposing Envelopes of Rational Hypersurfaces
The envelope of a family of real, rational hypersurfaces is defined by an implicit equation in the parameter space. This equation can be decomposed into factors that are mapped to varieties of different dimension. The factorization can be found using solely gcd computations and polynomial divisions. The decomposition is used to derive some general results about envelopes, which also contribute ...
متن کاملRational Erd} Os Numbers
The concept of Erd} os number is well known among mathematicians and somewhat known more generally (see, for example, de Castro & Grossman, 1999] or the web site Paul Erd} os, who died in late 1996, was a mathematician who was author or coauthor|most often the latter|of nearly 1500 papers and had nearly 500 coauthors. By deenition, Erd} os had Erd} os number zero, his collaborators had Erd} os ...
متن کاملApproximating Rational Numbers by Fractions
In this paper we show a polynomial-time algorithm to find the best rational approximation of a given rational number within a given interval. As a special case, we show how to find the best rational number that after evaluating and rounding exactly matches the input number. In both results, “best” means “having the smallest possible denominator”.
متن کاملAutomatic Sets of Rational Numbers
The notion of a k-automatic set of integers is well-studied. We develop a new notion — the k-automatic set of rational numbers — and prove basic properties of these sets, including closure properties and decidability.
متن کاملThere are less transcendental numbers than rational numbers
According to a basic theorem of transfinite set theory the set of irrational numbers is uncountable, while the set of rational numbers is countable. This is contradicted by the fact that any pair of irrational numbers is separated by at least one rational number. Hence, in the interval [0,1] there exist more rational numbers than irrational numbers.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2010
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa145-3-1